Temperature versus composition phase diagrams and spin glass behavior in low dimensional, mixed
magnetic systems
by Gerald Victor Rubenacker
A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in
Physics
Montana State University
© Copyright by Gerald Victor Rubenacker (1988)
Abstract:
The temperature versus composition phase diagrams for several low dimensional, mixed magnetic
systems have been investigated. . The magnetic behavior of the pseudo-onedimensional mixed systems
[(CH3)3NH]A(1_x)BxCl 3•2H2O where A and B are Co, Ni, and Mn, was investigated as a function of
x. The mixture with Co and Ni was found to exhibit spin glass behavior below a characteristic
temperature Tg as evidenced by the onset of time dependent tnermoremanent magnetization. The phase
diagram of temperature versus x showed a very broad and deep spin glass region with unusually thin
antiferromagnetic phase regions above it. A tetracritical point near x = 0.58 was indicated.
Thermoremanent magnetization versus time below Tg was fit to a stretched exponential function plus a
constant offset term. Mixtures of Mn with Co and Mn with Ni showed no spin glass behavior above 2
K and had a deep depression in the center of their temperature versus x phase diagrams. The
pseudo-two-dimensional mixed systems, [NH.3(CH2)nNH3]CuCl4xBr4( 1-x) for n = 5 and 7 were also
investigated. The temperature versus x phase diagrams for. these systems also showed evidence of
tetracritical points but with mixed phase regions rather than spin glass phases. From an examination of
the differences in these systems, criteria for development of mixed phases and spin glass phases were
discussed. ,1
TEMPERATURE VERSUS COMPOSITION PHASE DIAGRAMS AND. SPIN
GLASS BEHAVIOR IN LOW DIMENSIONAL,
MIXED
MAGNETIC SYSTEMS
by
Ger al d V i c t o r
Rubenacker
A t h e s i s submi t t ed i n p a r t i a l f u l f i l l m e n t
of t he r e qu i r e me nt s f o r t he degr ee
of
Doct or of Phi l osophy
in
Physi cs
MONTANA STATE UNIVERSITY
Bozeman, ■Montana
May,
1988
11
APPROVAL
of a t h e s i s
submi t t ed by
Ger al d V i c t o r Rubenacker
Thi s t h e s i s has been r ead by each member of t he
t h e s i s commi t t ee and has been found t o be s a t i s f a c t o r y
r e g a r d i n g c o n t e n t , Engl i sh usage, f o r m a t , c i t a t i o n s ,
b i b l i o g r a p h i c s t y l e , and c o n s i s t e n c y , and i s r eady f o r
submi ssi on t o t he Col l e ge of Gr aduat e S t u d i e s .
Date
Approved f o r t he Maj or Depart ment
N
Date
im
y
Approved f o r t he Col l e ge of Gr aduat e St udi es
/ 9 fry
iii
STATEMENT OF PERMISSION TO USE
In p r e s e n t i n g t h i s
t he r e q u i r e me n t s
University,
for
thesis
a doctoral
in p a r t i a l
fulfillment
degree at Montana St at e
I agr ee t h a t t he L i b r a r y s h a l l
make i t
a v a i l a b l e t o bor r ower s under r u l e s
of t he L i b r a r y .
further
thesis
agree t h a t
onl y f o r
copyi ng of t h i s
s c h o l a r l y pur poses,
prescribed
c o n s i s t e n t wi t h
in t he U. S. Copyr i ght
Law.
r e f e r r e d to U n i v e r s i t y Mi crofi l ms
gr ant ed
Ann A r b o r ,
"fair
copi es of t he d i s s e r t a t i o n
right
Request s f o r
Si gnat ure
Date
/f
z?
shoul d be
t o whom I have
t o r epr oduce and d i s t r i b u t e
in and from m i c r o f i l m and the
t o r epr oduce and d i s t r i b u t e
format. "
use" as
I n t e r n a t i o n a l , 300 North
Mi chi gan 48106,
"t he e x c l u s i v e r i g h t
I
is al l owabl e
e x t e n s i v e copyi ng or r e p r o d u c t i o n of t h i s t h e s i s
Zeeb Road,
of
by a b s t r a c t
in any
iv
ACKNOWLEDGMENTS
I would l i k e
t o ext end my s p e c i a l
t hanks t o Pr of es sor
John Dr u mh e l I e r who has been my a d v i s o r on t h i s
I am al so g r a t e f u l
f o r t he hel p of many ot h e r s
P r o f e s s o r Kenneth Emerson, Donal d Hai nes,
and t he M. S. U. A g r i c u l t u r a l
Analytical
project.
i ncluding:
Stuart
Hut ton
Lab.
•
Thi s work was suppor t ed by N a t i o n a l
Foundat i on gr a n t
!i
Sci ence
DMR- 8702993.
I
V
TABLE OF CONTENTS
INTRODUCTION................................................................................
I
P r o p e r t i e s of S i n g l e Met al MTAC Compounds.................................. 3
Pr evi ous Work on Mi xed MTAC S y s t e m s ................................. .... . . 9
M u l t i c i r t i c a i l P o i n t s . . ................................. . . ........................ 12
Spin G l a s s e s ................................................................................ .... . . . 16
EXPERIMENTS ....................................................................................................... 19
Sample P r e p a r a t i o n and Ana l y s i s .................................................... 19
The V i b r a t i n g Sample Magnet omet er .. . ....................... .... . . 2 2
Measurements on C o N i T A C .................................................................. . 26
M a g n e t i z a t i o n Versus Temper at ur e Measurement s. . . 26
Ma g n e t i z a t i o n Versus Appl i ed F i e l d Measur ement s. . 34
Thermoremanent Ma g n e t i z a t i o n D a t a ......................................... .40
AC S u s c e p t i b i l i t y of C o N i T A C ............................ .... . . . 41
EPR Measurements on CoNi TAC........................................................50
MnCoTAC and MnNiTAC Ma g n e t i z a t i o n Measurement s. . . . .
50
7-DA and 5-DA Magnet i c M e a s u r e m e n t s .............................................. 54
DISCUSSION.
....................................................................................................... 63
Phase Di agram of CoNi TAC.....................................
63
Model and F i t of t he TRM. . ................................................................. 69
Spin Gl ass D i m e n s i o n a l i t y .................................................................. 74
Phase Di agrams of MnCoTAC and M n N i T A C ........................ . . . .
75
Phase Di agrams f o r t he 7-DA and 5-DA Compounds. . . . .
78
Low Di mensi onal Mi xed Systems:
A Compari si on . . . . .
84
CONCLUSI ONS.........................................................................................
86
REFERENCES CI TED............................................................................................. 88
vi
. LI ST OF TABLES
Tabl e
Page
1.
Low t e mp e r a t u r e phases and c r i t i c a l
t e mp e r a t u r e s f o r n-DACuX^ ( F = f e r r o ­
magnet i c o r d e r i n g and AF = a n t i f e r r o m a g n e t i c
o r d e r i n g ) .................................................................................................. 58
2.
Ant i f e r r o ma g n e t i c t r a n s i t i o n t e mp e r a t u r e s Tc
and spi n gl ass t r a n s i t i o n t e mpe r a t ur e s Tg f o r
v a r i o u s per cent ages of n i c k e l inCoNiTACs ..........................65
3.
Best f i t s of t he par amet er s t n , n and M1 t o
Equat i on ( 9) f o r TRM measurements at t he gi ven
t e mp e r a t u r e s and n i c k e l c o n c e n t r a t i o n s ........................
73
Cur i e and Neel t e mp e r a t u r e s f o r MnCoTAC and
MnNiTAC mi x t u r e s al ong wi t h t h e i r cor r espondi ng
met al p e r c e n t a g e s ........................................................
78
T r a n s i t i o n t e mp e r a t u r e s f o r va r i o us val ues of x
in S-DACuCl 4 x Br4 ,
............................
79
4.
5.
6.
T r a n s i t i o n t e mp e r a t u r e s f o r va r i o us val ues of x
in 7- DACuCl 4 x Br 4 ( J _x ) ......................................................................82
vii
LI ST OF FIGURES
Fi g u r e
Page
1.
The c o b a l t - c h l o r i d e chai n of CoTAC wi t h t he a
ax i s p e r p e n d i c u l a r t o t he d r a wi n g .......................................5
2.
A s i m p l i f i e d vei w of CoTAC l ooki ng al ong t he
chai n d i r e c t i o n .
Limes r e p r e s e n t t he
o r i e n t a t i o n of t he wat er mo l e c ul e s .
Arrows
on t he l e f t and r i g h t r e p r e s e n t two p o s s i b l e
spi n o r i e n t a t i o n s wi t h r e s p e c t t o t he wat er s
.
.
.
.6
3.
Thermoremanent ma g n e t i z a t i o n ( I kOe i n i t i a l
f i e l d ) versus t e mp e r a t u r e f o r v a r i o u s w a i t i n g
t i mes in t he 65% n i c k e l s a m p l e ................... ....................... 13
4.
Sket ch of a t e mp e r a t u r e versus x phase di agram
wi t h a t e t r a c r i t i c a I p o i n t and a mixed phase
r e g i o n ......................................................... .. ....................................... 15
5.
Per cent n i c k e l i n t he s o l u t i o n s used t o pr epar e
t he mixed CoNiTAC samples versus pe r c e nt n i c k e l
in t he r e s u l t a n t c r y s t a l s ................... ..
6.
Ma g n e t i z a t i o n versus t e mp e r a t u r e at 50 Oe f o r a
powder sample c o n t a i n i n g 53% n i c k e l .
Both zero
f i e l d cool ed and f i e l d cool ed curves ar e shown .
21
. 27
7.
M a g n e t i z a t i o n versus t e mp e r a t u r e at 50 Oe f o r a
s i n g l e c r y s t a l of CoNiTAC c o n t a i n i n g 30% n i c k e l .
T r i a n g l e s ar e f o r t he c a x i x ( a n t i f e r r o ­
magnet i c) and c i r c l e s ar e f o r t he a ax i s
( f e r r o m a g n e t i c ) ................................................................................ 29
8.
M a g n e t i z a t i o n versus t e mp e r a t u r e at 50 Oe f o r a
s i n g l e c r y s t a l of CoNiTAC c o n t a i n i n g 37% n i c k e l .
. Open c i r c l e s a r e " f o r t he c a x i s ( a n t i f e r r o ­
magnet i c) and s o l i d c i r c l e s ar e f o r t he a axi s
( f er r omagnet i c ) ......................................................... .......................30
viii
Figure
9.
10.
11.
12.
13.
14.
15.
16.
17.
Page
M a g n e t i z a t i o n versus t e mp e r a t u r e at 50 Oe f o r a
s i n g l e c r y s t a l of CoNiTAC c o n t a i n i n g 44% n i c k e l .
T r i a n g l e s ar e f o r t he c a x i s ( a n t i f e r r o ­
magnet i c) and c i r c l e s ar e f o r t he a axi s
( f er r omagnet i c ) ................................................................................31
Ma g n e t i z a t i o n versus t e mp e r a t u r e at 50 Oe f o r a
s i n g l e c r y s t a l of CoNiTAC c o n t a i n i n g 58% n i c k e l .
T r i a n g l e s ar e f o r the. c axi s ( a n t i f e r r o ­
ma g n e t i c ) and s o l i d c i r c l e s ar e f o r t he a a x i s '
( f e r r o m a g n e t i c ) . . ..................................................................
. 32
Ma g n e t i z a t i o n versus a p p l i e d f i e l d f o r a s i n g l e
c r y s t a l of CoNiTAC c o n t a i n i n g 37% n i c k e l and
o r i e n t e d al ong t he c or a n t i f e r r o m a g n e t i c axi s .
. 35
M a g n e t i z a t i o n versus a p p l i e d f i e l d f o r a s i n g l e
c r y s t a l of CoNiTAC c o n t a i n i n g 58% n i c k e l and
o r i e n t e d along, t he c or a n t i f e r r o ma g n e t i c ax i s .
. 36
Ma g n e t i z a t i o n versus a p p l i e d f i e l d f o r a s i n g l e
c r y s t a l of CoNiTAC c o n t a i n i n g 37% n i c k e l and
o r i e n t e d al ong t he a or f e r r o ma g n e t i c a x i s . . . .
38
Ma g n e t i z a t i o n versus a p p l i e d f i e l d f o r a s i n g l e
c r y s t a l of CoNiTAC c o n t a i n i n g 58% n i c k e l and
o r i e n t e d al ong t he a or f e r r o ma g n e t i c a x i s . . . .
39
Thermpremanent ma g n e t i z a t i o n versus t i me ( 50 Oe
i n i t i a l f i e l d ) f o r t he 34% sample at 2 . 4 , 2 . 6 ,
2 . 8 , 3 . 0 and 3 . 2 K.
The s o l i d l i n e s ar e f i t to
a s t r e t c h e d e x p o n e n t i a l wi t h a c o ns t a nt o f f s e t .
. 42
Thermoremanent ma g n e t i z a t i o n versus t i me ( 50 Oe
i n i t i a l f i e l d ) f o r t he 58% sampl e.
The l i n e s
from t op t o bottom were t aken at 2 . 4 , 2 . 6 , 2 . 8 ,
3 . 0 and 3 . 2 K.
The s o l i d l i n e are f i t t o a
s t r e t c h e d e x p o n e n t i a l wi t h a const ant o f f s e t . . .
43
Thermoremanent, ma g n e t i z a t i o n versus t i me ( 50 Oe
i n i t i a l f i e l d ) f o r t he 72% sampl e.
The l i n e s
from top t o bottom were t aken at 2 . 4 , 2 . 6 and
2 . 8 K.
The s o l i d l i n e s ar e f i t t o a s t r e t c h e d
e x p o n e n t i a l wi t h a c o n s t a n t o f f s e t .................................
44
ix
Figure
18.
19.
Page
S u s c e p t i b i l i t y versus t e mp e r a t u r e f o r a 49% Ni
sample of CoNiTAC.
S o l i d l i n e i s t he r e a l pa r t
of t he s u s c e p t i b i l i t y al ong t h e . a a x i s .
Dashed
l i n e i s t he r e a l p a r t . o f t he s u s c e p t i b i l i t y
al ong c a x i s .
Dot t ed l i n e i s t he i magi nar y
p a r t of t he s u s c e p t i b i l i t y al ong t he a a x i s . . . .
46
Real p a r t of t he s u s c e p t i b i l i t y versus
t e mp e r a t u r e f o r a 60% Ni sample of CoNiTAC
al ong t he a a x i s .
S o l i d l i n e is f o r a
f r e q ue n c y of 160 Hz and dashed l i n e i s f o r
80 Hz. .....................................................................................
49
20.
I n v e r s e s u s c e p t i b i l i t y versus t e mp e r a t u r e f o r
MnCoTAC powders.
Mi x t ur e s c o n t a i n i n g 20, 30,
40 and 60 p e r c e nt Co ar e r e p r e s e n t e d
r e s p e c t i v e l y by c i r c l e s , squar es, t r i a n g l e s and
doubl e t r i a n g l e s . ....................................................................... 5.2
21.
I n v e r s e s u s c e p t i b i l i t y versus t e mp e r a t u r e f o r
MnNiTAC powders.
Mi x t ur e s c o n t a i n i n g 10, 20,
30 and 60 per cent Ni ar e r epr e s e nt e d
r e s p e c t i v e l y by c i r c l e s , s q u a r e s , t r i a n g l e s and
doubl e t r i a n g l e s ........................................................................... 53
22.
Uni t c e l l of 2-DACuC14 showing t he p o s i t i o n s
of t he i ons ( e xce pt hydr ogen) .
Some of t he
CuCl bonds ar e i n c l ud e d t o hel p show t he
" p uc k e r i ng" of t he l a y e r s . . . . .......................... ....
23.
24.
25.
Powder magnet i c s u s c e p t i b i l i t y versus
t e mp e r a t u r e dat a f o r n-DACuBr^ wi t h n = 5 - 1 0 .
S o l i d dat a p o i n t s ar e r e f e r e n c e d t o t he l e f t
s c a l e and open dat a po i n t s t o t he r i g h t s c a l e .
55
.
. 57
S u s c e p t i b i l i t y versus t e mp e r a t u r e f o r
5-DACuCl 4x Br 4 M _ x ) wi t h x = . 12 ( c i r c l e s ) , . 47
( s q u a r e s ) , . 65 ( t r i a n g l e s ) , . 76 ( doubl e
...................
t r i a n g l e s ) , and . 88 ( + 1s ) . . . . . . . .
59
S u s c e p t i b i l i t y versus t e mp e r a t u r e f o r
7-DACuCI 4 x Br 4 ( I - x ) wi t h x = 0 ( c i r c l e s ) , . 24
( s q u a r e s ) , . 35 ( t r i a n g l e s ) , . 47 ( doubl e
t r i a n g l e s ) , . 53 ( x ' s ) , and 1. 0 ( + 1s ) ............................ 60
X
Fi gure .
.
Page
26.
S u s c e p t i b i l i t y versus t e mp e r a t u r e f o r
a 7- DACuCl 4x B r 4 ( i _ x ) s i n g l e c r y s t a l wi t h
x = . 24 both p a r a l l e l ( t r i a n g l e s ) and
p e r p e n d i c u l a r ( c i r c l e s ) t o t he f e r r o ma g n e t i c
p l a n e s ...................................................................................................62
27.
Phase di agr am of t e mp e r a t u r e versus x (mol e
f r a c t i o n of n i c k e l ) f o r CoNiTAC showing t he
p a r a ma gne t i c , a n t i f e r r o m a g n e t i c , and Spin
gl ass r e g i o n s . ........................................... .... ....................... ....
. 64
28.
Phase di agr am of t e mp e r a t u r e versus x (mol e
f r a c t i o n of c o b a l t ) f o r MnCoTAC............................................. 76
29.
Phase di agr am of t e mp e r a t u r e versus x (mol e
f r a c t i o n of n i c k e l ) f o r MnNiTAC. . . .............................77
30.
Phase di agr am of t e mp e r a t u r e versus x f o r
B-DACuCl 4x Br 4 ^ x ) ................... ■.................................................. 80
31.
Phase di agr am of t e mp e r a t u r e versus x f o r
7-DACuCI 4xBr 4 ^ j _x ) .....................................
8i
ABSTRACT
The t e mp e r a t u r e versus composi t i on phase di agrams f o r
s e v e r a l low d i m e n s i o n a l , mixed magnet i c systems have been
i n v e s t i g a t e d . . The magnet i c be ha v i or of t he pseudo- onedi mensi onal mixed systems [ ( CH3 ) 3NH] A ( | _ x ] Bx CI 3 • 2H2O where
A and B ar e Co, N i , and Mn, was i n v e s t i g a t e d as a f u n c t i o n
of x.
The mi x t u r e wi t h Co and Ni was found t o e x h i b i t
spi n gl ass be ha v i or bel ow a c h a r a c t e r i s t i c t e mpe r a t ur e
Tg as evi denced by t he onset of t i me dependent
t ner mor emanent m a g n e t i z a t i o n .
The phase di agr am of
t e mp e r a t u r e versus x showed a ve r y broad and deep spi n
gl ass r e g i o n wi t h u n u s u a l l y t h i n a n t i f e r r o m a g n e t i c phase
r e gi ons above i t .
A t e t r a c r i t i c a I p o i n t near x = 0 . 5 8 was
indicated.
Thermoremanent ma g n e t i z a t i o n versus t i me below
Tg was f i t t o a s t r e t c h e d e x p o n e n t i a l f u n c t i o n pl us a
c o n s t a n t o f f s e t t er m.
Mi x t u r e s of Mn wi t h Co and Mn wi t h
Ni showed no spi n gl ass be ha v i or above 2 K and had a deep
de pr ess i on in t he c e n t e r of t h e i r t e mp e r a t u r e versus x
phase d i a g r a ms .
The ps e udo- t wo- di mens i onal mixed syst ems,
[NH.3 (CH2 )nNH3 ] Cu Cl 4XBr 4 ( i _ x ) f o r n = 5 and 7 were al so
investigated.
The t e mp e r a t u r e versus x phase di agrams f o r .
t hese systems al s o showed evi dence of t e t r a c r i t i c a l po i nt s
but wi t h mixed phase r e gi ons r a t h e r t han spi n gl ass
phases.
From an e x a mi na t i on of t he d i f f e r e n c e s in t hese
syst ems, c r i t e r i a f o r devel opment of mixed phases and spi n
gl ass phases were di scusse d.
I
INTRODUCTION
Systems wi t h r a nd oml y mixed magnet i c
i mpo r t a nt t o t he f i e l d
of c r i t i c a l
interactions
are
phenomena because t h e i r
t e mp e r a t u r e versus composi t i on phase di agrams can cont a i n
mu l t i c r i t i c a l
frustration
points.
In a d d i t i o n ,
i f there
in t he magnet i c i n t e r a c t i o n s ,
be a t ype of magnet i c m a t e r i a l
purpose of t h i s work i s t o
is a
t he system may
known as a spi n g l a s s .
The
i n v e s t i g a t e t he t e mp e r a t u r e
versus composi t i on phase di agr am and spi n gl ass behavi or
for
several
di mensi onal
low d i me n s i o n a l ,
mixed magnet i c syst ems.
systems were chosen f o r
di scuss t he e f f e c t s
Low
s t u d y ' i n or de r to
of d i m e n s i o n a l i t y in mi xed magnet i c
syst ems.
The mi xed systems consi der ed here i n c l u d e t h r e e s i t e
disordered,
gener al
pseudo- one di mensi onal
f o r mu l a ,
[ ( CH3 ) 3NH]MCI 3 • ZH2O in which M r e p r e s e n t s
a mi x t u r e of C o - N i , Mn-Co or Mn- N i .
cobalt-nickel
one.
For exampl e,
in t he
mi x t u r e M would be r e pl a c e d by Co( i _ x ) N'i x i n
which x i s t he mole f r a c t i o n
contai n ni ckel
m a t e r i a l s w.ith t he
of t he met al
s i t e s which
and can have va l ue s r angi ng f rom zer o t o
For ease in r e a d i n g , t r i met hyl ammoni um met al
trichloride
henceforth
d i hy dr a t e or [ ( C H 3 ) 3NHl MCl 3 -ZH2O w i l l
be a b b r e v i a t e d as MTAC.
For t he c o b a l t
and
2
nickel
exampl e a bove, t he a b b r e v i a t i o n
therefore
be used.
The o t h e r mixed systems t o be
consi der ed ar e two bond d i s o r d e r e d ,
syst ems,
CoNiTAC would
pseudo- t wo di mensi onal
S-DACuCl 4x Br 4 ^1 - x ) and T-DACuCl 4x Br 4 ^ ^ x ) •
Her e,
S-DA and 7-DA ar e a b b r e v i a t i o n s f o r p e n t a n e d i ammonium,
N H g ( C H 2 ) 5N H 3 ,
respectively,
that
and h e p t a n e d i ammonium,
N H 3 ( C H 2 ) 7N H 3 ,
x i s t he mole f r a c t i o n
of t he t o t a l
halide
is chl or i de.
Among t hese syst ems,
as a spi n g l a s s ,
and because of t he i n t e r e s t i n g
of a spi n g l a s s e s ,
Specifically,
o n l y CoNiTAC was f ound t o behave
it
was s t u d i e d
t he r e s u l t s
properties
in t he most d e t a i l .
include:
single crystal
measurements of both dc ma g n e t i z a t i o n and ac
susceptiblity;
t her moremanent ma g n e t i z a t i o n
measurements and a f i t
to a t h e o r e t i c a l
(TRM)
mode l ; and an
i mproved t e mp e r a t u r e versus x phase di agr am.
Ma g n e t i z a t i o n measurements f o r t h e ot h e r systems r e s u l t
di s c u s s i o n of t h e i r
Finally,
in
t e mp e r a t u r e versus x phase di agr ams.
by compari ng t hese r e s u l t s ,
d i m e n s i o n a l i t y of t he
t he e f f e c t s
of t he
i n t e r a c t i o n s can be di scusse d.
Bef or e d i s c u s s i n g t he p r e s e n t ex per i ment s and t h e i r
results,
will
a r e v i e w of pr ev i ous work on t he MTAC systems
be p r e s e n t e d .
mi xed systems w i l l
theoretical
Both p u r e , s i n g l e met al
be c o n s i d e r e d .
and e x p e r i me n t a l
compounds and
In a d d i t i o n ,
some
background conce r ni ng what t o
3
expect from a. random mi x t u r e phase di agr am and from a spi n
gl ass w i l l
be d i s c u s s e d .
No pr evi ous work o t h e r than our
own has been done on t he 5 -DA and 7-DA copper h a l i d e s .
Properties
of S i n g l e Met al MTAC Compounds
In or de r t o di scuss t he mixed met al
first
necessar y t o de s c r i b e t he s t r u c t u r a l
properties
of t he p u r e , s i n g l e met al
be pr epar ed wi t h t he d i v a l e n t
Fe.
syst ems,
The t r i m e t h y l ammom'urn met al
Ni,
Mn,
MTAC can
Cu and
c h l o r i d e s formed wi t h t he
above f i v e met al s ar e a 11 i s o s t r u c t u r a l
differences
is
and magnet i c
compounds.
met al s Co,
it
wi t h onl y smal l
in bond l engt hs and bond a n g l e s .
As such t h e y
make good c a n d i d a t e s f o r mixed magnet i c systems si nce
changes in magnet i c p r o p e r t i e s
can be a s s o c i a t e d wi t h t he
change in t he p r o p e r t i e s of t he met al
ve r y weakl y wi t h changes
structure
of CoTAC w i l l
members of t h i s
structurally
and r e l a t e d
in t he c r y s t a l
onl y
structure.
be de s c r i b e d in d e t a i l .
The
The ot he r
s e r i e s of compounds can be consi der ed
identical
t o CoTAC wi t h t he mi nor di s t a n c e
and angl e c o r r e c t i o n s menti oned, above.
The s t r u c t u r e of CoTAC was f i r s t
aI .
I
1
In CoTAC t he c o b a l t
sol ved by Losee et
i ons ar e o c t a h e d r a l I y
c o o r d i n a t e d by two wat er mol ecul es and f o u r c h l o r i d e
wi t h t he wat er s
bei ng t r a n s t o each o t h e r .
on each edge ar e shared wi t h a d j a c e n t c o b a l t
i ons
Two c h l o r i d e s
oct ahedr a t o
4
f orm b i br i dged chai ns of c o b a l t
s t o c h i o me t r y Co( H2O) 2C l 2 .
oct ahedr a wi t h t he
A p o r t i o n of t h i s
al ong t he a a x i s of t he c r y s t a l
I.
is
chai n
illustrated
l ooki ng
in Fi gur e
The wat er mol ecul es hydrogen bond wi t h t he r emai ni ng
chloride
i ons t o form weakl y bound pl anes of c o b a l t
chains.
The t h r e e di memsi onal
structure
i s formed by
s t a c k i n g t hese pl anes wi t h t he t r i me t h y I a mmo n i urn c a t i on s
spaced between them.
cobalt
chai ns
The pl anes ar e st agger ed such t h a t
in one pl ane
lie
next n e a r e s t nei ghbor, p l a n e .
between t he chai ns of t he
A simplified
s t r u c t u r e of
CoTAC5 l ooki ng al ong t he chai n or b a x i s d i r e c t i o n ,
shown in Fi g u r e
orientation
2.
The shor t
lines
of t he HgO l i g a n d s .
i n d i c a t e t he
They ar e t i l t e d
a p p r o x i ma t e l y 10 degrees away f rom t he c a x i s ,
angl e
in t he di agr am has been exagger at ed
emphasi ze t he
that
i n e q u i v a l e n c e of a d j a c e n t
t he wat er
l i g a n d s ar e t i l t e d
alternate
directions
structure
itself
in t he c o b a l t
t hen
however t he
i n or de r to
pl anes.
Not i ce
away from t he c ax i s but
in each successi ve p l a n e .
i n t r o d u c e s an a l t e r n a t i n g
The
anisotropy
sites.
M a g n e t i c a l l y each c o b a l t
t hr ough two C o - C l -Co bonds.
i s coupl ed al ong t he chai ns
Thi s
exchange path wi t h J^/ k = 15 . 4 K.
crystallographic
direction.)
is
Thi s
b direction
interaction
i s t he S t r ong e s t
( b denot es t he
and al so t he chai n
is f err omagnet i c,
as i s t he
O Co
Fi g u r e
I.
• Cl
0 H2O
The c o b a l t - c h l o r i d e chai n of CoTAC wi t h t he a axi s p e r p e n d i c u l a r t o
t he dr awi ng.
C
Fi g u r e 2.
A s i m p l i f i e d vi ew of CoTAC l ooki ng al ong t he chai n d i r e c t i o n .
Li nes r e p r e s e n t t he o r i e n t a t i o n of t he wat er mol e c ul e s .
Arrows on
t he l e f t and r i g h t r e p r e s e n t two p o s s i b l e spi n o r i e n t a t i o n s wi t h
r e s p e c t t o t he wa t e r s .
7
next
s t r o n g e s t c o upl i ng
in t he c axi s d i r e c t i o n .
Si nce
t h i s exchange i s t hr ough hydrogen bonds wi t h t he HgO
ligands,
t he c o up l i ng
There i s v i r t u a l l y
direction
i s much s ma l l e r ;
no d i r e c t
and J3Zk = - . O l K
exchange i s n e g a t i v e ,
ordering
exchange path
i s s ma l l e r
in t he t h i r d
still.
be ha v i or
Thi s
3 - di me ns i ona l
The c r i t i c a l
The a n t i f e r r o m a g n e t i c
al ong t he c d i r e c t i o n .
f e r r o ma g n e t i c
= 0. 1 K.
t h e r e f o r e t he o v e r a l l
is a n t i f e r r oma g ne t i c .
i s Tc = 4 . 2 K.
J /k
t e mp e r a t u r e
or easy a x i s
is
The a a x i s shows weak
i n d i c a t i n g t h a t t he spi ns are
cant ed away from t he c ax i s
in t he a d i r e c t i o n .
There are
two ways in which t he spi ns may be cant ed wi t h r e s p e c t t o
t he symmetry of t he c o b a l t
sites.
They may o r i e n t
either
near t he wat er ax i s or near t he c h l o r i d e pl ane as shown
r e s p e c t i v e l y on t he r i g h t
axis s u s c e p t i b i l i t y
and l e f t
i s ver y smal l
of Fi gur e 2.
The b
indicating that
the
spi ns ar e c o n f i n e d t o t he ac p l a n e .
The s u s c e p t i b i l i t y
dat a was f i t
S = 1/2,
t o t he one d i me n s i o n a l ,
f o r t he c and a - a x e s .
susceptibility
2 3
’
The c - a x i s
.
(I)
or p e r p e n d i c u l a r s u s c e p t i b i l i t y
X = ( Ng2uB2/ 8 J ) [ t a n h (
The s t andar d
(easy axis)
i s gi ven as
X = ( Ng2uB2/ 4 k T ) e x p ( 2 J / k T )
and t he b - a x i s
I s i n g model
I s i n g model ,
i s gi ven as
J /kT)sech2( J / k T ) ] .
however,
coul d not f i t
( 2)
t he
a - a x i s s u s c e p t i b i l i t y because of t he f e r r o m a g n e t i c c a n t i n g
8
in t h i s
direction,.
I n s t e a d t he expr ess i on
X = Ng2uB2 (T - T0 ) / [ 4 k ( T 2 - Tq2 ) ]
( 3)
f o r a weak f e r r oma g ne t was us e d.
NMR s t u d i e s by Spence
'5
and Bot t erman
p r e d i c t t he c a n t i n g angl e t o be about 10
degr ees from t he c d i r e c t i o n .
They a l s o show a t r a n s i t i o n
at about 60 Oe from an a n t i f e r r o ma g n e t i c t o par amagnet i c
s t a t e al ong t he c a x i s ,
Further
making t h i s
compound a metamagnet.
ac s u s c e p t i b i l i t y measurements by Gr oe ne ndi j k ^ and
van Duyneve I d t ^ s^ c o nf i r m t he met amagnet i c be ha v i or and
refine
t he va l ue of t he zer o f i e l d
c a nt i n g angl e t o be 22
de gr ees.
The d e u t e r a t e d form of CoTAC was al so
0
i n v e s t i g a t e d by Gr oenendi j k et a I .
in or de r t o det er mi ne
t he e f f e c t
on t he J g exchange c ons t a nt whi ch oper at es
t hr ough t he hydrogen bonds.
J 0 was found in t h i s
a
However,
onl y a 6,% change in
case.
NiTAC i s n e a r l y i d e n t i c a l
s t r u c t u r a l l y t o CoTAC as
Q
det er mi ned by O' Br i e n et a I .
The r e p o r t e d magnet i c
par amet er s ar e al so s i m i l a r wi t h Tc = 3 . 7 K, J^/ k = 14 K,
Jc/ k
= 0 . 0 7 K and Jg/ k = - 0 . 0 0 6 K as r e p o r t e d by
Hooger beet s et a I . ^
The spi ns ar e agai n c o n f i n e d t o t he
ac pl ane wi t h a c a n t i n g angl e of 21 degree f rom t he c
direction.
Further
EPR s t u d i e s
by Hooger beet s et a I .
11
c o n f i r m t he c a x i s t o be t he easy ax i s and b t o . b e t he
hard a x i s .
9
The s t r u c t u r e of MnTAC was det er mi ned by Caputo et
aI .
12
13
and by Depmei er and Kl aska
t o t he c o b a l t
however,
it
and n i c k e l
and i s a l s o i somorphi c
a nal ogs.
In c o n t r a s t t o t h e s e ,
has a n t i f e r r o ma g n e t i c c o up l i ng al ong t he
chai ns wi t h a Neel t e mp e r a t u r e of Tn = 4. 1 K as det er mi ned
by Si mi zu et a I . ^
The phase di agr am f o r t h i s
near t he b i c r i t i c a l
poi nt
compound
has been de s c r i be d by Megy et
a l . 15
The s t r u c t u r e of CuTAC was det er mi ned by Losee et
aI . ^
and i s s i m i l a r t o CoTAC except t h a t t he b i b r i d g e s
ar e a s s y me t r i c a I and CuTAC1s c r y s t a l l o g r a p h i c space group
is d i f f e r e n t .
Stirrat
et a I . ^
found a ver y weak c o upl i ng
al ong t he chai ns wi t h J / k .= 0 . 8 5 K and Tc = 0. 1 65 as
refined
t he
by Al g r a et
isotropic
aI .
Ri t t e r
symmet r i c,
dipolar,
et a I . ^
have det er mi ned
anisotropic
symmet ri c
and a n t i s y mme t r i c exchange par amet er s from epr
measur ement s.
FeTAC was i n v e s t i g a t e d by Landee et a l .
3 . 2 8 K.
axis.
The spi ns ar e
Ising-Iike
The one di mensi onal
an o v e r a l l
and l i e
ordering
t h r e e di mensi onal
?o
wi t h
Jq
al ong t he chai n
i s f e r r o ma g n e t i c wi t h
a n t i f e r r o ma g n e t i c o r d e r i n g .
Pr evi ous Work on Mi xed MTAC Systems
Some work on mixed MTAC systems has a l r e a d y been
published.
Schouten et a l .
21
=
r e p o r t e d heat c a p a c i t y
10
measurements dnCoCuTAC.
of CuTAC i s so l ow,
Si nce t he t r a n s i t i o n
0 . 1 5 7 K, copper
r esembl e a di ama gnet i c
i s expect ed t o
i m p u r i t y and l ower t he t r a n s i t i o n
t e mp e r a t u r e of CoTAC as t he c o n c e n t r a t i o n
It
in f a c t
ex pec t ed.
does t h i s
II
i n c r e a s e d.
might be
Thi s system i s best de s c r i be d as a bond
J,
ar e used.
= 0.02J|_|^.
refer
is
but not wi t h t he sl ope t h a t
i m p u r i t y system in whi ch t h r e e
constant,
t e mper at ur e
val ues of t he coupl i ng
The best f i t
is to J
JH„ and
Using Schouten 1s nomencl at ur e
, J ^ ^ and
r e s p e c t i v e l y t o c o up l i ng between two ne a r e s t
nei ghbor c o b a l t
at oms,
one copper atom.
two copper atoms and one c o b a l t
The s u b s c r i p t
I r e f e r s t o t he
and
Ising
c h a r a c t e r of c o b a l t and H r e f e r s t o t he Hei senber g
character
usual
fit
of copper .
The val ue of J^^ d i s a g r e e s wi t h t he
a p pr ox i ma t i on
=
i s f ound by l e t t i n g
J
1/ 2
( J I I JHH)
IH
and a much c l o s e r
HH
Some magnet i c r esonance work on MnCoTAC has al so been
??
OO '
done by Mat subar a e t a I .
and by Pha f f et a I .
They
find
a limiting
of t he spi n d i f f u s i o n
manganese i s added t o t he c r y s t a l .
r a t e as more
Thi s
indicates a
decr eased c o u p l i n g between manganese and c o b a l t ,
t he nomencl at ur e
i nt r oduc e d
i s much l ess t han
a surprising r esult
axes ar e not
in t he pr evi ous
or J^ ^ in t h i s
si nce t he c o b a l t
in t he same d i r e c t i o n .
syst em.
or usi ng
pa r a gr aph,
J^^
Thi s i s not
and manganese easy
11
Susceptibility
on MnCoTAC f o r
smal l
Chei khrouhou et a I .
this
system f o r
2.9% Mn,
and remanence s t u d i e s
have been done
manganese c o n c e n t r a t i o n s
24
by
They f i n d spi n gl ass behav i or
ve r y low manganese c o n c e n t r a t i o n s .
Tg = 3 . 6 K and f o r
in
For
9.3% Mn, Tg .= 1. 7 6 K.
M a g n e t i z a t i o n measurements on powder samples of
CoNiTAC have been done by R a f f a e l Te. ^
Susceptibility
as a f u n c t i o n of t e mp e r a t u r e was found f o r
v a r i o us n i c k e l
I/X
and c o b a l t met al
versus T gi ve s t r a i g h t
which when e x t r a p o l a t e d
pe r c e n t a g e s .
lines
intersect
t he Cur i e t e m p e r a t u r e , Tc ,
CoNiTAC wi t h
Graphs of
at hi gh t e mper at ur e s
t he t e mp e r a t u r e ax i s at
For a l l
mi x t u r e s t he val ue of
Tc was between 4 . 5 K and 4 . 1 K wi t h a s l i g h t
t he n i c k e l
l ower i ng as
per c ent age was i n c r e a s e d .
Two t ypes of exper i ment s were per f or med t o det er mi ne
t he f i e l d
dependence of t he m a g n e t i z a t i o n .
method was t o cool
The f i r s t
t he sample f rom above Tc i n a f i e l d
2000 Oe, t hen r educe t he f i e l d
to
13 Oe and t a ke
measurements as t he t e mp e r a t u r e was i n c r e a s e d .
contrast,
measurements were t hen t aken
cool ed and zer o f i e l d
obtai ned.
In t h i s
field
( H < 4 Oe) ,
after
waiting
For
in 13 Oe as the
t e mp e r a t u r e was decr eased f rom above Tc .
field
of
A more st andar d
cool ed set of cur ves were al so
case t he sample was cool ed
in zero
t he f i e l d was t hen set t o 50 Oe and
3 mi nut es measurements were t aken as t he
12
t e mp e r a t u r e was r a i s e d .
field
cool ed c u r v e .
Thi s r e s u l t s
The FC or f i e l d
in t he ZFC or zero
cool ed cur ve was
obt a i ne d by l ower i ng t he t e mp e r a t u r e from above Tc in an
applied f i e l d
of 50 Oe and t a k i n g measurement s.
susceptibilities
field
The
s e p a r a t e bel ow a t e m p e r a t u r e , Tg f o r t he
cool ed versus zer o f i e l d
cool ed c u r v e s .
By doi ng t her mor emanent ma g n e t i z a t i o n s t u d i e s at
v a r i o u s t e mp e r a t u r e s Tg was a l s o det er mi ned by t he
t e mp e r a t u r e at whi ch t h e r e
i s no l onger a TRM.
A graph of
t he TRM versus t e mp e r a t u r e f o r v a r i o u s w a i t i n g t i mes
shown in F i gur e 3 f o r
a 65% Ni
is
sa mpl e. 26
Usi ng t hese val ues of T
and T a p r e l i m i n a r y
c
9
magnet i c phase- di agr am of t e mp e r a t u r e versus mole f r a c t i o n
of n i c k e l
refined
nickel
was c o n s t r u c t e d .
The phase di agram has been
in t h i s work by c o r r e c t i n g t he val ues of t he
c o n c e n t r a t i o n s and by addi ng more dat a po i n t s to
t he di agr am.
Multicritical
A tricritical
p o i n t occurs
Poi nt s
i n a magnet i c phase
di agr am where two second or de r phase t r a n s i t i o n
wi t h a l i n e of f i r s t
exampl e of t h i s
or der phase t r a n s i t i o n s .
i s seen in t he f i e l d
phase di agr am of an ant i f e r r o ma g n e t .
poi nt
l i n e s meet
The c l a s s i c
versus t e mp e r a t u r e
The t r i c r i t i c a l .
occur s where t he second or der par amagnet i c to
120 a
T(K)
F i g u r e 3.
Ther mor emanent m a g n e t i z a t i o n ( I
temperature fo r various w a iting
kOe i n i t i a l f i e l d ) v er sus
t i me s in t h e 65% n i c k e l sampl e.
14
a n t ! f e r r o m a g n e t i c and par amagnet i c t o spi n f l o p
wi t h t he f i r s t
or de r a n t i f e r r o ma g n e t i c t o spi n f l o p
A tetracriticaI
p o i n t occurs where f o ur
or der phase t r a n s i t i o n s
lines
field
lines
line.
of second
meet or e q u i v a l e n t l y where two
of second or de r phase t r a n s i t i o n s
Multicritical
l i n e s meet
p o i n t s not onl y occur
phase di agrams but al so
c r os s .
in t e mp e r a t u r e versus
in t e mp e r a t u r e versus
composi t i on phase di agrams where t h e r e ar e two competi ng
interactions.
t e t r a c r i t ical
it
How c r i t i c a l
poi nt
i s of
is pr edi ct ed t h a t
l i n e s come t o g e t h e r at a
interest t h e o r e t i c a l l y , ^ - ^
t he y shoul d meet t a n g e n t i a l l y
and
and not
at an a n g l e .
An exampl e of t h i s
can be found in t he t e mp e r a t u r e
versus composi t i on phase di agr am of two a n t i f e r r o ma g n e t s
wi t h d i f f e r e n t
easy axes.
A representation
of t h i s t ype
of phase di agr am i s shown s c h e m a t i c a l l y in F i g u r e 4 and
would be a p p r o p r i a t e f o r a system such as
F e ( i _ x ) Cox C12 * 2H20 .
31
each have t r a n s i t i o n s
antiferromagnetic
The pure
i r on and c o b a l t
from a par amagnet i c t o
phase as t e mp e r a t u r e
easy axes ar e i n d i f f e r e n t
in a n i s o t r o p y between
compounds
between t hese two a n t i f e r r o m a g n e t i c
Thi s mixed phase r e g i o n
l ower ed,
but t he
d i r e c t i o n s due t o d i f f e r e n c e s
i r on and c o b a l t .
a spi n a l i gnme n t whi ch i s
is
A new phase l i e s
phases and r e p r e s e n t s
i n an i n t e r m e d i a t e d i r e c t i o n .
i s not c h a r a c t e r i z e d
by a s i n g l e
MIXED
0
Fi g u r e 4.
x
1
Sket ch of a t e mp e r a t u r e versus x phase di agram wi t h a t e t r a c r i t i c a I
p o i n t and a mixed phase r e g i o n .
16
i nt er medi at e
direction
orientation.
but by a gr adual
For a c o ns t a nt
change in t he spi n
Tow t e mp e r a t u r e but wi t h
i n c r e a s i n g x , t he spi n d i r e c t i o n
remai ns c ons t a nt u n t i l
t he a n t i f e r r o m a g n e t i c t o mixed phase boundary i s r eached.
The spi n d i r e c t i o n
orientation
t hen g r a d u a l l y s h i f t s
until
t he hi gh x
i s r eached and t he second mixed t o
antiferromagnetic
phase boundary i s cr ossed.
tetracritical
poi nt
di agr am meet .
If
occurs where t he f o ur
The
lines
in t he
t he compet i ng a n i s o t r o p y between t he two
magnet i c s i t e s were made l a r g e r , t he mixed phase would
become nar r ower u n t i l
f orm a s i n g l e f i r s t
t he c r i t i c a l
or der
Ti ne wi t h a t r i e r i t i c a l
The 5 -DA and y - D A C u C T ^ B r ^ , ^ ^
in t erms of a t e t r a c r I t i c a T
Fi g u r e 4,
however t h e r e
l i n e s came t o g e t h e r t o
systems wi l T
point.
be di scussed
system as i TT us t r a t e d in
i s not onl y competi ng a n i s o t r o p y
but a l s o a compet i ng a n t i f e r r o ma g n e t i c t o f e r r o ma g n e t i c
compet i t i on.
In c o n t r a s t , t he
l arge a ni sot r opi e s
CbNiTAC suggest a ve r y narrow or n o n e x i s t e n t
in
mixed phase
region.
Spin Gl asses
E x t e n s i v e r evi e ws on t he spi n gl ass phenomena have
been p u b l i s h e d by Ander son, ^
Bi nder and Young.
36
Mydosh^5 F i s h e r ^ ’ ^
The word " gl as s"
and
as used here r e f e r s
t o an amorphous or random system in which t h e r e
is a
17
"viscosity"
variable.
or t i me dependent change in some thermodynami c
For an o r d i n a r y gl ass t h i s
shape ( vol ume)
i ntroduced;
cor r esponds t o a
change wi t h t i me when a pr essur e change is
for
a ferroelectric
gl ass t h i s
is a d i e l e c t r i c
s u s c e p t i b l i t y change wi t h t i me f o r a change in the. a p p l i e d
electric
field;
and f o r a spi n gl ass t h i s
ma g n e t i z a t i o n wi t h t i me f o r
i s a change in
a change in t he a p p l i e d
magnet i c f i e l d .
Two p r o p e r t i e s
al ways s u f f i c i e n t
First,
ar e r e c o gni z e d as necessar y but not
c o n d i t i o n s t o produce a spi n g l a s s .
t h e r e must be randomness
in t he ar r angement of at
l e a s t two t ypes of s p i n s ,
and second,
frustration.
r e s u l t s when two compet i ng
interactions
Frustration
t r y t o d r i v e t he spi ns t owar d d i f f e r e n t
l owest ener gy s t a t e s .
For spi n gl asses t h e r e ar e t h r e e
common t ypes of f r u s t r a t i o n :
lattice
t h e r e must be
sites,
magnet i c versus non- magnet i c
f e r r o m a g n e t i c versus a n t i f e r r o m a g n e t i c
exchange and compet i ng an i s o t r o p i e s .
Gi ven t he mi ni mal
c o n d i t i o n s t o ob t a i n a spi n g l a s s ,
one must t hen ask what p r o p e r t i e s must such a system
possess t o be c a l l e d a spi n g l a s s .
r e c o gni z e d p r o p e r t i e s : " ^
frozen
results
first,
Again t h e r e
magnet i c moments must be
in bel ow a t e m p e r a t u r e , T , such t h a t
i n ac s u s c e p t i b i l i t y
measurements at
; second,
are t h r e e
a cusp
versus t e mp e r a t u r e
t h e r e must be magnet i c
18
relaxation
on a macr oscopi c t i me s c a l e bel ow T
t h e r e ar e changes
l ack of
however,
in t h i s
in t he magnet i c f i e l d ;
l on g - r a n g e magnet i c o r d e r .
Thi s t h i r d
when
there
is a
condition,
can be r e l a x e d as in t he CoNiTAC system pr esent ed
work in which t he spi n gl ass s t a t e occurs al ong
wi t h a f e r r o m a g n e t i c
state.
The dc ma g n e t i z a t i o n and ac
s u s c e p t i b i l i t y dat a f o r CoNiTAC w i l l
relation
third
9
t o t he f i r s t
two c r i t e r i a .
be cons i de r e d in
19
EXPERIMENTS
Sample P r e p a r a t i o n and Ana l y s i s ■
Many of t he CoNiTAC c r y s t a l s
and powders and t he n -DA
powders were pr epar ed f o r t hese exper i ment s by Pr of es sor
Kenneth Emerson of t he MSU Chemi st r y De p a r t me nt .
(n-DA i s
used here as an a b b r e v i a t i o n f o r t he whol e s e r i e s
of
diammonium copper t e t r a c h l o r i d e s . )
samples were pr epar ed
in t h i s
The r e s t
laboratory.
of t he
In ge ne r a l
t he
met al
h a l i d e s and t he ammonium h a l i d e s were d i s s o l v e d
in
wat er
such t h a t
The
met al
ratio
t he r a t i o
of met al
t o amine was 1 : 1 .
in t he MTAC compounds and t he h a l i d e r a t i o
in
t he n-DA compounds were a d j u s t e d t o o b t a i n t he v a r i ous
mixed compounds.
One drop of c o n c e n t r a t e d HCl was added
t o each MTAC s o l u t i o n
to increase c r y s t a l
si nce an a c i d i c
size
s o l u t i o n was found
in N i T A C The s o l u t i o n s
were al l owed t o e v a po r a t e u n d i s t u r b e d and t he r e s u l t i n g
p r e c i p i t a t e s were removed by f i l t r a t i o n .
The MTAC c r y s t a l s
met al
formed do not c o nt a i n t he same
per cent ages as t he s o l u t i o n s from which t he y were
prepared.
The met al
per cent ages
in MnCoTAC and MnNiTAC
samples were o b t a i ne d f rom graphs of manganese as per cent
of t o t a l
met al
in s o l u t i o n
versus mole f r a c t i o n manganese
20
in t he c r y s t a l s
pe r c ent age s
as det er mi ned by L i n d b e c k . ^
in CoNiTAC were det er mi ned by at omi c
a b s o r p t i o n anal yses f o r c o b a l t
and n i c k e l .
commi ssi oned from t he MSU A g r i c u l t u r a l
from G a l b r a i t h
Laboratories.
as pe r c e nt of t o t a l
solutions
versus mole f r a c t i o n
met al
errors
in t he p e r c e nt
random v a r i a t i o n s
Lab and
a graph
nickel
in t he c r y s t a l s
for
in Fi g u r e 5.
in Fi g u r e 5 is not due t o
nickel
anal yses of t he c r y s t a l s
Analytical
in t he p r e p a r a t i v e
CoNiTAC was ob t a i n e d and i s pr es ent ed
in' t he dat a p o i n t s
Anal yses were
Using t hese r e s u l t s ,
of n i c k e l
Scatter
The metal
in t he s o l u t i o n s
or t he metal
and so must be a t t r i b u t e d to
in how t he c r y s t a l l i z a t i o n
t akes p l a c e .
The sl ope of t he cur ve in F i g u r e 5 is not as st eep as t he
curve det er mi ned by Li ndbeck
result
and agai n may be a
of t he method of p r e p a r a t i o n .
Smal l
crystals
ob t a i n e d f rom t he
large,
smal l
37
of CoNiTAC wei ghi ng up t o 0 . 3 mg were
initial
preparations.
Because of t he
low t e mp e r a t u r e magnet i c moment of CoNiTAC,
s i z e was s u f f i c i e n t
crystals
this
f o r magnet i c measur ement s.
The
ar e uni f or m in appear ence and t he t h r e e
c r y s t a l T o g r a p h i c axes ar e e a s i l y
identified
crystals
ar e n e e d l e - l i k e wi t h t he
b-axis.
They ar e a l s o d i c h r o i c and ar e p u r p l e t o brown
when l ooked at al ong t he c - a x i s
a-axis.
l ong a x i s
visually.
bei ng be
and green al ong t he
The
— 50
v- 40
45
60
65
70
%Ni, Solution
Figure
5.
P e r c e n t n i c k e l i n t h e s o l u t i o n s used t o p r e p a r e t h e mixed CoNiTAC
Samples v e r s u s p e r c e n t n i c k e l in t h e r e s u l t a n t c r y s t a l s .
22
A c o n s t a n t ' t e m p e r a t u r e and h u mi d i t y box was b u i l t
o r d e r t o grow c r y s t a l s
evaporation.
Seve r a l
were o b t a i n e d .
of t he n-DA compounds by slow
crystals
o f 7-DA wei ghi ng about 5 mg
Whi l e t hese c r y s t a l s
are s m a l l e r than was
hoped f o r and of a ve r y poor q u a l i t y ,
coul d s t i l l
some i n f o r m a t i o n
be o b t a i n e d from t hem.
The V i b r a t i n g
Sample Magnetometer
Most o f t he measurements which w i l l
o b t a i n e d usi ng a v i b r a t i n g
magnetization
temperature,
subsystems
be r e p o r t e d were
sample magnetometer.
i s al so a f u n c t i o n
Since
of a p p l i e d f i e l d
our appar at us c o n s i s t s
of s e v e r a l
in a d d i t i o n t o t he magnetometer
i n c l u d e an e l e c t r o m a g n e t wi t h f i e l d
and
other
itself.
control,
wi t h t e m p e r a t u r e measurement and c o n t r o l
computer
in
These
a cryostat
c a p a b i l i t y and a
i n t e r f a c e d t o t hese o t h e r systems.
The c l a s s i c
desi gn of a v i b r a t i n g
was devel oped by F o n e r .
38
Our magnetometer
commercial
model,
specifically
mechani cal
assembly v i b r a t e s
mounted a t the
noise).
i s however a
an EG&G PAR model
a rigid
f r e q u e n c y o f 8 2 . 5 Hz (60 Hz and i t s
because o f power l i n e
sample magnetometer
155.
A
sample rod at a
harmonics ar e avoided
The sample in quest i on
is '
lojwer end of t h e sample rod which is
usually situated
between t he c o i l s
of a magnet.
The lower
p o r t i o n o f t he rod is made of non- magnet i c m a t e r i a l s to
23
mi ni mi z e background s i g n a l s .
induces an ac c u r r e n t
The ac s i g n a l
As the sample v i b r a t e s
in p i c k - u p c o i l s
it
mounted near by.
from the sample has a f r e q u e n c y of 8 2 . 5 Hz
and an ampli tude, p r o p o r t i o n a l
t o t he m a g n e t i z a t i o n of the
sample and t o t he a mp l i t u d e of t he v i b r a t i o n .
f o r which t he a i r
Charged
capacitor
plates
gap changes wi t h the
vibration
p r o v i d e a st andar d so t h a t the d e t e c t e d s i g n a l
can be made i ndependent of v i b r a t i o n a l
signal
amplitude.
then passes through a phase s e n s i t i v e
the r e s u l t a n t m a g n e t i z a t i o n
magnetometer
d e t e c t o r and
i s d i s p l a y e d in emu.
is c a l i b r a t e d wi t h a n i c k e l
The
The
st andar d f o r
which t he s a t u r a t i o n m a g n e t i z a t i o n per gram i s w e l l
The appar at us
liquid
is equipped wi t h a Jani s Model
known.
153
hel i um c r y o s t a t made s p e c i f i c a l l y f o r magnetometer
measurements.
Bef ore a dat a c o l l e c t i n g
cryostat reservoir
is f i l l e d
wi t h
liquid
sessi on the
helium.
The
hel i um is then metered through a needl e v a l v e and
v a p o r i z e d by a v a r i a b l e
heater.
The hel i um gas f l ows by
t he sample and t he t e mp e r a t u r e of t he sample is c o n t r o l l e d
by r e g u l a t i n g
the f l o w r a t e
and t he h e a t e r c u r r e n t .
Temper at ures from 300 K t o 4 K can thus be a c h i e v e d .
By
pumping on t he sample chamber, t h e t e m p e r a t u r e o f the
hel i um gas can be reduced so t h a t t e mp e r a t u r e s down t o
K can be a t t a i n e d
by t h i s
cryostat.
1. 7
24
The t e mp e r a t u r e
is moni t or ed by carbon gl ass
r e s i s t a n c e t her momet r y.
The carbon gl ass r e s i s t o r
is
mounted on t he sample rod as cl ose to t h e sample as
possible.
resistor
A well
controlled current
i s passed through t he
and t he v o l t a g e drop across the r e s i s t o r
measured in or der t o de t er mi ne
from a c a l i b r a t i o n
Carbon gl a s s
its
is
r e s i s t a n c e , and then
c h a r t the t e mp e r a t u r e
is de t e r mi ne d .
i s used f o r t he sensor because o f two
important p r o p e r t i e s .
The r e s i s t a n c e changes are. l a r g e at
low t e mp e r a t u r e s making the thermometer s e n s i t i v e t o
changes of
l ess t han one m i l l i k e l v i n
at 4 K.
Al so ,
the
resistance
i s v e r y i n s e n s i t i v e t o the magnet i c f i e l d s
which must be a p p l i e d t o make m a g n e t i z a t i o n measurements.
The magneti c f i e l d
is ge ne r a t e d by a WaI ker / Magni on
l a b o r a t o r y e l e c t r o m a g n e t wi t h a 3 1/ 2 inch pol e gap.
magnet
i s powered by a B r i d g e w a t e r ,
bipolar
power suppl y
which s u p p l i e s c u r r e n t s of -25 t o +25 amperes.
magnet pol e gap t h i s
corresponds t o f i e l d s
The
In the
of - 5 5 0 0 . to
+5500 O e r s t e d .
The power suppl y is b i p o l a r which means
t h a t the f i e l d
can be swept c o n t i n u o u s l y from p o s i t i v e to
n e g a t i v e val ues w i t h o u t mechani cal
i mp o r t a n t f o r
low f i e l d
switching.
Thi s is
measurements (bel ow 50 Oe) and f o r
obtaining hysteresis
loops which need t o be scanned
t hrough zer o f i e l d .
A Bell
t h e a ppl i e d
field.
Model
160 Gaussmeter moni tors
25
The ex per i ment can be computer c o n t r o l l e d through an
Apple 11E computer and an IEEE bus t o a EG&G PAR model
VSM i n t e r f a c e .
t he f i e l d
The i n t e r f a c e
145
has two i n put s which r ecord
bei ng measured on t h e gaussmeter and the
magnetization
d i s p l a y e d on t he magnet omet er ' s panel m e t e r .
There i s al so one out put f o r r e m o t e l y c o n t r o l l i n g the
a p p l i e d magnet i c f i e l d .
apparatus, a direct
As a f u t u r e
IEEE l i n e
improvement to t h i s
to a d i g i t a l
voltmeter
is
bei ng cons i de r e d so t h a t t e mp e r a t u r e can a l s o be recorded
d i r e c t l y by the computer.
from t he computer
i n c l ud e s a IEEE i n t e r f a c e d
I n t r u me n t s DMP- 40 P l o t t e r
printer.
and a p a r a l l e l
The s o f t w a r e
Houston
inch f l o p p y
purposes.
s u p p l i e d wi t h t he magnetometer system is
u n f o r t u n a t e l y not s u i t a b l e
done in t h i s
dat a output
interfaced
Al I dat a are al so s t o r e d on 5 1 / 4
di sks f o r a r c h i v a l
written
Other hardware f o r
laboratory.
f o r the type o f measurements
A set o f r o u t i n e s
t o a l l o w one t o u t i l i z e
has been
t he t i me savi ng power of
computer s t o r a g e and r e t r i e v a l .
These programs are
written
A menu program f o r
i n modules and i n c l u d e :
in itiating
for
other options;
setting-the
magnetometer o p e r a t i o n programs
magneti c f i e l d ,
collecting
versus t e m p e r a t u r e and c o l l e c t i n g
field;
o u t p u t programs f o r
plotting
magnetization
printing
dat a and t h e o r e t i c a l
magnetization
lines;
data f i l e s
versus
and f o r
and m a n i p u l a t i o n
26
programs f o r
c o n v e r t i n g carbon gl ass r e s i s t a n c e val ues' to
temperature,
mo d i f y i n g data set s and f i t t i n g
theoretical
models.
Al I dat a f i t t i n g
was done by computer usi ng the
simpl ex method. 3 9 ’
space i s
data to
set-up.
n par amet er s an n - d i me n s i on a I
( n + I)
guesses are made f o r
a best f i t ,
and t hese guesses form t he c o r n e r s of a si mpl ex
bei ng d e f i n e d as a f i g u r e
in an n - d i m e n s i onal
(a si mpl ex
space having
n+ 1 v o r t e x e s ) . .. By c a l c u l a t i n g t h e st andar d d e v i a t i o n f o r
t hese p o i n t s ,
repeatedly,
a d j u s t i n g t he si mpl ex and r e c a l c u l a t i n g
the si mpl ex moves and c o n t r a c t s
until
it
converges on t he best f i t .
Measurements on GoNiTAC
M a g n e t i z a t i o n Versus Temper at ure
Measurements
In a d d i t i o n t o samples p r e v i o u s l y s t u d i e d ,
powder samples c o n t a i n i n g 50,
nickel
53,
58,
25
60 and 65 per cent
were examined in or der t o det er mi ne t h e i r
antiferromagnetic
and spin gl ass t r a n s i t i o n
temperatures.
The powder s u s c e p t i b i l i t y versus t e mp e r a t u r e curve f o r
both zero f i e l d
cool ed and f i e l d
sample i s shown in F i g u r e 6.
At
cool ed runs f o r the 53%
low t e mp e r a t u r e s the
upper set of dat a r e p r e s e n t s t he f i e l d cool ed c u r v e , and
t
t he lower set o f dat a r e p r e s e n t s t he zero f i e l d Cooled
curve.
The t e m p e r a t u r e at which the curves j o i n
is the
T (K)
Figure
6.
M a g n e t i z a t i o n v e r s us t e m p e r a t u r e a t 50 Oe f o r a powder sampl e
c o n t a i n i n g 53% n i c k e l .
Both z e r o f i e l d c ool e d and f i e l d cool ed
c ur v e s a r e shown.
28
spi n gl ass t r a n s i t i o n
transition
steepest
temperature.
temperature
The a n t i f e r r o m a g n e t i c
is det er mi ned as t he p o i n t of
sl ope as t e m p e r a t u r e
is
increased.
These values
in c o n j u n c t i o n wi t h p r e v i o u s l y det er mi ned val ues were used
t o c o n s t r u c t the CoNiTAC phase- di agram which w i l l
pr es ent ed and di scussed
Single c r y s t a l
in a subsequent c h a p t e r .
samples of CoNiTAC wei ghi ng 0. 1 t o 0 . 3
mg were measured wi t h magneti c f i e l d s
t h r e e c r y s t a l og r a phi c axes.
in an f i e l d
applied
along t h e i r
Measurements were performed
of 50 Oe in or der t o remain in t he
f e r r o m a g n e t i c and a n t i f e r r o m a g n e t i c r e g i o n s a t
t e mp e r a t u r e and t o avoi d t he high f i e l d
region.
A lower f i e l d
proportional
sample s i z e
be
low
par amagnet i c
was not used si nce s e n s i t i v i t y
t o both t he f i e l d
is
and sample s i z e and the
i s a l r e a d y ver y s m a l l .
The b or chai n a x i s which
is the
long a x i s
m o r p h o l o g i c a l l y gave no measurabl e s i g n a l .
Thi s
is
u n d e r s t a n d a b l e si nce both CoTAC and NiTAC have t h e i r
spins
c o n f i n e d t o t he a - c p l a n e .
T h e r e f o r e no dat a
this
be c o n f i n e d . t o t h e a - c pl a ne .
axis
and i n t e r e s t w i l l
Magnetization
versus t e m p e r a t u r e from 2 t o 6 K was
measured along t he a and c axes f o r v a r i o u s
pe r c ent age s
in CoNiTAC.
magnetization
for
30,
36,
i s shown f o r
F i g u r e s 7,
8,
nickel
9 and 10 show the
versus t e m p e r a t u r e along t he a and c axes
44 and 58 p e r c e n t n i c k e l .
In a l l ,
14 CoNiTAC
I—
—
I—
I-------------- 1-------------- 1--------------
—
I
(emu-Oe)
6
—
— I—
E -3
8
* .o ° o o ° %
o°
—
«
O
O
O
Mag.
•
2
O0o0tPrfjo
.4
O
0
I
____I___
I
2
* * * *
A A f A
«
A
3
A
A
^
“
^ A A *
* *
I
4
5
‘
6
T (K)
Figure
7.
M a g n e t i z a t i o n v e r s us t e m p e r a t u r e a t 50 Oe f o r a s i n g l e c r y s t a l of
CoNiTAC c o n t a i n i n g 30% n i c k e l .
T r i a n g l e s are f o r t he c axi s
( a n t i f e r r o m a g n e t i c ) and c i r c l e s a r e f o r t h e a a x i s ( f e r r o m a g n e t i c ) .
••
•* •••
x ° V
O0
F i g u r e 8.
%
M a g n e t i z a t i o n versus t e mp e r a t u r e at 50 Oe f o r a s i n g l e c r y s t a l of
CoNiTAC c o n t a i n i n g 37% n i c k e l .
Open c i r c l e s are f o r the c axi s
( a n t i f e r r o m a g n e t i c ) and s o l i d c i r c l e s are f o r t he a axi s
( ferromagnetic ).
—
I—
I
I
I------------- 1-------------
CO
I
LU
—
CU
O
I
D
E
CU
O
O
I
/X . -
—
CD
<0
I
------- 1------------- 1
------------- 1-----------
3
T
Figure
9.
( K)
M a g n e t i z a t i o n v e r s us t e m p e r a t u r e a t 50 Oe f o r a s i n g l e c r y s t a l of
CoNiTAC c o n t a i n i n g 44% n i c k e l .
T r i a n g l e s a r e f o r t he c a x i s
( a n t i f e r r o m a g n e t i c ) and c i r c l e s a r e f o r t h e a a x i s ( f e r r o m a g n e t i c ) .
OOOu Oo
OO
T (K)
Figure
10.
M a g n e t i z a t i o n v e r s us t e m p e r a t u r e a t 50 Oe f o r a s i n g l e c r y s t a l of
CoNiTAC c o n t a i n i n g 58% n i c k e l .
T r i a n g l e s a r e f o r t he c a x i s
( a n t i f e r r o m a g n e t i c ) and c i r c l e s a r e f o r t he a a x i s ( f e r r o m a g n e t i c ) .
33
samples wi t h
nickel
were measur ed.
of a l l
per c ent age s r angi ng from 30% t o 70%
The f o u r r e s u l t s
samples s t u d i e d .
In some cases,
t r a n s i t i o n t e mp e r a t u r e s
contained s u b s t a n t i a l
crystals
used.
shown ar e r e p r e s e n t a t i v e
w h i l e the
could be o b t a i n e d , t he data
noi se due t o the small
In F i g u r e s
7 t hrough
10,
s i z e of the
open c i r c l e s
r e p r e s e n t t h e c a x i s and cl osed c i r c l e s
r e p r e s e n t the a
axis
shows an o v e r a l l ,
susceptibility.
three dimensional,
The c ( e a s y )
ax i s
ant!ferromagnetic ordering,
w h i l e the a
axis
shows a f e r r o m a g n e t i c o r d e r i n g due t o spin c a n t i n g
this
direction.
Thi s
I
1n
CoTAC
axis
and N i TAC.
is
Fi gur e s
s u s c e p t i b i l i t y at
crystallites
s i m i l a r t o t he r e s u l t s
in
found f o r
7 and 9 show a drop in the a
low t e mp e r a t u r e s owing t o small
which were a t t a c h e d to the main c r y s t a l
but
m i s a l i g n e d wi t h r e s p e c t to t he a x i s under c o n s i d e r a t i o n .
Nevertheless,
the t r a n s i t i o n
t e mp e r a t u r e s
can s t i l l
be
det er mi ned from t hese g r a p h s .
The dat a ar e a combi nat i on
of f i e l d
cool ed d a t a ,
cool ed and zer o f i e l d
and t h e r e f o r e
show a s e p a r a t i o n
in t h e dat a below T .
Thi s is
9 t he h i s t o r y dependence of t h e sample w h i l e in t h e spin
gl ass s t a t e .
These s e p a r a t i o n s
and d i s t i n c t ,
and so t hey coul d not be s t u d i e d
quantitatively.
percent
are,
not uni f orm
A c l o s e comparison of t h e 30,
samples wi t h the 58 p e r c e n t
transition
however,
temperature
is s l i g h t l y
36 and 44
sample shows t h a t the
lower in the
latter
34
cases.
Thi s
indicates
l o wer i ng of the t r a n s i t i o n
t e mp e r a t u r e near t h e t e t r a c r i t i c a I
p o i n t as de scr i bed
l a t e r wi t h r e s p e c t t o t he t e mp e r a t u r e versus composi ti on
phase di agr am.
The f e r r o m a g n e t i c t r a n s i t i o n
has a l s o been seen t o s h i f t
wi t h r e s p e c t t o the
antiferromagnetic tr a n s itio n .
For t he examples shown
h e r e , t he f e r r o m a g n e t i c t r a n s i t i o n
in t he 58. p e r c e n t
nickel
30 and 44 p e r c e n t
samples.
effect
t e mp e r a t u r e
shifted
slightly
sample and s l i g h t l y
A careful
h i ghe r
lower
in t he
e x a mi n a t i o n o f t h i s
in many samples r e v e a l e d no c o r r e l a t i o n
wi t h the
composi t i on o f the samples and thus no e x p l a n a t i o n f o r
this
shift
is concl usi ve.
M a g n e t i z a t i o n Versus Appl i ed
F i e l d Measurements
Figures
applied f i e l d
nickel
11 and '12 are p l o t s
al ong t he c a x i s
sampl es,
of m a g n e t i z a t i o n versus
at 3 K f o r t h e 37% and 58%
respectively.
The magneti c f i e l d
was
scanned from +1000 Oe t o - 1000 Oe and then back t o +1000,
Oe.
As expect ed t h e r e
is no h y s t e r e s i s
m a g n e t i z a t i o n al ong t h i s
curve in F i g u r e
11 i t
axis.
In f a c t ,
in t he
f o r most of t h e .
is not even e v i d e n t t h a t
measurements were t aken wi t h both i n c r e a s i n g and
d e c r e a s i n g magneti c f i e l d .
separation
Figure
in m a g n e t i z a t i o n f o r
r e p e a t i n g t he ex pe r i me n t wi t h
12 shows a small
low f i e l d s ,
but by
an, empt y sample h o l d e r ,
this
Mag. (emu -Oe x IO"2)
- 1 000
-500
Field (Oe)
Figure
11.
M a g n e t i z a t i o n v e r s us a p p l i e d f i e l d
c o n t a i n i n g 37% n i c k e l and o r i e n t e d
antiferromagnetic axis.
for a single crystal
a l ong t he c or
o f CoNiTAC
4 —T-
Mag.
(emu-Qe)
E-2
a O•
o
OO
OO
-e-----
B
8
8
8
8
Oo
-500
-1000
8
8
8
oo
500
8
8
1000
8
-2
—
8
-4-
Field
Figure
12.
(Ge)
M a g n e t i z a t i o n v e r s us a p p l i e d f i e l d
c o n t a i n i n g 58% n i c k e l and o r i e n t e d
antiferromagnetic axis.
for a single crystal
a l ong t he c or
of CoNiTAC
37
s e p a r a t i o n was found t o be due t o the magnetometer and not
the sample.
The f l a t
p o r t i o n of t he curve near zero f i e l d
is where the samples are
in t h e i r
ant ! ' f e r r o ma g n e t i c phases
wi t h a n t i f e r r o m a g n e t i c to par amagnet i c t r a n s i t i o n s
about 200 Oe.
Thi s
is s i g n i f i c a n t l y
at
h i ghe r t han the
metamagneti c t r a n s i t i o n s which f o r pure CoTAC and NiTAC
are at
about 60 Ge.
reflects
t he f r o z e n
Thi s h i g h e r f i e l d
transition
pr ob ab l y
na t u r e of t he spins at t h i s
temperature.
Figures
13 and 14 are p l o t s of m a g n e t i z a t i o n
applied f i e l d
nickel
along t he a a x i s
sampl es,
respectively.
at 3 K f o r t h e 37% and 58%
They show st eep
f e r r o m a g n e t i c curves which s a t u r a t e at about
field
versus
100 Oe.
The
was scanned from +200 Oe to - 2 0 0 Oe and then back t o
+200 Ge.
and t he
The upper set o f dat a
lower set f o r
an i n c r e a s i n g f i e l d .
experimental
error,
is
10 Oe wi de.
l ess than
t he h y s t e r e s i s
Thi s
ve r y s o f t magneti c m a t e r i a l s
not v e r y e f f e c t i v e
are mi xed.
Long r e l a x a t i o n
They most
phenomenon r a t h e r
Wi t h i n
loop in t h i s
indicates that
compound
t hese are
and t h a t domain pi nni n g
even though two kinds of metal
t he ac s u s c e p t i b i l i t y
section.
is f o r d e c r e a s i n g f i e l d
sites
t i mes which were observed in
are di scussed
likely
is
result
in t he next main
from the spin gl ass
than f e r r o m a g n e t i c domain p i n n i n g .
oog88888e88
(emu-Oe)
E -2
O0 OwO
.5
-200
e
OO
OO
O
O
O
-100
100
200
o O
Mag.
OO
-.5
o
o e o o e e e e 8 8 S°
—
I
■
Field
Figure
13.
(Oe)
M a g n e t i z a t i o n v e r s us a p p l i e d f i e l d
c o n t a i n i n g 37% n i c k e l and o r i e n t e d
axis.
f o r a s i n g l e c r y s t a l o f CoNiTAC
a l ong t h e a or f e r r o m a g n e t i c
i -T-
E -2
(emu-Oe)
Mag.
.5—
8
-200
8
O
OO
O
OO
OO
•100
8
100
OO
O
08
e8°
8
8
oo
8
8o8
200
CO
LO
5 ----
ocooSpeBB
-I
Field
Figure
14.
(Ge)
M a g n e t i z a t i o n v e r s us a p p l i e d f i e l d
c o n t a i n i n g 58% n i c k e l and o r i e n t e d
axis.
f o r a s i n g l e c r y s t a l o f CoNiTAC
a l ong t he a or f e r r o m a g n e t i c
40
The 37% and 58% n i c k e l
examples s i n ce a l l
show n e a r l y
t he m a g n e t i z a t i o n versus a p p l i e d f i e l d
identical
curves o b t a i n e d f o r
per c ent age s o f 38,
samples have been used as
results.
M a g n e t i z a t i o n versus f i e l d
both t he a and c axes f o r
42,
44,
54,
nickel
59 and 64% ar e t h e r e f o r e
not shown e x p l i c i t l y .
Thermoremanent M a g n e t i z a t i o n
Data
Single c r y s ta l
samples of CoNiTAC were al s o examined
f o r thermoremanent m a g n e t i z a t i o n
( TRM) .
A magnetic f i e l d
of 1000 Oe was a p p l i e d above T q and then t he
t e m p e r a t u r e was lowered to 2 . 4 K.
removed,
t he decr ease
(c a x i s )
direction
direction.
direction
the
dropped to zero w i t h i n a ti me equal
response t i me, of the magnetometer i n d i c a t i n g
this
was then
in t h e m a g n e t i z a t i o n was moni t or ed.
Along t he a n t ! f e r r o m a g n e t i c
magnetization
When t h e f i e l d
Along t he f e r r o m a g n e t i c
to the
no TRM in
(a a x i s )
a much l onger t i me was necessary f o r the
magnetization to s t a b l i z e ,
as expect ed f o r t h e TRM e f f e c t
found in spin g l a s s e s .
Thermoremanent m a g n e t i z a t i o n was
therefore
in t he f e r r o m a g n e t i c d i r e c t i o n .
o n l y observed
Because of. t he weak s i g n a l s o b t a i n e d from t he small
crystals,
However,
small,
single
no good q u a n t i t a t i v e measurements could be made.
because the b a x i s m a g n e t i z a t i o n
and t he c a x i s m a g n e t i z a t i o n
i s always very
as shown in Fi gur es
11
41
and 12 i s near zero a t
low f i e l d s ,
TRM measurements on
powder samples are in e f f e c t measurements of t he a axi s
magneti z a t i o n .
The TRM versus ti me was t h e r e f o r e examined f o r
CoNiTAC powder samples f o r which
a l l owed q u a n t i t a t i v e
l a r g e r sample s i z e s
r e s u l t s t o be o b t a i n e d .
t i me was examined in d e t a i l
for
34%,
TRM versus
58% and 72% n i c k e l
and f o r t e mp e r a t u r e s between 2 . 4 and 3 . 2 K in or der t o
de t e r mi ne t h e f u n c t i o n a l
magnetization.
A field
form o f the decay of t he
of 50 Oe was a p p l i e d above Tc ,
t e m p e r a t u r e was lowered at a r a t e
of about 0 . 0 5 K / s e c , t he
system was al l o we d t o s t a b i l i z e
at the d e s i r e d t e mp e r a t u r e
for
was swi t ched t o 0 ± 0 . 0 5
Oe.
about 30 sec,
TRM versus t i me f o r the v a r i o u s t e mp e r a t u r e s
in F i g u r e s
15,
respectively.
w ill
and the f i e l d
16,
The s o l i d
be co ns i de r e d
a mechani cal
and 17 f o r
lines
58% and 72% n i c k e l ,
are f i t s
t o t he data and
in the d i s c u s s i o n s e c t i o n .
d e l a y of 5 sec in
and a I sec t i me c o n s t a n t
t i mes s h o r t e r t han
34%,
is shown
Because of
l ower i ng t h e f i e l d
in t h e magnetometer,
to zero
data f o r
10 sec coul d not be t aken wi t h .
confidence.
AC S u s c e p t i b i l i t y of CoNiTAC.
Since a cusp in AC s u s c e p t i b i l i t y
criteria
for
labelling
a material
s u s c e p t i b i l i t y measurements
is one of t he major
as a spin g l a s s ,
in zero f i e l d
AC
on s e v e r a l
of
900
E 600
Cn 300
20
180
Time (Sec)
Figure
15.
Ther mor emanent m a g n e t i z a t i o n ver sus t i me ( 5 0 Oe i n i t i a l f i e l d ) f o r
t h e 34% sampl e a t 2 . 4 , 2 . 6 , 2 . 8 , 3 . 0 and 3 . 2 K .
The s o l i d l i n e s
a r e f i t t o a s t r e t c h e d e x p o n e n t i a l wi t h a c o n s t a n t o f f s e t .
Mag.
(emu O e / m o l )
800
Figure
16.
Ther mor emanent m a g n e t i z a t i o n ver sus t i me ( 50 Oe i n i t i a l f i e l d ) f o r
t h e 58% sampl e.
The l i n e s f r om t op t o bot t om were t aken at 2 . 4 ,
2 . 6 , 2 . 8 , 3 . 0 and 3 . 2 K .
The s o l i d l i n e a r e f i t t o a s t r e t c h e d
ex p o n e n t i a l wi t h a const ant o f f s e t .
(emu G e / m o l )
Mag.
Figure
17.
Ther mor emanent m a g n e t i z a t i o n v er sus t i me ( 5 0 Oe i n i t i a l f i e l d ) f o r
t h e 72% sa mpl e .
The l i n e s f r om t op t o bot t om were t aken a t 2 . 4 ,
2 . 6 and 2 . 8 K .
The s o l i d l i n e s a r e f i t t o a s t r e t c h e d e x p o n e n t i a l
wi t h a const ant o f f s e t .
45
t he CoNiTAC mixed c r y s t a l s
Differential
have been c a r r i e d
out.
s u s c e p t i b i l i t y measurements were performed by
using a m u t u a l - i n d u c t a n c e b r i d g e which in t u r n u t i l i z e s
SQUID ( s u p e r c o n d u c t i n g quantum i n t e r f e r e n c e
null
detector.
device)
The a mp l i t u d e o f the e x c i t a t i o n
a
as a
field
was
a p p r o x i m a t e l y 0 . 0 0 7 5 Oe, and t he f r e q u e n c y of e x c i t a t i o n
was e i t h e r
liquid
80 or
160 Hz.
hel i um dewar
external
fields.
A magneti c s h i e l d
in or d e r to e l i m i n a t e t h e e f f e c t s
A superconducting,
s h i e l d t he
sur r oundi ng t he sample.
Single c r y s t a l s
wei ghi ng a p p r o x i m a t e l y 0 . 3 mg were mounted wi t h t h e i r
and t hen t h e i r
c axis p a r a l l e l
measurement c o i l s .
at
6 K (in
of
lead s h i e l d was
pl aced in t he hel i um dewar to f u r t h e r
measurement c o i l s
surrounded the
t o t he e x c i t a t i o n
a
and
The t e mp e r a t u r e of t he sample was hel d
the par amagnet i c p h a s e ) .
A f t e r t he system had
stab I i z e d , t he t e m p e r a t u r e was s l o w l y lowered through the
transition
t e mp e r a t u r e w h i l e t e mp e r a t u r e and
. s u s c e p t i b i l i t y were r ecor ded on an x - y p l o t t e r .
Figure
18 shows t he r e s u l t s
f o r a CoNiTAC c r y s t a l
wi t h 49% Ni
at an e x c i t a t i o n
f r e q u e n c y of 80 Hz..
dashed l i n e
is the c a x i s s u s c e p t i b i l i t y .
the easy or a n t i f e r r o m a g n e t i c
lowered t h e r e
is a r i s e
in the
a decr ease as T , the c r i t i c a l
i s r e a c he d .
Thi s
indicates
axis,
The
Since t h i s
as t e m p e r a t u r e
is
is
s u s c e p t i b i l i t y f o l l o w e d by
temperature f o r
normal
ordering,
t h r e e di mensi onal
3.0
4.0
5.0
6.0
T (K)
Figure
18.
S u s c e p t i b i l i t y versus t e mp e r a t u r e f o r a 49% Ni sample of CoNiTAC.
S o l i d l i n e is the r e a l p a r t of the s u s c e p t i b i l i t y along the a
axis.
Dashed l i n e is the r e a l p a r t of the s u s c e p t i b i l i t y along
c axis.
Dot ted l i n e is t he i magi nar y p a r t of t he s u s c e p t i b i l i t y
along the a a x i s .
47
o r d e r i n g and t he DC m a g n e t i z a t i o n data of Fi gur es
through
10 f o l l o w t h i s
shape q u i t e c l o s e l y .
7
The
q u a d r a t u r e or o u t - o f - p h a s e component of t h e s u s c e p t i b i l i t y
along t h i s
a x i s was e s s e n t i a l l y
p e r c e n t o f the
i n - p h a s e component).
are c o n s i s t e n t wi t h
axis
zero ( l e s s than one
These measurements
no TRM having been seen along t h i s
in t he m a g n e t i z a t i o n measurements.
The zero f i e l d ,
illustrated
different
a axis
in F i g u r e
behavior.
susceptibility
susceptibility,
18 wi t h a s o l i d
As t e mp e r a t u r e
line,
is
to
10)
is
in itially
No t i c e t h a t t he
spans a ver y narrow t e mp e r a t u r e r a n g e ,
the peak in the s u s c e p t i b i l i t y
M a g n e t i z a t i o n measurements
on the o t h e r
hand show a sharp r i s e
lowered but then g r a d u a l l y
large magnetization at
a signal
shows a q u i t e
i n c r e a s e s r a p i d l y and then s h a r p l y
temperature axis
q u i t e nar r ow.
is
lowered t he
decr eases as t he g l a s s y phase is e n t e r e d .
and t h e r e f o r e
which
low t e m p e r a t u r e s .
is
indeed
(see Fi gur es 7
as t e mp e r a t u r e
level
o f f to a
That p l a t e a u
is
about t w i c e the s i z e of the ac s u s c e p t i b i l i t y
peak as de t er mi ned by comparison wi t h the c a x i s s i g n a l s .
In the AC ex p e r i me n t the spi ns are f r o z e n and cannot
respond t o a r a p i d l y o s c i l l a t i n g
susceptibility
region
field,
thus t h e measured
d i mi n i s h e s a b r u p t l y when t he spin gl ass
is entered.
Thi s i s r e f l e c t e d
in m a g n e t i z a t i o n when measuring TRM.
in t he slow change
The sharp peak in
48
t he s u s c e p t i b i l i t y
is in c o n t r a s t to pure CoTAC f o r which
the AC s u s c e p t i b i l i t y
a large
i n cr e as es
but then c o nt i nue s to have
s u s c e p t i b i l i t y , in t he r e g i o n of 3 t o 4 K . 1
The dashed l i n e
in F i g u r e
18 shows t h e o u t - o f - p h a s e
component of t he AC s u s c e p t i b i l i t y .
l ower ed,
its
val ue
As the. t e mp e r a t u r e
i nc r e a s e s r a p i d l y as t he
i n- phase
component d e c r e a s e s , i n d i c a t i n g
that a relaxation
i s r e s p o n s i b l e f o r the decrease
in the
su s c e p tib ility rather
process
i n- phase
than a spin r e o r i e n t a t i o n .
In o t h e r
words as t he spins begin t o f r e e z e , t he o r i e n t a t i o n
magnet i c moments lag behind t he 80 Hz e x c i t a t i o n
d e c r e a s i n g the
i n- phase s i g n a l
out-of-phase s ig na l.
increases,
small
all
both
is
of the
field
and i n c r e a s i n g the
As t he f r e e z i n g
of t he spins
i n - ph a s e and q u a d r a t u r e s i g n a l s become
si nce the spi ns are now too s l u g g i s h t o respond at
t o the .80 Hz o s c i l l a t i o n .
Figure
19 shows t he a a x i s
a t both 80 Hz and 160 Hz.
t e mp e r a t u r e t h e r e
Above the t r a n s i t i o n
is no f r e q u e n c y dependence.
below t he t r a n s i t i o n
decreases f a s t e r
s u s c e p t i b i l i t y of 60% Ni
t e mp e r a t u r e t he hi ghe r f r e q ue n c y
si n c e t he slow t i me cons t a nt
gl ass has more e f f e c t
in t h i s
case..
in t he t r a n s i t i o n
frequency, c h a r a c t e r i s t i c
f o r the spin
Whi l e a f r e q ue n c y
dependence c o n s i s t e n t wi t h a spin gl ass
shift
However,
is demonst r at ed,
t e mp e r a t u r e as a f u n c t i o n
o f a spin gl ass
of
is not se e n.
a
T (K)
Figure
19.
Real p a r t of t he s u s c e p t i b i l i t y versus t e mp e r a t u r e f o r a 60% Ni
sample of CoNiTAC along t he a a x i s .
S o l i d l i n e is f o r a f r equency
of 160 Hz and dashed l i n e is f o r 80 Hz.
50
Since t he SQUID probe is tuned over a smal l
frequencies,
definite
and s h i f t s
onl y f o r
magni t ude,
t he
in t he t r a n s i t i o n
range of
t e mp e r a t u r e are
f r e q u e n c i e s measured over many or ders of
l ack o f a t r a n s i t i o n
t e mp e r a t u r e s h i f t
is
not s u r p r i s i n g .
In c o n c l u s i o n ,
the AC s u s c e p t i b i l i t y of t he CoNiTAC
system is c o n s i s t e n t wi t h t h a t
The spi n gl a s s b e h a v i o r
ferromagnetic axis
single crystal
expected of a . s p i n g l a s s .
is al so co n f i n e d t o the
supporting the r e s u l t s
o b t a i n e d from
DC measurements.
EPR Measurements on CoNiTAC
Electron
par amagnet i c resonance
(EPR)
spect r oscopy
can complement bulk m a g n e t i z a t i o n measurements by y i e l d i n g
information
Particularly
on t he envi r onment of i n d i v i d u a l
spins.
magneti c a n i s o t r o p y but al so t r a n s i t i o n
t e mp e r a t u r e s and exchange f i e l d s
can be o b t a i n e d from EPR.
U n f o r t u n a t e l y , wi t h t he c o b a l t
and n i c k e l
proximity spin-spin re la x a tio n
broadens the resonance
lines
considerably for
impossible.
sites
CoNiTAC making d e t a i l e d
The h a l f wi dt h of t he
line
in cl ose
analysis
i s about 500 Oe at
300 K, but no i n f o r m a t i o n about t h e spin a n i s o t r o p y could
be o b t a i n e d between 4 and 300 K.
MnCoTAC and MnNiTAC M a g n e t i z a t i o n Measurements
■
for
Magnetization
versus t e m p e r a t u r e dat a were obt ai ned
v a r i o u s mole f r a c t i o n s
of n i c k e l
or c o b a l t
in MnTAC.
51
As more c o b a l t
transition
or n i c k e l
was added t o MnTAC, the
t e m p e r a t u r e became ve r y low and then e v e n t u a l l y
i nc r e a s e d agai n as pure CoTAC and pure NiTAC composi ti ons
were appr oached.
transition
Because of t he severe
t e mp e r a t u r e
l o we r i n g of the
in t he mixed syst ems, on l y metal
per c ent age s around 100% Mn coul d be i n v e s t i g a t e d below
T^.
Al though spi n gl ass b e ha v i or has been r e p o r t e d f o r
low c o n c e n t r a t i o n s of manganese,
therefore
24
no t i me dependence and
no spi n gl ass b e h a v i o r was seen in t hese
mi x t u r e s due t o t he
Cur i e and Neel
low t e mp e r a t u r e s of the t r a n s i t i o n s .
t e mp e r a t u r e s however can be det er mi ned from
the high t e m p e r a t u r e d a t a .
P l o t s of i n v e r s e
s u s c e p t i b i l i t y versus t e m p e r a t u r e ,
were found t o be l i n e a r except at ver y low t e mp e r a t u r e s
and were o b t a i n e d from 2 K t o 20 K.
examples of t he dat a f o r
20,
30,
Fi gur e
40 and 60 p e r c e n t c o b a l t
in MnCoTAC and F i g u r e 21 shows t he data f o r
60 p e r c e n t n i c k e l
an a p p l i e d f i e l d
field
in MnNiTAC•
of
Al I v a l ue s have u n i t s
30 and
in
of
The decr ease in t he sl ope of the, l i n e s
is due t o t he
equal s z e r o .
20,
Al I data were c o l l e c t e d
F i g u r e s 20 and 21 as manganese c o n c e n t r a t i o n
manganese.
10,
1000 Oe and t hen c o r r e c t e d f o r a p p l i e d
and sample s i z e .
mo I e s / e mu .
20 shows
larger,
S = 5/2,
is
i ncr eased
spin quantum number f o r
The l i n e a r r e g i o n was e x t r a p o l a t e d t o
The i n t e r c e p t
in
1/X
of t h e t e mp e r a t u r e a x i s
is t he
( m o l / emu
T
F i g u r e 20.
(K)
I n v e r s e s u s c e p t i b i l i t y versus t e mp e r a t u r e f o r MnCoTAC powders.
M i x t u r e s c o n t a i n i n g 20, 30, 40 and 60 pe r c ent Co are r e p r e s e n t e d
r e s p e c t i v e l y by c i r c l e s , s q u a r e s , t r i a n g l e s and double t r i a n g l e s .
ft
A
□
□
o
o
-OS
8
6
D
E
Qj
O
E
^
eS
5 "
I
5
20
T
Figure 2 1.
(K)
I n v e r s e s u s c e p t i b i l i t y versus t e mp e r a t u r e f o r MnNiTAC powders.
M i x t u r e s c o n t a i n i n g 10, 20, 30 and 60 per cent Ni are r e p r e s e n t e d
r e s p e c t i v e l y by c i r c l e s , squar es, t r i a n g l e s and double t r i a n g l e s .
54
Cur i e t e mp e r a t u r e f o r
a positive
intercept
n e g a t i v e of t he Neel t e mp e r a t u r e f o r
and the
a negat i ve
intercept.
The Tc versus x phase di agr am formed from t hese val ues
will
be pr e s e n t e d and di scussed in a l a t e r
section.
7,- PA and 5-DA Magnet i c Measurements
The magnet i c p r o p e r t i e s
r e p o r t e d by von Kanel
41
of S-DACuCl^ were f i r s t
, and t he magnet i c p r o p e r t i e s
of n-DACuCl ^ f o r
n = 6 to
to
r e p o r t e d by Rubenacker et a I .
10 were f i r s t
structures
structure
which
10 and n-DACuBr^ f o r n = 5
4?
The
of t hese compounds ar e expect ed t o r esembl e t he
of 2-DACuCl ^ which i s shown in Fi g u r e 22 and
i s t aken from Rubenacker et a I .
increased,
except t h a t
t he u n i t c e l l
larger
42
r emai ns q u a l i t a t i v e l y
interplanar
f e r r o m a g n e t i c a I I y coupl ed s p i n s .
layers
43
pl anes of
The exchange w i t h i n t he
is t hr ough a n e a r l y
h a l i d e br i d g e and because of J a h n - T e l I e r
ferromagnet i c.
similar
s e p a r a t i o n s ar e o b t a i n e d .
Al I t hese compounds f orm two di mensi onal
two di mensi onal
As n is
linear,
si ngl e
splitting,
it
is
Near t he o r d e r i n g t e mp e r a t u r e t he weak
i n t e r p lanar
interaction
di mensi onal
character
t hr ough a t w o - h a l i d e
de t er mi nes t he o v e r a l l
of t he compound.
a n t i f err omagnt i c f or
Thi s exchange i s
super exchange b r i d g e .
c h l o r i d e s e r i e s t he weak,
i n t e r p l a n e c o upl i ng
n = 2 t o 9,
three
For t he
i s al ways
w h i l e f o r t he bromi de
55
• Cu
O Cl
e N
(D
F i g u r e 22.
C
Un i t c e l l of 2-DACuC14 showing t he p o s i t i o n s
of t he i ons ( e x c e pt hy dr ogen) .
Some of t he
CuCl bonds ar e i nc l ude d t o hel p show t he
" p uc k e r i ng" of t he l a y e r s .
56
series
there
coupling.
is a s u r p r i s i n g
alternation
a n t i f e r r o m a g n e t s f o r even n , but f o r
n t he y become t h r e e di mensi onal
alteration
42
The r e s u l t
antiferromagnetic
odd
Thi s
10.
both n-DA s e r i e s ar e gi ven in
is t h a t f or
T- DACuCl 4x Br 4 ^ _x j t h e r e
possible
f e r r o magnets.
i s shown in Fi gur e 23 f o r n = 5 t o
T r a n s i t i o n t e mp e r a t u r e s f o r
I .
interplane
For n g r e a t e r t han 4 t he compounds behave as
t h r e e di mensi onal
Tabl e
of t he
S-DACuCl 4x Br 4 ^
and
i s a competi ng f e r r o ma g n e t i c t o
interaction,
and i t
is t her ef ore
in t hese systems t o have a mixed p h a s e . r e g i o n ,
tetracriticaI
point,
One f u r t h e r
a
and perhaps even spi n gl ass b e h a v i o r .
not e concer ni ng S-DACuBr4 shoul d be made.
The shape of t he s u s c e p t i b i l i t y curve shown in Fi gur e 23
i s q u i t e unusual .
I n s t e a d of t he c o n t i n u a l
ma g n e t i z a t i o n as t e mp e r a t u r e
characteristic
is
l owered t h a t
of a f e r r o m a g n e t , t h e r e
bel ow t he c r i t i c a l
agai n begi ns t o
i n c r e a s e in
would be
is a pl ateau
just
t e mp e r a t u r e be f or e t he ma g n e t i z a t i o n
i n c r e a s e as t e mp e r a t u r e
coul d p o s s i b l y be i n t e r p r e t t e d
is
l ower ed.
Thi s
as a cant ed f e r r o ma g n e t i c
phase i n S-DACuBr4 r a t h e r t han a normal
f e r r o ma g n e t i c
phase.
The powder magnet i c s u s c e p t i b i l i t y
was o b t a i ne d f o r
v a r i o us mole f r a c t i o n s ,
5- DACuCl 4x Br 4 ( 1 _x)
versus t e mp e r a t u r e
x,
and T- DACuCl 4x Br 4 ( ^ x ) .
in
The
s u s c e p t i b l i t y versus t e mp e r a t u r e curves f o r t hese systems
57
IODA ■
5 DA ♦
F i g u r e 23.
Powder magnet i c s u s c e p t i b i l i t y versus
t e mp e r a t u r e dat a f o r n-DACuBr4 wi t h n = 5 - 1 0 .
S o l i d dat a p o i n t s ar e r e f e r e n c e d t o t he l e f t
s c a l e and open dat a po i n t s t o t he r i g h t s c a l e .
58
ar e shown in Fi gur es 24 and 25,
respectively.
From t hese
curves t he par amagnet i c t o a n t i f e r r o ma g n e t i c and
par amagnet i c t o f e r r o ma g n e t i c t r a n s i t i o n s were o b t a i n e d .
Al so f o r
i nt er medi at e
c o mp os i t i on s ,
a second i n c r e a s e
in
s u s c e p t i b i l i t y was observed as t e mp e r a t u r e was l ower ed,
and from t h i s
transitions
Tabl e
I.
n
f e a t u r e t he a n t i f e r r o m a g n e t i c t o mixed phase
were o b t a i n e d .
Low t e mp e r a t u r e phases and c r i t i c a l t e mpe r a t ur e s
f o r n -DACUX4 ( F = f e r r o ma g n e t i c o r d e r i n g and
AF = a n t i f e r r o m a g n e t i c o r d e r i n g ) .
X = Cl
2
3
4
5
6
7
8
9
10
AT
AF
AF
AF
AF
AF
AF.
AF
F
Tc (K)
X = Br
31.5
14. 9
8.9
7.6
9.3
8.3
8,2
6.0
. 7.0
AF
AF
AF
F
AF
F
AF
F
F
C r y s t a l s of t hese compound ar e smal l
however ,
some q u a l i t a t i v e
•
T C l K l
72
42
19
12. 2
13. 0
12. 2
12. 6
10. 0
10. 0
and ver y poor;
i n f o r ma t i o n can be o b t a i n e d .
S u s c e p t i b i l i t y ver sus t e mp e r a t u r e dat a were o b t a i ne d f o r
7-DACuCl^Br^
parallel
wi t h x = 0 . 2 4 and x = 0 . 3 5 both
and p e r p e n d i c u l a r t o t he pl ane o f t he c r y s t a l s .
The x = 0 . 2 4 dat a
i s shown in Fi g u r e 26.
The compound
shows a mi xed phase by behavi ng as an a n t i f e r r o ma g n e t when
Susc.
(e m u /m o l)
59
T (K)
F i g u r e 24.
S u s c e p t i b i l i t y versus t e mp e r a t u r e f o r
5-DACuCl 4x Br 4 ( i _ x ) wi t h x = . 12 ( c i r c l e s ) ,
( squar es ) , . 65 ( t r i a n g l e s ) , . 76 ( doubl e
t r i a n g l e s ) , and . 88 ( + 1s ) .
. 47
60
*
:
:
:
+ X
A
x i n
T
F i g u r e 25.
( K)
S u s c e p t i b i l i t y ver sus t e mp e r a t u r e f o r
7- DACuCl 4x Br 4 ( i _ x ) wi t h x = 0 ( c i r c l e s ) ,
( s q u a r e s ) , . 35 ( t r i a n g l e s ) , . 47 ( doubl e
t r i a n g l e s ) , . 53 ( x ' s ) , and 1. 0 ( + 1s ) .
. 24
61
measured p a r a l l e l
t o s t r o n g l y coupl ed pl anes and as
f e r r o ma g n e t i c when p e r p e n d i c u l a r t o t hose p l a ne s .
t he a c t u a l
directions
Thus
of t he c h l o r i d e ant ! ' f er r omagnet i c
easy a x i s and t he bromi de f e r r o ma g n e t i c easy ax i s are
found t o be,
respectively,
parallel
and p e r p e n d i c u l a r to
t he s t r o n g l y coupl ed pl anes of t he c r y s t a l s .
5usc.
( e m u /m o l)
62
T
F i g u r e 26.
(K)
S u s c e p t i b i l i t y versus t e mp e r a t u r e f o r
a 7-DACuCI 4x Br 4 ( i _ x ) s i n g l e c r y s t a l wi t h
x = . 24 both p a r a l l e l ( t r i a n g l e s ) and
p e r p e n d i c u l a r ( c i r c l e s ) t o t he f e r r o ma g n e t i c
pl anes.
63
DISCUSSION
Phase Di agram of CoNiTAC
At Ji i gh t e mp e r a t u r e s CoNiTAC i s
phase,
and as t e mp e r a t u r e
antiferromagnetic
Tabl e 2 l i s t s
transition
studied.
Towered,
enters
a cant ed
phase and t hen t he spi n gl ass phase.
t he n i c k e l
per cent ages and a n t ! f e r r o m a g n e t i c
Al so l i s t e d
in Tabl e 2 ar e t he h i g h e s t
at whi ch t her moremanent ma g n e t i z a t i o n was
Those t e mpe r a t ur e s f o r each sample were t aken
t o be T , t he a n t i f e r r o m a g n e t i c
transition
it
t e mp e r a t u r e s f o r t he powder CoNiTAC samples
t e mp e r a t u r e s
obser ved.
is
in a par amagnet i c
t e mp e r a t u r e .
t o spi n gl ass
From t he val ues
in Tabl e 2,
t he
t e mp e r a t u r e versus composi t i on phase di agr am shown in
F i gur e
27 was c o n s t r u c t e d .
We have consi der ed t he p o s s i b i l i t y t h a t t he observed
t i me dependent be ha v i or may be due t o random f i e l d s .
Fishman and Aharony
fields
44
showed,
f o r exampl e,
ar e ge ner at ed by uni f or m f i e l d s
ant i f e r r o ma g n e t s .
gl ass t h e o r y
47
that
in d i l u t e
random
I s i ng
The r a n d o m - f i e l d p r o b l e m ^ ’ ^® and spi n
ar e s i m i l a r
in t h a t t he i r r e v e r s a b i I i t y
t i me dependence can be a s s o c i a t e d wi t h
and.
large f ree- energy
b a r r i e r s whose minima can di s a p pe a r as t he t e mp e r a t u r e and
I—
(Ti
-P-
F i g u r e 27.
Phase di agr am of t e mp e r a t u r e versus x (mole f r a c t i o n of n i c k e l )
f o r CoNiTAC showing t he p a r a ma g n e t i c , a n t i f e r r o m a g n e t i c , and spin
gl ass r e g i o n s .
65
field
ar e v a r i e d .
In t he random f i e l d
case t he f r e e
ener gy minima ar e a s s o c i a t e d wi t h domain wa l l
pi nni ng at
impurities.
Tabl e 2.
A n t i f e r r o m a g n e t i c t r a n s i t i o n t e mpe r a t ur e s T
spi n gl ass t r a n s i t i o n t e mp e r a t u r e s T g f o r
v a r i o u s per cent ages of n i c k e l in CoNiTAC.
% Ni
O
21
34
42
50
53
56
58
60
65
68
72
100
a)
b)
c)
d)
Ref er ence
Ref er ence
Cor r e ct e d
Thi s work
and
Ref .
T C
Tg
4. 135
4.14
■ 4. 1 2
4. 14
4. 14
4. 18
4. 1 0
4.02
4.08
4. 18
4.10
4.10
3.6
3.5
3.6
3.6
3. 5 5
3. 75
3.75
3.9
3. 75
3. 55
3.4
34
a
6.
10.
val ues from r e f e r e n c e
C
C
C
d
d
•
C
d
d
d
c.
C
b
26.
•
Whi l e r a n d o m - f i e l d systems ar e g e n e r a l l y d i l u t e
antiferromagnets,
u n d i l u t e d mixed magnet i c systems have
al s o been d e s c r i b e d
in t erms of random f i e l d s .
One
such exampl e i s F e i - x Cox C12 as r e p o r t e d by Wong and
Cable. ^8
In t h a t
sample was f i e l d
system t i me dependence was seen when t he
cool ed but not when z e r o - f i e l d
wi t h a magnet i c f i e l d
s ubs e que nt l y a p p l i e d .
cool ed
Thi s was
66
interpreted
as a domain s t a t e f or mi ng
p r o c e s s , whereas in t he z e r o - f i e l d
in t he f i e l d - c o o l e d
process
long range
o r d e r i n g was o b t a i n e d . I n
CoNiTAC no t i me dependence
was seen upon f i e l d
but r a t h e r t he t i me dependent
be ha v i or r e s u l t e d
cooling,
from magnet i c f i e l d
changes and al so
caused a cusp in t he ac s u s c e p t i b i l i t y versus t e mpe r a t ur e
at zer o f i e l d .
The r e s u l t s
on CoNiTAC ar e t h e r e f o r e
di scussed in t erms of a s p i n - g l a s s
system.
Both CoNiTAC and NiTAC have s i m i l a r magnet i c
properties
at
low t e m p e r a t u r e s .
That
is,
both ar e cant ed
a n t i f e r r o m a g n e t i c s wi t h a net f e r r o ma g n e t i c moment al ong
t he a c r y s t a l l o g r a p h i c
axis.
The i n t e r a c t i o n s which
)
produce t he cant ed t h r e e di mensi onal
however be q u i t e
different
spi n s t r u c t u r e s may
in CoTAC and NiTAC,
and t he
o b s e r v a t i o n of spi n gl ass be ha v i or suggest s t h a t
i mp o r t a n t
an
d i f f e r e n c e must be p r e s e n t .
Ther e ar e two ways i n whi ch f r u s t r a t i o n
may be
i n t r o d u c e d and y e t not change t he observed magnet i c
properties.
The f i r s t
mechanism i s t o d e s c r i b e CoNiTAC as
a mixed cant ed a n t i f e r r omagnet
and cant ed f e r r o m a g n e t .
CoTAC has a ve r y weak ant i f e r r o m a g n e t ic c o u p l i n g between
f e r r o ma g n e t i c a I I y coupl ed pl a n e s ;
cant ed because of
that
We suggest
a ver y weak f e r r o ma g n e t i c c o upl i ng e x i s t s
be t wee n. t he
NiTAC b u t ,
single-ion
t he spi ns are
anisotropy.
pl anes f o r
l arge
however,
as b e f o r e ,
t he
l arge s i n g l e - i o n
67
a n i s o t r o p y f o r c e s t he c a n t i n g o f t he spi ns and r e s u l t s
antiferromagnetic
be ha v i or
in t he c d i r e c t i o n .
c o mp e t i t i o n between t he i n t e r p l a n a r f e r r o antiferromagnetic
"cant i ng"
coul d t hen
obser ved spi n gl ass b e h a v i o r .
in
The
and
l ead t o t he
Such a change in si gn f o r
weak i n t e r p l a n a r c o upl i ng accompani ed by mi nor s t r u c t u r a l
change has been obser ved by us in t he d i ammonium
te t r a c h loro-
and t e t r a b r o mocuprat e syst ems.
suggest i on t h a t t he f e r r o ma g n e t i c c o upl i ng
42
Our
i s weak in
NiTAC i s prompted by t he s i n g l e c r y s t a l
dat a which
indicate
ant!ferromagneti c
a l ower t e mp e r a t u r e f o r
o r d e r i n g above 60% Ni
c-axis
and a l ower t e mp e r a t u r e f o r a - a x i s
f er r omagnet i c or der i ng
bel ow 60% Ni
The second mechanism f o r
i s a compet i ng a n i s o t r o p y .
in t he c r y s t a l s .
introduction
As i l l u s t r a t e d
of f r u s t r a t i o n
in Fi gur e 2
t h e r e ar e two ways i n which t he spi ns can a l i g n
sublattice
and s t i l l
They can e i t h e r
chloride
gi ve a c a n t i n g angl e of 20 degr ees.
align
ligands.
near t he wat er
it
l i g a n d s or near t he
Si nce t h e r e ar e two s u b l a t t i c e s
both spi n o r i e n t a t i o n s
but
in a gi ven
pr esent
ar e seen i n both CoTAC and NiTAC
i s not p o s s i b l e t o de t e r mi ne which o r i e n t a t i o n
wi t h whi ch s u b l a t t i c e
for
goes
CoNi TAC. However , a system
s i m i l a r t o CoNi TAC, t he mixed a n i s o t r o p y system
N i x Cou
x ) c ^2?6H2°
de s c r i b e d by Takeda and Mat sur a
be used as evi dence f o r
a different
49
can
ani sot r opy pref erence
68
between c o b a l t
cobalt
and n i c k e l .
chloride
ar e
The pure n i c k e l
c h l o r i d e and
i somor phi c and t h r e e di mensi onal
a n t i f e r r o m a g n e t s wi t h easy axes in t he a- c
c r y s t a l l ogr aphi c pl ane.
apart,
making t h i s
coordination
chlorides
is
The easy axes ar e 115 degrees
a mixed a n i s o t r o p y syst em.
The metal
sphere c o nt a i ns f o ur wat er mol ecul es and two
in a t r a n s
configuration.
The c o b a l t
easy axi s
in t he pl ane of t he wat er mol ecul es w h i l e t he n i c k e l
easy a x i s
is
in t he met al
al i gnme nt p r e f e r e n c e
i s t hus
chloride direction.
i s assumed f o r
CoNiTAC,
I f t he same
a frustration
introduced.
The u n c e r t a i n t i e s
shown in Fi gur e 27 ar e
a p p r o x i ma t e l y t he s i z e of t he dat a c i r c l e s
e x i s t e n c e of a t e t r a c r i t i c a I
so t h a t t he
or t r i c r i t i c a l
poi nt
shape of t he mul t i c r i t i cal
r e g i o n cannot y e t
usi ng t h i s
The r egi on
phase di agr am.
t he TCP mi ght occur
around 60% Ni
i s not we l l
f rom low t o hi gh n i c k e l
in t he di agr am where
d e f i n e d but appears t o be
i s u n u s u a l l y b r o a d , ext endi ng
concentrations.
caused by t he ps eud o- one - di me n s i o na l
That
is,
We f e e l
a s ma l l e r amount of n i c k e l
frustration
this
is
na t ur e of t he
in an o t h e r wi s e pure sample i s necessar y t o
sufficient
be conf i r med
(x = 0 . 6 ) .
The spi n gl ass r e g i o n
crystals.
and t he
or c o ba l t
i n t r o du c e
al ong t he chai ns t o cause ent r ance
i n t o a spi n gl ass as opposed t o a s t r i c t l y
three
69
di mensi onal
magnet i c system.
Thi s t ype of ver y broad spi n
gl ass r e g i o n was al so obser ved by DeFot i s
Co ( i _ x ) Mnx CI £ • 2 ^ 0
and M a n t u s ^
in
which i s al s o a pseudo- one- di mensi on a I
system al t hough wi t h c o n s i d e r a b l y hi ghe r
interchain
coupling.
Model
and F i t
of t he TRM
TRM measurements have p r e v i o u s l y been f i t
to a l ogar i t hmi c decay^*’ ^
empirically
of t he form
MTRM = Mo [1 " (1 - n ) l n ( t ) ]
in whi ch t
( 4)
i s t he t i me and Mq and n are c o n s t a n t s .
l o g a r i t h m i c dependence
A
is o v i o u s l y not a p p r o p r i a t e at
shor t t i mes and i s t hus an appr oxi mat e form of t he decay
onl y over some f i n i t e
Calculations
t i me
interval.
based on t he S h e r r i n g t o n - K i r k p a t r i c k
m e a n - f i e l d mode 1 0
have p r e d i c t e d an a l g e b r a i c decay of
t he f orm
1TRM
However,
M0Zt
I -n
( 5)
no dat a have been p u bl i s he d s u pp or t i ng t h i s
form
of t he decay.
E mp i r i c a l
fits
t o an exponent a I f u n c t i o n
of t he
f orm
MTRM = M0e x p [ - C ( w t ) 1" n/ ( 1
have been o b t a i n e d .
- n)]
Thi s t ype of e x p o n e n t a I
s t r e t c h e d exponent a I si nce t *
( 6)
is cal l ed a
n i n t he exponent
70
effectively
s t r e t c h e s out t he exponent a I cur ve f o r
val ues of t .
In- t h i s
f orm t he r e l a x a t i o n
and t he exponent a I f a c t o r ,
l ar ge
frequency,
w,
C have been made i ndependent of
t e mp e r a t u r e t hr oughout t he spi n gl ass r e g i o n .
54
Temper at ur e . dependence i s found onl y in Mq and t he
exponent n ,
The p o t e n t i a l
in spi n c o n f i g u r a t i o n
complex f u n c t i o n ^
ener gy s u r f a c e of a spi n gl ass
space can be i magi ned as a very
or as a f r a c t a l
t h e r e ar e many l o c a l
minima and maxi ma.
of a group of spi ns t r a v e l s
in which
The c o n f i g u r a t i o n ,
t hr ough t h i s
r eaches a ground s t a t e minimum.
Procaccia^
surface^
space u n t i l
it
Gr assber ger and
found t he number of ground s t a t e c o n f i g u r a t i o n s
t o be
Nc = f ( t ) e x p [ - g ( n ) ' ( w t ) ^- n Z U
- n) ]
'
(7)
which in t u r n was r e l a t e d t o t he remanent m a g n e t i z a t i o n ,
Mt r m .
If
it
i s assumed t h a t t he f u n c t i o n s f ( t ) and g ( n )
ar e c o n s t a n t s ,
e q ua t i on
f orm and p r o v i d e a l i n k
( 6 ) and e qua t i on
in e qua t i on
( 6 ) yields
mTRM = Mc , e x p [ - ( t / t p ) ! - " ] .
Thi s f orm can be p a r t i c u l a r l y
relaxation
aI .
have t he same
between t h e o r y and e x p e r i me n t .
Combi ni ng t he const ant s
.
(7)
rate,
(8)
instructive
i n t h a t t he
1/t
has been shown by Hooger beet s et
P
t o var y e x p o n e n t a I I y wi t h i n v e r s e t e mp e r a t u r e .
Thi s
t e mp e r a t u r e dependence has al so been c a l c u l a t e d by De
7.1
Domi ni c i s ,
et a I .
59
f o r t i me e v o l u t i o n of spi n gl ass s t a t e
occupanci es usi ng m e a n - f i e l d a p p r o x i m a t i o n s .
The s t r e t c h e d exponent al
quite
sufficient
However,
f orm of e q ua t i on
( 8 ) was not
f o r t he dat a from t he CoNiTAC system.
by addi ng a const ant M1 t o e qua t i on
M1 would r e p r e s e n t s t he z e r o - f i e l d
( 8 ) in which
ma g n e t i z a t i o n expect ed
in a f e r r o m a g n e t i c system such as CoNiTAC al ong
axis,
t he CoNiTAC dat a coul d be f i t
e n t i r e t i me
fit.
interval
quite w e l l .
a
The
from 10 seconds t o 300 seconds was
The magnet omet er t i me c o ns t a nt
s h o r t e r t han
its
10 seconds t o be f i t ,
i s t oo l ong f o r t i mes
and ma g n e t i z a t i o n
changes become compar abl e t o t he magnetometer noi se f o r
t i mes
l onger t han 300 seconds;
c o ns t a nt e q ua t i on
Wi th t h i s
additional
( 8 ) becomes
Mtrm = Moe x p [ - ( t / t p ) 1- n] + M1.
( 9)
Mq was chosen so t h a t Mtrm at t equal s zer o was t he
initial
ma g n e t i z a t i o n be f or e t he f i e l d
i s swi t ched o f f .
Even though t her moremanent ma g n e t i z a t i o n was seen
al ong onl y one c r y s t a l l o g r a p h i c a x i s ,
p o s s i b l e t o t a k e advant age of t he
a l a r g e powder sample over a smal l
measurement s,
was s t i l l
i mproved s e n s i t i v i t y of
single c r y s t a l
use powder sampl es t o det er mi ne TRM.
50 Oe f o r t he f i e l d
it
and t o
By usi ng a f i e l d o f
cool ed s t a r t i n g p o i n t o f t he TRM
t he b and c a x i s c o n t r i b u t i o n s t o t he
ma g n e t i z a t i o n can be e s t i ma t e d and then i g nor e d .
At a l l
72
t i mes t he ma g n e t i z a t i o n al ong t he b ax i s was ve r y smal l
and bel ow t he r e s o l u t i o n of t he magnet omet er .
ma g n e t i z a t i o n was zer o at a l l
seen from Fi gur es
7 t hr ough
fields
10.
The c axi s
below 50 Oe as can be
The powder ma g n e t i z a t i o n
was t hus a measure of t he a a x i s TRM when f i e l d
c o ol i n g
in
50 Oe.
Si nce t he va l ue of Mq was f i x e d by t he zer o t i me val ue
of t he m a g n e t i z a t i o n ,
t hen be f i t
tp,
t h r e e par amet er s t ^ , n and M1 must
t o t he e x p e r i me n t a l
data.
The t h r e e par amet er s
n and M1 were t hen det er mi ned such t h a t
squar e d e v i a t i o n
between t he model
dat a was mi ni mi z e d .
listed
Al so,
and. t he e x pe r i me n t a l
The val ues of t hese par amet er s are
in Tabl e 3 f o r n i c k e l
72 p e r c e nt
t he mean
concent r at i on' s o f 34,
58 and
and t e mp e r a t u r e s of 2 . 4 K to 3 . 2 K.
f rom Tabl e 3 i t
is cl e a r t h a t
there
t e mp e r a t u r e dependence t o t he r e l a x a t i o n t i m e .
is a
Th e r e f o r e
in an at t e mpt t o c l a s s i f y t he spi n gl ass r e g i o n as a
f u n c t i o n of x , we have made a rough f i t
relaxation
Ag: Mn.
proposed by Hooger b e e t s , Lou and Orbach
58
for
T h e i r model .is c o n s i s t e n t wi t h an e x p o n e n t i a l
distribution
of
i ndependent ,
random f r e e - e n e r g y
that
ar e assumed t o e x i s t
this
case t he e x p r e s s i on f o r r e l a x a t i o n
1/t
A plot
t o t h e model of
of
= A
i n t he spi n gl ass phase.
e x p [ - c ( T g/ T ) ] .
In(IZtp)
levels
In
is w r i t t e n
( 10)
versus TgZT from Tabl es 2 and 3 does
73
not show a s t r a i g h t
line
so t h a t
over our r ange of t e mp e r a t u r e ,
definite
t endency f o r
faster
A and c ar e not const ant
nevertheless
relaxation
there
is a
as t e mper at ur e
i ncr e as es
Tabl e 3.
%
Best f i t s of t he par amet er s t D, n and M1 to
Equat i on ( 9) f o r TRM measurements at t he gi ven
t e mp e r a t u r e s and n i c k e l c o n c e n t r a t i on s .
T( K)
Ni
34
34
34
34
34
58
58
58
58
58
.
72
72
72
tP
n
M'
2.4
2.6
2.8
3.0
3.2
38.8
12. 7
4.43
2.80
1. 91
0.644
0.610
0.657
0.607
0. 5 89
265
214
161
135
105
2.4
2.6
2.8
3.0
3.2
13. 2
5. 57
2. 42
2.94
2.60
0.524
0. 6 39
0.670
0. 5 63
0. 4 45
324
262
221
189
149
2.4
2.6
2.8
22.5
5. 3 2
2. 51
0. 4 2 7
0.514
0.493
127
69
41
Our ver y rough val ues from t hese p l o t s y i e l d
for
a val ue
c = 9 over t he e n t i r e r ange of x and val ues of
A = 2 x 10
4
- 1
sec"
near t he e d ge s ( x = 0 . 2 6 and 0 . 7 2 )
I x I O5 s e c " * f o r x = 0 . 5 8 .
relaxation
f o r Ag:Mn.
and
These numbers i n d i c a t e a f a s t
pr ocess compared t o e =
2 . 5 and a = 10
-
3
sec
-1
We f i n d t h a t t h e t e mp e r a t u r e dependence of M1
f o l l o w s t he be ha v i or of I ;
t e mp e r a t u r e s ,
that
is,
it
is
al most d i s a p p e a r i n g near T .
largest
at
low
Further, for
74
a gi ven t e mp e r a t u r e
in t he SG r e g i o n ,
t endency f o r t he o v e r a l l
near t he
relaxation
our numbers show a
processes t o be f a s t e r
"edges" of t he SG r e gi o n where t he systems behave
more l i k e
t he unmixed compounds and sl ower
where t he mi x t u r e
in t he c e n t e r
i s more compl et e.
Spin Gl ass D i m e n s i o n a l i t y
The ps e udo- one - di me ns i ona l
compound r e f e r s
intrachain
t o t he f a c t
that
char act er i zation
there
exchange wi t h much s ma l l e r
i s a st r ong
interchain
t he weaker exchange a l l o w i n g t he system t o o r de r
di mensi ons.
It
is
of t h i s
exchange,
in t h r e e
i n t e r e s t i n g t o ask whet her a p a r t i c u l a r
d i m e n s i o n a l i t y can be a s s o c i a t e d wi t h t he spi n gl ass
be ha v i or
find that
in t h i s
compound.
Gr assber ger and Pr o c a c c ia
a d i m e n s i o n a l i t y of t he d i f f u s i v e
r e l a t e d t o n of e q ua t i on
(9)
57
space is
by
n = I - d/(d + 2).
( 11)
Si nce our val ues of n var y f rom 0 . 4 t o 0 . 6 7 ,
t he
c or r es pondi ng d i m e n s i o n a l i t y d v a r i e s from 3 t o
respectively.
seems t o d e r i v e
di mensi onal
CoNiTAC,
its
as we have a l r e a d y c o n s i d e r e d ,
frustration
ordering.
MnCoTAC
expect ed t o d e r i v e a f r u s t r a t i o n
from t he weak t h r e e
and MnNiTAC shoul d be
from t h e i r
f e r r o m a g n e t i c - a n t i f e r r o m a g n e t i c compet i t i on.
gl ass be h a v i o r
I,
i s obser ved in t hese systems
ID
That no spi n
is consi stent
75
wi t h
a critical
d i m e n s i o n a l i t y g r e a t e r t han one f o r t he
devel opment of spi n gl ass b e h a v i o r .
Phase Di agrams of MnCoTAC and MnNiTAC
Cur i e and Neel t e mp e r a t u r e s obt ai ned f o r MnCoTAC and
MnNiTAC from i n v e r s e s u s c e p t i b i l i t y
Tabl e 4.
The upper p o r t i o n s
pl ots
ar e compi l ed in
of t he phase di agrams f o r t he
mixed MnCoTAC and MnNiTAC ar e shown in Fi gur e s 28 and 29.
As t e mp e r a t u r e was l ower ed,
t he systems go f rom t he
par amagnet i c r e gi o n to. a one di mensi onal
r e g i o n oh t he
On t he r i g h t
left
di mensi onal
or hi gh manganese si des of t he gr aphs.
side,
one di mensi onal
a n t i f e r r o ma g n e t i c
t he t r a n s i t i o n
i s from par amagnet i c t o
f e r r o ma g n e t i c wi t h o v e r a l l
antiferromagnetic
behavi or.
three
No mixed phase or
spi n gl ass phase was seen because of t he
low val ues of t he
t r a n s i t i o n t e mp e r a t u r e s .
t e mpe r a t ur e s of
The t r a n s i t i o n
Tabl e 4 were e x t r a p o l a t e d from t he h i g h e r t e mp e r a t u r e
data.
These r e s u l t s
ar e not s u r p r i s i n g
an a n i s o t r o p y al ong t h e chai ns t h a t
that
i n CoTAC and Ni TAC.
a n t i ferromagnet.
Al so,
si nce pure MnTAC has
is perpendi cul ar to
MnTAC i s a one di mensi onal
Note t h a t t he magnet i c d i f f e r e n c e s
al ong t he chai n so t h a t
c o mp e t i t i o n here w i l l
di mensi onal
effects
r a t h e r t han t he o v e r a l l
di mensi onal
effects
in t he CoNiTAC system.
are
reflect
weak t h r e e
one
6
Ot
X
F i g u r e 28.
Phase d i a g r a m o f t e m p e r a t u r e
f o r MnCoTAC.
v e r s us x (mol e f r a c t i o n
of c o b a l t )
■^J
F i gur e 29.
Phase di a g r a m o f t e m p e r a t u r e
f o r MnNiTAC.
ver s us
x ( mol e f r a c t i o n
of n i c k e l )
78
Tabl e 4.
Cur i e and, Neel t e mp e r a t u r e s f o r MnCoTAC and
MnNi TAC mi x t ur e s al ong wi t h t h e i r cor r espondi ng
met al pe r c e nt a ge s .
% Mn
100
95
80
70
60
50
40
90
80
70
40
a)
b)
c)
d)
% Co
% Ni
Tc ( K ) 8
■ 10
20
30
60
' 100
-4.Ib
-4.1
-3.5
-0.7
+ 0. 3
+ 0. 9
+ 2. 5
+4.135C
-4.2
-4.2
+ 0. 2
+!.Sd
+3.6°
5
20
30
40
50
60
100
Tr is used here f o r e i t h e r Cur i e ( p o s i t i v e
or Neel t e mper at ur e s ( n e g a t i ve v a l u e s ) .
From r e f . 14.
From r e f . I .
From r e f . 9.
As p r e v i o u s l y not ed Mat subar a et a I .
aI . ^
22
v a l ue s )
and Phaf f et
di d spi n r esonance work on MnCoTAC and i n f e r r e d
a l ower Mn-Co c o up l i ng t han t he Mn-Mn or Co-Co c o up l i ng s .
That t he SMn"S^0 t er m in t he H a mi l t o n i a n has a low
exchange c ons t a nt
i s expect ed from t he compet i ng
anisotropy.
Phase Di agrams f o r t he 7-DA and 5-DA Compounds
From t he powder magnet i c s u s c e p t i b i l i t y dat a t he
phase t r a n s i t i o n s
from par amagnet i c t o a n t i f e r r o m a g n e t i c .
79
from par amagnet i c t o f e r r o ma g n e t i c and from
antiferromagnetic
5-DACuCI ^x Br 4
ar e r e p o r t e d
t o mixed phase we r e . o b t a i n e d f o r
_x j and 7-DACuCI ^ B r 4 ^^_x ^.
in Tabl es
These val ues
5 and 6 r e s p e c t i v e l y .
Whi l e t he
a n t i f e r r o m a g n e t i c t o mixed phase t r a n s i t i o n s were r e a d i l y
identified,
t he f e r r o ma g n e t i c t o mixed phase t r a n s i t i o n s
coul d not be seen in t he powder samples due t o t he l a r ge
f e r r o ma g n e t i c moments.
The t e mp e r a t u r e ver sus composi t i on
phase di agrams c o n s t r u c t e d f rom t hese val ues ar e shown in
Fi gur e s 30 and 31 r e s p e c t i v e l y .
Tabl e 5.
T r a n s i t i o n t e mp e r a t u r e s f o r
in 5- DACuCl 4x Br 4 ( 1 _x) .
hZ
a)
Ta (K)
fb
0.00
0. 1 2
0.24
0. 3 5
0. 4 7
0.53
0. 6 5
0.76
0.88
1. 00
Tp(K)
val ues of x
I-
X
va r i o us
12. 2
12. 2
11. 4
10. 8
10. 6
10. 5
8.7
' 8.4
8.0
7. 6
8.8
8.3
6. 5
In t h i s t a b l e Tp, Ta and T m r e f e r t o par amagnet i c t o
f e r r o ma g n e t i c , par amangnet i c t o a n t i f e r r o m a g n e t i c and
a n t i f e r r o m a g n e t i c t o mixed phase t r a n s i t i o n
temperatures, r e s p e c t i v e l y .
F i g u r e 30.
Phase di agr am of t e mp e r a t u r e versus x f o r
5- DACuCl ^xB r ^ ^ _ x
15
X
Figure
31.
Phase d i a g r a m o f t e m p e r a t u r e
v er sus x f o r
7-DACuCl^^Br^^^
82
Tabl e 6 .
a)
T r a n s i t i o n t e mp e r a t u r e s f o r
in 7- DACuCl 4x Br 4 ( 1 _x ) .
X
T f (K)
0.00
0. 1 2
0.24
0. 35
0.47
0. 5 3
0.65
0. 7 6
0.88
1. 00
12. 2
11. 0
10. 4
v a r i o us val ues of x
T m (K)
Tfl(K)
9.0
6.2
9.6
9.6
9.4
8.9
8.6
8.4
8.3
In t h i s t a b l e Tp9 T/\ and Tjv] r e f e r t o par amagnet i c t o
f e r r o m a g n e t i c , par amangnet i c t o a n t i f e r r o m a g n e t i c and
a n t i f e r r o m a g n e t i c t o mixed phase t r a n s i t i o n
t e mp e r a t u r e s , r e s p e c t i v e l y .
Both of t hese systems show f o u r phases:
ferromagnet ic,
a n t i f e r r o ma g n e t i c and mixed phases.
upper phase l i n e s
decr eases as c h l o r i d e
o r d e r i n g t e mp e r a t u r e which
i ons ar e s u b s t i t u t e d
i ons i n t he f e r r o ma g n e t i c p l a n e s .
two di mensi onal
illustrated
which
for
bromide
Because of t he pseudo-
na t u r e of t hese compounds,
l i n e of phase t r a n s i t i o n s
tetracriticaI
The
have a n e g a t i v e sl ope and ar e a measure
of t he two di mensi onal
t he
pa r a ma gne t i c ,
t he minimum in
i s p r e d i c t e d at t he
p o i n t f o r a t h r e e di mensi onal
system and
in Fi g u r e 4 was not s e e n.
For T- DACuCl 4x Br 4 ^
x ) at
low t e m p e r a t u r e s , t he
system i s f e r r o ma g n e t i c wi t h t he easy ax i s p e r p e n d i c u l a r
83
t o t he two d i m e n s i o n a l , f e r r o ma g n e t i c pl anes f o r x = 0 .
At t he f e r r o ma g n e t i c - mi x e d phase boundar y, t he spi ns begi n
t o cant away from p e r p e n d i c u l a r
antiferromagnet i c-mi xed
parallel
until
at t he
phase boundary t he spi ns are
t o t he pl ane and a n t i f e r r o m a g n e t i c a l l y a l i g n e d .
Al most t he same c o n d i t i o n s a ppl y t o S-DACuCl 4x Br 4 ( ^ x )
except t h a t
increases,
i ncrease
f o r x = 0,
t he p o i n t
indicates
t he spi ns ar e a l r e a d y cant ed.
at which t he ca nt i n g angl e s t a r t s t o
e nt r a nc e
i n t o t he mixed phase.
From t he phase di agrams t he p o s i t i o n
tetracriticaI
poi nt s
can be e s t i ma t e d .
t he y woul d occur at x = 0 . 4 3 and I
at x = 0 . 3 2 and I
for
= 9.8 K for
7-DA may be caused by t he
larger
As x
o f t he p o s s i b l e
If
they e x i s t ,
= 10. 2 K f o r
7- DA;
S-DA and
The l ower val ue of x
l a r g e r amine and t h e r e f o r e
s e p a r a t i o n between t he pl anes which may a l l o w t he
weak i n t e r p l a n a r exchange t o change more r e a d i l y .
The q u e s t i on of why spi n gl ass be ha v i or was not seen
in t he S-DA and 7-DA systems where t he f r u s t r a t i o n
i n t he t h r e e di mensi onal
In t he s e syst ems,
has o v e r a l l
o r d e r i n g needs t o be addr essed.
t he f e r r oma gne t i s m a s s o c i a t e d wi t h hi gh
bromi de c o n c e n t r a t i o n s
bromi de i t s e l f
occurs
i s not a p r o p e r t y
si nce f o r
n = 2,
t h r e e di mensi onal
I n s t e a d t he t h r e e di mensi onal
3,
4,
intrinsic
t o t he
6 and 8 H-DACuBr4
ant!ferromagnetic or deri ng.
f e r r o ma g n e t i c
orderi ng f or
S-DACuBr4 and 7- DACuBr4 must be due t o a change,
84
p r ob a b l y s t r u c t u r a l ,
weak i n t e r p l a n e
illustrated
for
in t he superexchange pat h f o r the
coupling.
The " pucker i ng"
of t he pl anes
in Fi gur e 22 may t hen be s l i g h t l y
5-DA and 7- DACuBr^.
In t r a v e l i n g
different
acr oss t he phase
di agr am from pure c h l o r i d e t o pure bromi de t h i s
change in
t he super exchange pat h i s s l o wl y i nt r oduced at a l l
and t hus t he f r u s t r a t i o n
necessar y f o r
a spi n gl ass
Mi xed Systems:
A Comparison
sites
i s not
developed.
Low Di mensi onal
In CoNiTAC,
S- DACuCl 4x Br 4 ^
t he compet i ng i n t e r a c t i o n s
interactions.
transition
x J and T- DACuCl 4x Br 4 ^ _x j
ar e t he weak t h r e e di mensi onal
The par amagnet i c t o or der ed s t a t e
t e mp e r a t u r e s remai n r e l a t i v e l y c o n s t a n t .
t he one or two d i me n s i o n a l ,
det er mi nes t he t r a n s i t i o n
It
is
f e r r o ma g n e t i c o r d e r i n g t h a t
t e m p e r a t u r e , and t h a t
val ue
changes on l y s l i g h t l y wi t h a change in composi t i on f o r
t hese syst ems.
Thi s
i s i n c o n t r a s t t o t he MnCoTAC and
MnNiTAC systems
i n whi ch t he compet i ng i n t e r a c t i o n
st r ong one di mensi onal
interaction.
i n s t e a d of a r e l a t i v e l y f l a t
line
in t he phase di agr ams,
In t hose cases
par amagnet i c t o or der ed s t a t e
there
i s deep depr ess i on
t he c e n t e r of t he di agrams due t o a f r u s t r a t i o n
mai n,
or one d i me n s i o n a l ,
As di scussed e a r l i e r ,
be h a v i o r
i s t he
in
i n t he
order.
t he absence of spi n gl ass
in MnCoTAC and MnNiTAC i s c o n s i s t e n t wi t h a
85
critical.dimensionality
g r e a t e r t han one si nce the
frustration
in t he one di mensi onal
here occurs
For t he 5-DA and 7-DA syst ems,
di mensi onal
al t hough t he t h r e e
o r d e r i n g changes from a n t i f e r r o m a g n e t i c to
f e r r o ma g n e t i c as t he composi t i on
is changed from pure
c h l o r i d e t o pure bromi de f r u s t r a t i o n
introduced.
may a l t e r
sites
is
ordering.
As di scussed above,
i s not n e c e s s a r i l y
smal l
structural
changes
t he exchange u n i f o r m l y r a t h e r t han at fandom
and t hen no spi n gl ass be ha v i or would be seen.
in c o n t r a s t t o t he d i f f e r e n t
nickel
on random s i t e s
interactions
That
of c o b a l t
and
in CoNiTAC which does i n t r o du c e
frustration.
One f i n a l
difference
in t he 5-DA and 7 -DA systems
versus CoNiTAC i s t h e pr esence of t he mixed phase in t he
5-DA and 7-DA sy st e ms.
The smal l
a n i s o t r o p y i n t hese
systems a l l ows t he spi ns t o change o r i e n t a t i o n
relatively
smal l
ener gy c o s t .
Thi s
in t u r n
relatively
broad mixed phase r e g i o n .
ani sotropy is
l a r g e enough so t h a t
e x pe c t e d .
a mixed r e g i o n e x i s t s ,
If
at a
a l l ows f o r a
I n CoNiTAC t he spi n
no gr adual
it
shift
is
i s expect ed t o be
ver y narrow and was not seen i n t he CoNi TAC d a t a .
86
CONCLUSIONS .
The ps eudo- one - di mensi onal
been found t o e x h i b i t
mixed syst em,
spi n gl ass behav i or bel ow a
t e m p e r a t u r e , Tg , w h i l e t he MnCoTAC,
systems do no t .
concentration
5-DA and 7-DA
shows a ver y broad and deep spi n gl ass
antiferromagnetic
phase r egi ons
Below Tg t her moremanent ma g n e t i z a t i o n versus
t i me has been f i t t e d
wi t h a new c ons t a nt
crystal
MnNiTAC,
The phase di agr am of t e mp e r a t u r e versus
r e g i o n wi t h u n u s u a l l y t h i n
above i t .
CoNiTAC has
to a stretched exponential
o f f s e t t e r m.
In a d d i t i o n
function
both s i n g l e
dc and ac s u s c e p t i b i l i t y measurements have
det er mi ned t he magnet i c be ha v i or of t he
individual
c r y s t a l l ographi c o r i e n t a t i o n s .
The phase di agrams f o r MnCoTAC and MnNiTAC show a
deep de pr ess i on of t he par amagnet i c t o or der ed phase
critical
lines for
one di mensi onal
val ues of x near 0 . 5 .
Thi s
r a t h e r t han t h r e e di mensi onal
i s due t o a
frustration
in t he spi n o r d e r i n g .
The phase di agrams f o r
S-DACuCl 4x Br 4 ^ ^ _x ^ and
T- DACuCl 4x Br 4 ^^_x ) ar e more s i m i l a r t o t he CoNiTAC
phase di agr am wi t h r e l a t i v e l y f l a t
par amagnet i c t o
f e r r o ma g n e t i c or a n t i f e r r o ma g n e t i c c r i t i c a l
lines.
Whi l e
87
CoNiTAC shows a spi n gl ass phase t he 5-DA and 7-DA systems
show mixed phase r e g i o n s .
F u r t h e r ex per i ment s on t hese systems shoul d be
undertaken.
The
MnCoTAQ and MnNiTAC systems shoul d tie
i n v e s t i g a t e d at t e mp e r a t u r e s bel ow I K in or der t o
de t er mi ne under what ci r cumst ances a spi n gl ass phase
mi ght e x i s t
and in or de r t o ext end t h i s work and t he work
of C h e i khrouhou , et a I .
become a v a i l a b l e ,
single c r ys t al s
coul d be i mpr oved.
sufficiently
large cr yst al s
t he CoNiTAC system shoul d be
i n v e s t i g a t e d ver y near i t s
wi t h
If
t e t r a c r i t i c a I region.
t he phase di agrams f o r
Also
5-DA and 7-DA
The mixed a n i s o t r o p y 6 -DA system,
which i n f o r ma t i o n about t he mixed phase coul d not be
det er mi ned wi t h powder sampl es,
interesting
would be a not he r
c a n d i d a t e t o st udy wi t h s i n g l e
crystals.
for
88
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