Electron paramagnetic resonance of anilinium tetrachlorocuprate and ethylenediammonium
tetrachlorocuprate
by Richard Allen Bergstrom
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Physics
Montana State University
© Copyright by Richard Allen Bergstrom (1976)
Abstract:
High and low field g-values and the angular and temperature dependence of the linewidths for both
anilinium tetrachlorocuprate and ethylenediammonium tetrachlorocuprate were taken on a Varian E-3
spectrometer. The spin-orbit coupling constant λ was shown to lie between -200cm^-1 and -600cm^-1.
The data taken on the temperature dependence of linewidths was used as a further test of the model
proposed by Zaspel which has been shown to agree with data taken on other 2-dimensional
compounds. STATEMENT OF PERMISSION TO COPY
In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l l m e n t o f the
re qu ire m e nts f o r an advanced degree a t Montana S t a t e U n i v e r s i t y ,
I a gr e e t h a t t h e L i b ra r y s h a l l make i t f r e e l y a v a i l a b l e f o r
inspection.
I f u r t h e r a g re e t h a t permi ssi on f o r e x t e n s i v e
copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n te d
by my major p r o f e s s o r , o r , in his a bse n c e , by t h e D i r e c t o r o f
Libraries.
I t i s understood t h a t any copying or p u b l i c a t i o n
o f t h i s t h e s i s f o r f i n a n c i a l gain s h a l l n o t be allow ed w it h o u t
my w r i t t e n p e rm is si on .
Si g n a t u r e
Date
/0
, -----^
/
ELECTRON PARAMAGNETIC RESONANCE OF ANILINIUM
TETRACHLOROCUPRATE AND ETHYLENEDIAMMONIUM
TETRACHLOROCUPRATE
by
RICHARD ALLEN BERGSTROM
A t h e s i s s ubm itt ed in p a r t i a l f u l f i l l m e n t
o f t h e re quire m e nt s f o r th e degree
of
MASTER OF SCIENCE
in
Physics
Approved:
C h a i rp e r so n , Graduate Committee
Hfea ^ / r ^ o f ^ l l p K r tm en t
Graduate Dean
MONTANA STATE UNIVERSITY
Bozeman, Montana
August, 1976
ACKNOWLEDGMENTS
The a u t h o r i s g r a t e f u l f o r t h e f i n a n c i a l s u p p o r t o f Montana
S t a t e U n i v e r s i t y (1974-76).
He i s very g r a t e f u l to P r o f e s s o r
John E. Drumheller f o r h i s a d v ic e and encouragement i n t h e accomplish
ment o f t h i s work;
He wishes t o thank p r o f e s s o r K. Emerson f o r h is
he lp in d e t e r m i n i n g t h e c r y s t a l s t r u c t u r e o f ALTC, and he wishes to-,
thank P r o f e s s o r K. P. Larsen o f Aarhus U n i v e r s i t y , Aarhus, Denmark,
f o r p r o v i d i n g i n f o r m a t i o n on t h e c o r r e c t o r i e n t a t i o n o f th e copperc h l o r i n e bonds in ALTC (F ig . 3 ) .
'
A s p e c i a l thanks to Pr of e ss or. R. W i l l e t t o f Washington ■
S t a t e U n i v e r s i t y f o r a l lo w in g us t o use t h e i r Varian E-3
s p e c t r o m e t e r , and a s p e c i a l thanks t o Ann Hewitt f o r t y p i n g t h e
manuscript.
;
TABLE OF CONTENTS
Chapter
I
II
III
IV
. Page
INTRODUCTION....................................
. . . ....................................
I
THEORY.........................................,
................................................
4
D A T A .................................................
18
CONCLUSION..............................................................................................
31
APPENDIX................................................................................................
33
LITERATURE CITED
36
........................................................... . . . . '
V
LIST OF TABLES
Table
I
Page.
M easured
g V alues
and
L inew idths
24
vi
LIST OF FIGURES
.
'
Figure
I
II
III
IV
V
VI
VII
Page
D O r b i t a l s ..........................................................................................
5
D S p l i t t i n g ..........................................................
O r i e n t a t i o n of Cu-Cl bonds in ALTC
8
. . . . . . . . . . .
16
S e p a r a t i o n o f co pper p l a n e s by benzene
r i n g s in ALTC............................................................................................ 19.
Magnetic f i e l d vs. a n g l e f o r ALTC and EDTC
Linewidths vs. te m p e r a t u r e f o r ALTC and EDTC
Linewidths vs. ang le f o r ALTC and EDTC
\
.................................22
. . . . . . .
. ............................".
26
28
ABSTRACT
High and low f i e l d g - v a lu es and t h e a n g u l a r and te m p e ra t u re
dependence o f t h e l i n e w i d t h s f o r both a n i l i n i u m t e t r a c h l o r o c u p r a t e
and e t h y l e n e d i ammonium t e t r a c h l o r o c u p r a t e were taken on a Varian
E-3 s p e c t r o m e t e r . The s p i n - o r b i t c o u p li n g c o n s t a n t w a s shown
t o l i e between -BOOcm- I and -600cm"I . The d a ta taken on t h e
te m p e r a t u r e dependence o f l i n e w i d t h s was used as a f u r t h e r t e s t
o f t h e model proposed by Zaspel which has been shown t o a g r e e w it h
d a t a ta k e n on o t h e r 2-di m ens ion al compounds.
I.
INTRODUCTION
The main i n f o r m a t i o n gained from e l e c t r o n pa ramagnetic
r e s on an c e (EPR) s p e c t r a i s an e v a l u a t i o n o f t h e v a r i o u s terms in
the spin hamiltonian.
Although t h e c r y s t a l f i e l d and s p i n - o r b i t
e n e r g i e s a r e in d e p e n d e n t l y e v a l u a t e d from o p t i c a l s p e c t r a , they
can be c o r r e l a t e d w it h EPR d a t a .
The most i n f o r m a t i v e EPR d a t a
w i l l be t h a t which i s re c o rd e d a t more th a n one t e m p e r a t u r e ,
f r e q u e n c y , and microwave power.
EPR d a t a can be used t o i d e n t i f y
an unknown t r a n s i t i o n metal ion o r l a t t i c e d e f e c t .
I t can d i s ­
t i n g u i s h between s e v e r a l v a le n c e s i t e s o f t h e same i o n , and i t can
a l s o f r e q u e n t l y i d e n t i f y t h e l a t t i c e s i t e and symmetry o f t h e '
p a ra m ag ne tic s p e c i e s .
Much i n f o r m a t i o n can be e x t r a c t e d about
d i f f u s i o n c o n s t a n t s and c o r r e l a t i o n t i m e s , and sometimes r e l a x a t i o n time d a t a w i l l d e t e c t long ra nge e f f e c t s .
In t h i s t h e s i s , t h e a n g u l a r and t e m p e ra t u re dependence of
t h e g v a l u e s f o r t h e Cu++ ion i n am* I i n i urn t e t r a c h l o r o c u p r a t e
(ALTC) and e t h y l e n d i ammonium t e t r a c h l o r o c u p r a t e (EDTC) were
measured.
ALTC i s a q u a s i - 2 - d i m e n s i o n a l la y e r e d s t r u c t u r e .
There
i s a wide i n t e r e s t in s t r u c t u r e s o f t h i s type because th e y can be
used t o ap proxim ate a pla ne of magnetic atomic d i p o l e s .
For
example, t h e o r e t i c a l l y t h e r e should be no long range o r d e r i n g in
2-dim ens iona l c r y s t a l s t r u c t u r e s , b u t experiments have i n d i c a t e d
.
2
t h a t some o r d e r i n g does indeed e x i s t .
2
■ Both ALTC and EDTC w i l l
be e v e n t u a l l y s t u d i e d by o t h e r te c h n i q u e s to see i f t h e r e i s any
long ra nge o r d e r i n g .
Also, t h e exchange e n e r g i e s can be e s t i m a t e d
by comparison o f t h e exchange-narrowed l i n e w i d t h s with c a l c u l a t e d
second moment w i d t h s , and o t h e r i n t e r e s t i n g in fo r m a t io n comes from
t h e t e m p e r a t u r e dependence o f t h e l i n e w i d t h s .
Once t h e g v a l u e s and c r y s t a l f i e l d s p l i t t i n g a r e known,
t h e s p i n - o r b i t c o u p li n g c o n s t a n t
Xcan be
found.
We w i l l s e e t h a t
because o f t h e s t r u c t u r e , we w i l l only be a b l e t o s e t l i m i t s on
the values.
The s t r u c t u r e o f EDTC i s unknown but comparison o f
t h e g v a lu e s i n d i c a t e s t h a t i t i s much l i k e t h e s t r u c t u r e o f ALTC.
Paramagnetic r e s ona nc e i s t h e s p e c t r o s c o p y o f magnetic
d i p o l e t r a n s i t i o n s induced by an o s c i l l a t i n g magnetic f i e l d between
t h e energy l e v e l s o f a system o f paramagnets.
The magnetic d i p o l e s
w it h which we a r e concerned a r e th o s e on t h e atomic l e v e l .
An
atom may have a magnetic moment owing t o n u c l e a r s p i n , e l e c t r o n
s p i n , o r e l e c t r o n o r b i t a l a n g u l a r momentum, but because o f t h e i r
g r e a t e r o r d e r o f ma gnitu de , only t h a t due to e l e c t r o n s p i n S and
e l e c t r o n o r b i t a l a n g u l a r momentum L w i l l be c o n s i d e r e d .
Resonance
oc cur s in a s t a t i c magnetic f i e l d Hq when a small, p e r t u r b i n g tim e
de pen de nt magnetic f i e l d
causes t r a n s i t i o n s between t h e d i f f e r e n t
atomic energy l e v e l s c r e a t e d by Hq or quantum m e c h a n i c a l l y 6.
where h i s P l a n c k ' s c o n s t a n t , r i s t h e freque ncy o f H1 and
i s t h e ma gnetic moment which i s
where ^ i s t h e Bohr magneton, and g& i s t h e f r e e e l e c t r o n g v a l u e .
For a c r i t i c a l t r e a t m e n t o f n o n - s p h e r e i c a l symmetry, such as in a
s o l i d , i t i s c o n v e n ie n t t o d e f i n e a g f a c t o r which r e l a t e s t h e
a n g u l a r momentum to t h e d i p o l e moment i n g e n e r a l .
To measure t h e g v a lu e s a t r e s o n a n c e , one. must have a
s o u r c e f o r t h e Hq f i e l d and an r . f . s o u rc e f o r t h e ti m e -d e pe nden t
field.
The Varian E-3 EPR s p e c t r o m e t e r pro vid e s both .
The
fr eq u e n cy o f t h e H1 f i e l d i s ke pt c o n s t a n t and t h e H„ f i e l d i s
s low ly v a r i e d , so s lo w ly t h a t i t can be c o n s i d e r e d c o n s t a n t
compared t o H j , through re s o n a n c e .
At r e s o n a n c e , energy i s
ab sorbed by t h e c r y s t a l from t h e r . f . f i e l d .
The s p e c t r o m e t e r
w i l l d e t e c t t h i s energy a b s o r p t i o n and because of phase d e t e c t i o n
w i l l p l o t t h e d e r i v a t i v e o f t h e a b s o r p t i o n with r e s p e c t t o th e
f i e l d Hq .
This curve i s then used t o compute th e g v a lu e s f o r
II.
THEORY
The Cu++ ion has a ls^2s^2p^3s^3p®3d^ c o n f i g u r a t i o n in
t h e ground s t a t e so we can c o n s i d e r t h e c o l l e c t i v e motion o f th e
n in e 3d e l e c t r o n s as a hole in a Sd^ c o n f i g u r a t i o n .
F i r s t we c o n s i d e r t h e p e r t u r b a t i o n produced in t h e c r y s t a l
f i e l d due t o c u b ic and t e t r a g o n a l symmetry.
Then we i n c l u d e th e
e f f e c t o f s p i n - o r b i t c o u p l i n g , and f i n a l l y add t h e p e r t u r b a t i o n
of the external f i e l d H .
o
- -
The f r e e ion o r b i t a l can be r e p r e s e n t e d by
i s an e i g e n f u n c t i o n o f Lz .
.. This
For a f r e e i o n , t h e h a m i l t o n i a n w i l l
be i n v a r i a n t under r o t a t i o n a bout t h e Z a x i s , and so i t w i l l
commute w it h Lz -
But f o r an ion in t h e c r y s t a l l a t t i c e , t h e r e
i s n ' t s p h e r i c a l symmetry so t h a t t h i s commutation no lo n g e r
occurs.
In t h e lower symmetry we can choose t h e p r o p e r l i n e a r •
•2
c o m bi na tio ns o f t h e o r b i t a l s us in g a method developed by Bethe.
This r e s u l t s in a change from running t o s t a n d i n g waves and i s
done by forming:
5
FIGURE I
Diagrams o f d - e l e c t r o n o r b i t a l s a t a s i t e o f o c t a h e d r a l
symmetry in r e l a t i o n t o s i x e q u i v a l e n t p o i n t c h a r g e s , shown as
dots.
.
Consider
a
_L
(? )
81#
4 .4
36«
Co/
Ccs-©■1S -
G%
o r more simply
■z.
%
Now, c o n s i d e r n e g a t i v e p o i n t charg es s y m m e tr ic a ll y pla ced
al ong t h e a x i s (F ig . I ) .
The energy l e v e l s f o r
Lp+1
and
w i l l be r a i s e d t h e same amount and they w i l l be t r i p l y
degenerate.
I t i s not obvious t h a t
(7"
Sr
s7 o
y**
w i l l be ■
and
lowered by t h e same amount b u t t h i s i s indeed t h e c a s e . ^
This
w i l l c au s e a double degeneracy.
Now c o n s i d e r t h e non-symmetric s i t u a t i o n caused by moving
t h e c h a r g e s on t h e Z a x i s o u t by a small amount.
*
YiL'
and
lowered.
w i l l be r a i s e d t h e same b u t
The degeneracy in
(F ig. 2 ) .
and
We can s ee t h a t
w i l l be
w i l l a l s o be l i f t e d
This l e a d s to one doubly d e g e n e r a t e and t h r e e s i n g l e t
levels.
Now each o f t h e s e s t a t e s i s doubly d e g e n e r a t e because
-u
itT„ Io f s p i n , w it h
v'
. and
V r
as t h e low est o r ground
- s- B I
s t a t e (F ig . 2 ) , .where
i s s p i n up and B i s s p i n down.
Co nsider t h e e x p e c t a t i o n v a l u e o f -L
fo r the s t a t e
( s e e a p p e n d ix ) . ■ The v a n is h i n g o f t h e e x p e c t a t i o n valu e
8
FIGURE I I
S p l i t t i n g o f t h e D term by a t e t r a g o n a l Iy d i s t o r t e d cub ic
field.
= = yz,zx
\
XV
\
Free Ion
8
A
v
v
10
o f Lz
i s c a l l e d "quenching" o f th e o r b i t a l a n g u l a r momentum.
To s e e any e f f e c t o f t h e s p i n - o r b i t i n t e r a c t i o n t h e p e r t u r b e d
wave f u n c t i o n
must be used.
_L
Cf
where t h e summation, runs over a l l s t a t e s i n c l u d i n g s p i n , e xce pt
m=K.
11
The ex pec ta tio n- v a l u e o f
does n o t va ni sh ( s e e a p p e n d i x ) .
£ =
where
on t h e p e r t u r b e d wave f u n c t i o n
Then t o f i r s t o r d e r f o r t h e ground
4
e q u a ls t h e c r y s t a l f i e l d - s p l i t t i n g (Fig. 2).
We see
t h a t t h e s p i n - o r b i t i n t e r a c t i o n adds a small amount o f a n g u l a r
momentum and because o f t h i s , s p i n o nly p r o p e r t i e s ca nnot be
ex pe c te d.
Now l e t ' s c o n s i d e r t h e e f f e c t o f an e x t e r n a l magnetic
f i e l d Hq a p p l i e d to t h e c r y s t a l .
F i r s t we wi l l c o n s i d e r t h e
component o f t h e h a m i l t o n i a n in t h e Z d i r e c t i o n :
13
we g e t
5
X
&
We have an e f f e c t i v e "s pin " hamiI torn" an which can be w r i t t e n
where
K
F i n a l l y we s e e t h a t t h i s i s a t e n s o r £ which can be
r e p r e s e n t e d by a 3 x 3 m a t r i x which w i l l r e l a t e
Aa* to S:
The r e s u l t o f a l l t h i s i s t h a t t h e p e r t u r b a t i o n due t o a n g u l a r
momentum can be c o l l a p s e d i n t o t h i s £ t e n s o r and only t h e s p i n
needs t o be c o n s i d e r e d .
So f a r we have c o n s i d e r e d only t h e g v a l u e s along th e v a ri o u s
s i t e a x i s X5 Y5 and Z.
However5 t h e e x t e r n a l magnetic f i e l d Hq
14
can be i n any a r b i t r a r y d i r e c t i o n r e l a t i v e to t h e s i t e a x i s so we
must c o n s i d e r t h e h a m i l t o n i a n f o r any a n g le & .
The ham il to n ia n
th e n becomes
A
(A l.5. s 4©
a #
I
where Q
i s t h e a n g l e between Hq and t h e Z axis, and
where ^
i s an a n g l e in t h e X, Y p l a n e :
5-
=
-
.
S o lv i n g t h e s e c u l a r d e t e r m i n a n t
14
we have:
_£
- a
4SL
0 0
15
Now w i t h i n t h e c o p p e r - c h l o r i n e pla ne in ALTC, t h e Z a x i s
o f t h e n e ig h b o r in g Cu++ ions a r e p e r p e n d i c u l a r (F ig . 3 ) .
Because
o f t h e superexchange i n t e r a c t i o n between th e ne ig hb orin g copper
s i t e s th e g^
and a
v a lu e s wi l l be in te rm ix e d so t h a t
We w i l l s t i l l assume t h a t gx
e q u al s gy
gx , b u t g ^ w i l l now be c a l l e d Qm- .
and t h a t gx
i s equal to
FI GURE I I I
O r i e n t a t i o n o f t h e c o p p e r - c h l o r i n e bonds in ALTC.7
III.
DATA
Anilinium t e t r a c h l o r o c u p r a t e (ALTC)9 (CgHgNH^)2 CuCi^9 i s
m o no c lin ic with a s pac e group P2^/c and w it h a = 1 5 . OSOA0 9
b = 7.443A0 , o = 7 . 180A,
= 100.7° and Z = 2 as shown in
5
Fi gu re 3.
The co pper io n s l i e in a p la n e and a r e su rro unded by
s i x c h l o r i n e l i g a n d s ..
Four o f t h e s e c h l o r i n e l i g a n d s bind t h e
copper io ns to o t h e r copper ion s in t h e same p l a n e , and t h e two
o u t o f p l a n e c h l o r i n e l i g a n d s bind t h e copper ions to benzene
r i n g s which b r i d g e t h e c opper p la n e s ( s e e Fig. 4 ) .
. A d d it io n a l •
i n f o r m a t i o n prov ide d by Larsen giv e s t h e " c o r r e c t " o r i e n t a t i o n of
t h e c o p p e r - c h l o r i n e bonds.
The l e n g t h s o f t h e c o p p e r - c h l o r i n e
bonds a lon g t h e X9 Y9 and Z a x i s a r e 2 . 2804A°9 2 . SOOZA0 9 and .
2.9178A0 r e s p e c t i v e l y .
The Z a x i s a t one copper s i t e i s connected
by a c h l o r i n e l i g a n d t o t h e X a x i s o f t h e n e x t copper s i t e , and
t h e a n g l e s between t h e copper and c h l o r i n e a r e not a l l e x a c t l y
90° (F ig . 3).
Also t h e c o p p e r - c h l o r i n e bonds between t h e Y and
Z a x i s l i e o u t of t h e copper p l a n e , so t h e X a x i s does n o t l i e
along a l i n e p e r p e n d i c u l a r t o t h e c o p p e r -c o p p e r p l a n e s .
Since t h e
EPR d a t a f o r e t h y l enediammoniurn t e t r a c h l o r o c u p r a t e (EDTC)9
(C2H^(NHg)2 ) CuCl^9. i s s i m i l a r to t h a t o f ALTC9 t h e i r s t r u c t u r e s
were assumed t o be s i m i l a r .
/
19
FIGURE IV
Drawing o f copper pla nes s e p a r a t e d by benzene r i n g s .
21
Data f o r both ALTC and EDTC were taken on a s t a n d a r d Varian
E-3 EPR s p e c t r o m e t e r .
A scan time o f 8 minutes was used , th e
m odula tio n was 100 k i l o h e r t z , and t h e microwave fr equ en cy
was 9.523 megahertz f o r ALTC and 9.155 megahertz f o r EDTC a t room
t e m p e r a t u r e , and 9.155 megahertz f o r ALTC and 9.153 megahertz f o r
EDTC a t 77° Kv
The scan range was. 250 Gauss with a time c o n s t a n t
o f I second.
The r e s o n a n t magnetic f i e l d Hq
Fi g u r e 5.
vs.
a n g le Q
i s given in
These a r e t h e t y p i c a l c o s i n e curves one would e x p e c t
from t h e a n g u l a r dependence o f t h e g e q u a t i o n .
Solv in g t h e energy
equation f o r g gives:
C a l c u l a t e d v a lu e s o f g
■given in Table I .
and g .
f o r both ALTC and EDTC a r e
The d a t a was ta k e n a t both room t e m p e ra t u re
(300° K) and l i q u i d n i t r o g e n t e m p e r a t u r e (77° K).
W i l l e t t has shown in h is i n v e s t i g a t i o n s o f monomeric copper
( I I ) c h l o r i d e s t h a t A ~ IO5OOOcm"""*" a n d / s s .
Cu ( I I ) . ^
g
= k( q
constant
1 2 , OOOcrn""\
for
I f t h e assumption" i s made t h a t g^ = g^ and t h a t
+ q )
no c o n s i s t e n t v a l u e f o r t h e s p i n - o r b i t coup lin g
is possible.
This o f c o u r s e i s because t h e s t r u c t u r e ,
gi ve n e a r l i e r , of ALTC i s more c om plic at e d than t h e above assumptions
FIGURE V
Magnetic' f i e l d (H) versu s a n g l e ( H ) f o r ALTC and EDTC.
esv^©
3250 b
M C g l ^ t ' i H y g CvCzl4
3200 CO
I 31501
CD
CS
$1
1X3
CO
3! OO
3050
J ------- i____ i------ L
90
O
p
(°)
90
TABLE I
MEASURED g VALUES AND LINEWIDTHS
Compound
(C g H g N H g ig
C u C l^
C2H4 (NH3 ) 2 CuCl4
l i n e w i d t h gmax
lin e w id th
^min
^max
2.088+.01
2 .1 4 4 + .Ol
42.5
2 . 0 9 0 + . Ol
2 . 146±.Ol
9 .4
■ 15.6
77°K
2 . 097±.Ol
2.1 5 5 + .Ol
45.9
3 8 .7
300°K
2 . 097±.Ol
■ 2 .1 5 4 + .Ol
9.7
77°K
11.25
gauss
41.25 gauss
^rni n
300°K
25
The v a lu e s t h a t a r e c o n s i s t e n t with t h e above assumptions wi l l
range between -200cm
and -600cm"™ .
The I inew.idths
and 300° K in F ig ure 6.
a t an a ngle o f ©
= O0 a r e shown a t 77° K
These were t h e only te m p e r a t u r e s a v a i l a b l e
to use and a r e p r e l i m i n a r y t e m p e r a t u r e s t o be used to f u r t h e r t e s t
t h e model proposed by Zaspel in h i s Ph.D. t h e s i s . ®
.
By c o n s i d e r i n g
o p t i c a l phonon modul at ion o f t h e symmetric exchange i n t e g r a l , th e
model p r e d i c t s a l i n e a r te m p e r a t u r e dependence o f th e l i n e w i d t h s
.AH.
Although t h e model supposes no p r e f e r r e d geometry, l a y e r e d
compounds such as ALTC and EDTC a r e e xpect ed to behave i n t h i s
manner.
A l i n e a r te m p e r a t u r e dependence o f t h e exchange c o n s t a n t
in
has been shown f o r KgCuCl^ ? HgO and o t h e r l a y e r e d compounds.
Linewidths v s . a n g le a t both 77° K and 300° K a r e a l s o
i n t e r e s t i n g and a r e given in Fi g u r e 7.
ALTC d i s p l a y s t h e expected
a n g u l a r dependence w h i l e c u r i o u s l y EDTC shows j u s t t h e o p p o s i t e
a n g u l a r dependence.
Richards has proposed a model which gives
I i r e s h a p e as a f u n c t i o n o f a n g le by a F o u r i e r t r a n s f o r m o f a
r e l a x a t i o n f u n c t i o n which i s e xpre ss ed i n terms o f exchange modula­
tio n of the d ip o le -d ip o le p e rtu rb a tio n fo r S s t a t e ions.
In g e n e r a l ,
however, t h e p e r t u r b a t i o n s may i n c l u d e s p i n - o r b i t , c r y s t a l f i e l d
11
couplings, etc. .
Drumheller has found o t h e r compounds which
d e p a r t from t h e Richards model, such as t h e methyl and
26
FIGURE VI
Linewidths (4 H) versu s te m p e r a t u r e a t an a ngle o f zero
de gr e es f o r ALTC and EDTC.
\
O = (CgHgNHs ^CuCI^.
x =CgH^NHg ^CuCI^
5 0
i
A l-I(G o u ss)
40 h
50
ro
\i
20
!Or
0.
O
77
300
T^K
8=C
FIGURE VII
Linewidths ( i H) versu s a n g l e ( 8 ) f o r ALTC and EDTC.
O =(CsH5NH3)2CuCi4
50 H
40-
X
o
$
E
X
%
O
8
O
g .
=(C2H4(NH3)2)CuCi4
X
X
x
o
G
O
in
CO
O 30
CD
%
<i
PO
kO
2 0 r-
o
x
IO
O
O
x
X
O
20
40
X
O
G
(SC)
x
X
X
O
O
G
80
30 '
e th y l ammonium t e t r a c h l o r o c u p r a t e compounds.
e x p l a n a t i o n f o r t h i s anomalous b e h a v i o r .
12
So f a r t h e r e i s no.
IV.
CONCLUSION
By measuring t h e g valu es and obs ervin g t h e a n g u l a r and
te m p e r a t u r e dependence o f t h e l i n e w i d t h s f o r both ALTC and EDTC
we have shown in t h i s work s e v e r a l q u a l i t a t i v e f e a t u r e s which a r e
o f i n t e r e s t in t h e s t u d y o f 2-dim ensio na l magnetism.
F i r s t we have
shown t h a t t h e s t r u c t u r e o f EDTC i s l a y e r e d and s i m i l a r t o ALTC.
Also we have found two more examples t h a t , seem to s u b s t a n t i a t e th e
model proposed by Zaspel f o r te m p e r a t u r e dependence o f t h e l i n e - ,
w id th s and t h e r e f o r e t h e exchange e ner gy.
This i n f o r m a t i o n ,
however, does n o t g iv e t h e n a t u r e o f t h e exchange i n t e g r a l J ,
so t h e mag net ic s u s c e p t i b i l i t y f o r both ALTC and EDTC needs to
be measured.
From d a t a , t h e i n t e r - p l a n e and i n t r a - p l a n e exchange
can be found and t h e n a t u r e o f J d e te r m in e d.
E v e n t u a l l y d a t a on t h e magnetic s p e c i f i c h e a t Cffl w i l l be
ta k e n on t h e s e compounds, and i t may be p o s s i b l e t o de te r m in e from
t h i s d a t a i f t h e model proposed by Z a s p e l , which depends on t h e sym­
m e t r i c exchange i n t e r a c t i o n S - - S . , i s r e a l l y r e s p o n s i b l e f o r th e
• J
l i n e a r t e m p e r a t u r e dependence o f t h e l i n e w i d t h s , o r i f i t i s due t o
t h e a n ti s y m m e t r ic exchange i n t e r a c t i o n S. x S . .
13
Both models pre -
d i e t a l i n e a r te m p e r a t u r e dependence o f t h e l i n e w i d t h s .
Because we.
need n o n - c e n t r a l symmetry and n o n - S - s t a t e ions f o r t h e . a n t i ­
symmetric exchange to be p r e s e n t , t h e magnetic s p e c i f i c h e a t would
32
behave d i f f e r e n t l y f o r non-symmetric exchange than f o r symmetric
exchange.^
Also t h e a n g u l a r dependence on th e l i n e w i d t h s f o r
EDTC needs to be f u r t h e r i n v e s t i g a t e d and c o r r e l a t e d t o t h e
a p p a r e n t l y anomalous b e h a v io r in o t h e r .compounds.
..
APPENDIX
APPENDIX
To show t h a t t h e e x p e c t a t i o n va lu e o f L v a n is h e s o p e r a t e
on t h e ground s t a t e wave f u n c t i o n
so
Then we can s e e t h a t because o f t h e o r t h o g o n a l i t y o f t h e wave
f u n c t i o n s t h e e x p e c t a t i o n va lu e o f Lz v a n i s h e s .
The same, o f
c o u r s e , w i l l be t r u e f o r L and L .
x
y
Because t h e p e r t u r b e d wave f u n c t i o n f o r t h e ground s t a t e
< <
t z&
— 4 %.
>
-1 *
is a mixture o f a ll o th e r s t a t e s except 9 ^
j SC' >
^
■
= whose m a t r i x elements
w it h r e s p e c t t o t h e ground s t a t e v a n i s h , t h e e x p e c t a t i o n v a lu e o f
Lz no l o n g e r v a n i s h e s :
35
So t o f i r s t - o r d e r t h e e x p e c t a t i o n v a lu e o f L
on t h e p e r t u r b e d
ground s t a t e i s equal to
c o n s t a n t and
Si nc e
^
and
, where
X i s t h e s p i n - o r b i t cou plin g
tS.
<£ a r e t h e c r y s t a l f i e l d s p l i t t i n g ( F ig . 2).
i s on t h e o r d e r o f 10,000cm * a t room t e m p e r a t u r e t h e
population of the other s ta t e s is i n s ig n if ic a n t.
.
Now we can show t h a t t h e e x p e c t a t i o n valu e of t h e h a m i l t o n i an
) C ^ on t h e p e r t u r b e d ground s t a t e , where
i s equal to
-Jr- 4
A /t.
^ ^
^
^ ) /^2-
.
. Then t h e s p l i t t i n g
d
E - -
C g .-
x
2 ,
Now l e t ' s t a k e t h e e x p e c t a t i o n va lu e o f J f wi t h r e s p e c t
to
J jl
which because o f symmetry i s e q u i v a l e n t t o t h e e x p e c t a ­
t i o n va lu e o f
The dia gon al m a t r i x elements v a n is h .
i t can be shown t h a t t o f i r s t o r d e r
With a l i t t l e work
LITERATURE CITED
LITERATURE CI TED
'I.
C. P ool e , E l e c t r o n Spin Resonance, (John VJiley and S o n s „ New
York, 19677:
2.
;
I . J . de Jongh and A. Miedema5 Adv. in Physics 235 I (1974).
3. ' H. Beth, Ann. P h y s ic , _3, 133 (1929).
4.
G. Pake, Paramagnetic Resonance, (W. A. Benjamin, I n c . ,
New York, 1952).
5.
K. La rs e n , Acta Chemica S c a ndin av i ca A28, 194 (1974).
6.
K. Emerson, p r i v a t e d i s c u s s i o n .
7.
K. L a r s e n , p r i v a t e communication.
8.
R. W i l l e t t , 0. L i l e s , J r . , and C. Michel son, Ino rg . Chem.
6, 1885 (1967). •
9.
C. Z a s p e l , On The Temperature Dependence o f The Exchange
I n t e r a c t i o n , T h e s i s , (Montana S t a t e U n i v e r s i t y , 1975).
10.
C. Zaspel and J. Drumhelle r , S o li tf S t a t e Commun., 17, 1107
(1975)..
~~
11.
P. R i c h a r d s , Magnetic Resonance i n One- and Two-Dimensional
■ S ys te ms , (Sandia L a b o r a t o r i e s , Albuquerque, N. Mex., 1973)7
12.
H. Boesch, U; Schmocker, F. Waldner, K. Emerson, and J .
Drum he ller, Ph ysics L e t t e r s , 36A, 6 (1971).
.13.
M. Seehra and T. C a s t n e r , Phys. Kondens. M a t e r i a , 7, 185
(1968).
14.
C. Z a s p e l , to be p u b l i s h e d .
3 1762 10012907 9
N378
Bl+56
cop.2
Bergstrom, Richard A
Electron paramagnetic
resonance of anilinium
tetrachlorocuprate and
ethylenediammonium
tetrachlorocuprate
DATE
ISSUED
TO
A J S W