EPR study of the symmetry breaking effect
in ferroelectric cesium dihydrogen phosphate
doped with Cr5+ ions
Authors: S. Waplak & V. Hugo Schmidt
NOTICE: this is the author’s version of a work that was accepted for publication in Solid State
Communications. Changes resulting from the publishing process, such as peer review, editing,
corrections, structural formatting, and other quality control mechanisms may not be reflected in
this document. Changes may have been made to this work since it was submitted for
publication. A definitive version was subsequently published in Solid State Communications,
VOL# 52, ISSUE# 8, (DATE)] DOI# 10.1016/0038-1098(84)90394-6.
S. Waplak and V.H. Schmidt, “EPR study of the symmetry breaking effect in ferroelectric
cesium dihydrogen phosphate doped with Cr5+ ions,” Solid State Communications. 52,
709-712 (1984).
http://dx.doi.org/10.1016/0038-1098(84)90394-6
Made available through Montana State University’s ScholarWorks
scholarworks.montana.edu
Solid State Con~nunications, Vol.52,No.8, pp.709-712,
Printed in Great Britain.
1984.
0038-I098/84 $3.00 + .00
Pergamon Press Ltd.
EPR STUDY OF THE SYMMETRY BREAKING EFFECT IN FE~ROlg~ECFRIC CESIUM
DIHYDROGI~ PHOSPHATE DOPED WITH Cr 5+ IONS
S. W a p l a k * a n d V. Hugo S c h m i d t
Department
of Physics,
Montana State
University,
B o z e m a n , ~/"
59717, U.S.A.
(Received July 19 1984 by H. Suhl)
The
( P 0 4 ) 3 - u n i t s i n a CsBo~04 (CDP) c r y s t a l w e r e r e p l a c e d i n a s m a l l
fraction
o f s i t e s by ( C r 0 4 ~ 3 - g r o u p s a n d t h e EPR o f t h e C r 5+ c e n t e r
was i n v e s t i g a t e d .
S p l l t t l n s o f t h e EPR l l n e a p p e a r s a t T : = 2 4 5 K, 91 X
higher
than the ferroelectric
transition
t e m p e r a t u r e Tc=154 K.
The
electronic
wave f u n c t i o n o f CrS+(3d I ) i s i d e n t i f i e d
as dx2_ ~.
The
d 2_y2 f u n c t i o n c o u p l e s w i t h t h e n e a r p r o t o n s a n d t h e r e o r i e n t a t l o n
of
t~is
unit
in
the
two p o s s i b l e
configurations
occurs
in
the
paraelectric
p h a s e a n d b r e a k s t h e s y ~ e n e t r y f a r a b o v e Tc .
The o b s e r v e d
correlation
t i m e 10 - 9 s e c a n d a s s o c i a t e d a c t i v a t i o n
e n e r g y AU=0.215 eV
are discussed.
the hydrogen ordering
several
deviations
of
other atoms from their symmetric positions
in
the paraelectric
phase.
The d i s p l a c e m e n t o f t h e
0(1) oxyge~ is found to be a consequence
of a
s m a l l r o t a t i o n o f t h e PO4 t e t r a h e d r o n
around the
P-02 bond.
The a n g l e o f r o t a t i o n
was estimated
t o be a b o u t 3 ° . N e x t i s a d i s p l a c e m e n t
of the P
atom along the ~ direction
b y 0 . 0 6 A° .
These
d i s p l a c e m e n t s m i g h t be r e s p o n s i b l e
for generation of polarlzatlon,
but
the value of polarization evaluated
from this model did not give
good a g r e e m e n t w i t h t h e e x p e r i m e n t a l v a l u e .
I n t h l s _ p a p e r we p r e s e n t o u r EPR i n v e s t i g a tion
o f Cr 3+ a s a d o p a n t
i n a CDP c r y s t a l .
There are two reasons
w h y t h e Cr $+ p r o b e w a s
chosen.
First,
the 'Wformal" ionic charge of
t h e Cr 5+ i o n i s t h e s a m e a s t h a t o f t h e r e p l a c e d
u n i t P, a n d i t i s n e a r t h e a n i o n s i t e
where
moving of protons is expected.
S e c o n d , t h e Cr 5+
probe introduced
b y D a l a i and c o w o r k e r s 6,7 and
M u l l e r a n d B e r l l n s e r 8 i n t o KDP f a m i l y c r y s t a l s
has provided controversy
regarding what kind of
p h e n o m e n a Cr 5+ EPR s p e c t r a r e f l e c t ,
i.e., local
dynamics of ferroelcctric
clusters
in the par~electric
phase or Halperin-Varme-type
centers.
Because of the simpler proton ordering in a
two-dimeustonal
hydrogen-bond
network
we
expected
to clarify
this problem
i n CDP:Cr $+
crystals.
Introduction
C e s i u m d i h y d r o g e n p h o s p h a t e , CsH2P04 (CDP),
is well
known as a typical
example
of a
hydrogen-bonded ferroelectric
compound. Diffuse
neutron scattering
reveals the existence of onedimensional
ordering
of the hydrogen
bonds
parallel
to the ferroelectric
b axis. I The
crystal structure
o f CDP a t room t e m p e r a t u r e h a s
been determined
by Uesu and Kobayashi, ~ and by
Matsunaga, Itch and Nakamura. 3 They showed that
the symmetry
is monoclinic
with space group
P21/m and two formula units per unit cell.
In
the ferroelectric
phase the space group changes
t o P21 .
There are two kinds of one-dlmenslonal
chains
o f (PO 4) 3+ i o n s c o n n e c t e d
by hydrogen
b o n d i n g . 2 One c h a i n r u n s a l o n g t h e _b a x i s a n d
the other along the c axis.
The p h o s p h a t e
tet r a h e d r o n PO4 i s d e f o r m e d f r o m a r e g u l a r t e t r a hedron with the following
distances
between
phosphorus and oxygen atoms:
P - 0 1 = 1 . 6 0 7 A°, p - 0 2 = 1 . 4 6 4 A° ,
P - 0 3 = 1 . 5 3 9 A° a n d P - 0 4 = 1 , 5 3 9 A°.
The
length of the 0-H(1)...0 bonds along
t h e c a x i s i s 2 . 5 6 2 A° a n d t h e y a r e a l r e a d y
ordered
at
room
temperature
whereas
the
0-H(2)...0 bond
length along the ferroelectric
b a x i s i s 2 . 4 2 7 A° a n d t h e s e p r o t o n s a r e d i s o r dered.
This result
reflects
the
fact that a dielectric
a n o m a l y i n CDP i s o n l y o b s e r v e d
along
t h e b a x i s . 4 I w a t a , Koyano a n d S h i h u y a 5 r e p o r t
a structure
determination
o f t h e low t e m p e r a t u r e
p h a s e o f CDP by n e u t r o n d i f f r a c t i o n
with discussion of the transition
mechanism derived from
the resultant
atomic shifts.
They found besides
On l e a v e f r o m I n s t i t u t e
s i c s , P o l i s h Academy o f
Poland.
Experimental
Procedure
Single
crystels
o f CDP w e r e
grown by
evaporation
from saturated
water solution prep a r e d by m i x i n g Cs2CO3 a n d H3PO4 w i t h t h e m o l a r
r a t i o 1 : 2 t o g e t h e r w i t h 0 . 0 6 - 1 o i • o f K2Cr04.
The crystals
were
irradiated
with
a
40kV/10mA m o l y b d e n u m s o u r c e f o r 4 h o u r s a t room
temperature.
T h e EPR s p e c t r a
were obtained
using a Varian X-band spectrometer
w i t h I 0 0 ]dls
modulation and a gas nitrogen system for temperature control and stabillzatlo~
The orthogonal
a x e s f o r t h e EPR m e a s u r e -
of Molecular
PhySciences,
Poznan,
709
Vol. 52, No. 8
FERROELECTRIC CESIIJ}~DIHYDROGEN PHOSPHATE
710
merits was chosen as ~, b and~
withm e perpend i c u l a r t o t h e a_~b p l a n e o f t h e c r y s t a l l o g r a p h i c
axis system chosen by Uesu and Kobayashi. ~
Experimental
TABLE
g a t 300 K
Results
=~BH"g"S.
g at
bJ
/..0
. -O''O''O~
0
,0"
~"O
/ o,O,O
,
jo"
I
o
/
--O.o..,,
o..
"o.
o
"o,"k, b
Od~.
%-o,
o
o--o--o 160 K
cosines
m
n
gxx=l.9764
0, ~0.7071, +_0.7071
gyy=l.9848
1,
0,
0
T h e EPR l i n e s p l i t t i n g
versus temperature
measured with the magnetic field parallel
to
[011] direction
(l~ig. 2 ) .
Splitting
of the
l l n e a p p e a r s a t T : = 2 4 5 K, 91 K h i g h e r t h a n
ferroelectric
transition
temperature.
We h a v e u s e d t h e l i n e s p l i t t i n g
temperature
dependence to evaluate the correlation
time of
proton movement along the hydrogen bonds.
From
the Blocb equation
modified
by random jum~
b e t w e e n t w o e q u a l l y p r o b a b l e s i t e s one f i n d s
t h e c o m p l e x f r e q u e n c i e s •+ o f t h e d o u b l e t c o m p o nents as
was
the
EPR
the
~ + = i ( F +7)+_(52- r 2 ) 1 / 2 ,
(3)
w h e r e 25 i s t h e m a x i m u m d o u b l e t s p l i t t i n g ,
F is
t h e j u m p f r e q u e n c y b e t w e e n t h e two s i t e s ,
and 7
i s t h e w i d t h of t h e i n d i v i d u a l
components in the
absence of jumps.
The r e a l p a r t o f Eq. (3) g i v e s t h e p o s i t i o n
of the two doublet components relative
to the
center
of the doublet
and the imaginary
part
I
I
I
i
,
~
I
t
,
[
I
1
i
i
I
i
I
J
'
I
0
oo
_,4/'@3oo G
C~
~o,
~°'.o__o~
direction
0, +_0.7071, +_0.7071
60
?
'o "~ °'°-
n
gzz=l.9452
,
o.3.
320o
"o,
O
I O~/.~"
"O-" O, /
O~ /
,
o,
/
160 K
i
(2)
Here @ is the angle between
gll a n d t h e
external magnetic field.
N~o c h a n g e i n EPR s p e c trum was observed in the I00 to 300 K temperature reglo~ when the crystal
was rotated
round
the ~ or ~
axes.
~ig. I shows the spectrum
anisotropy
i n t h e bc s p l a n e a t room t e m p e r a t u r e
a n d 1 6 0 K. T h i s f i g u r e
is plotted
in the r,
c o o r d i n@a t e
system where 6 is the angle between
the ~
axis of our orthogonal
system and the
magnetic field which lies along the r-axis.
As i s s h o w n i n F i g . 1 t h e s i n g l e EPR l i n e
( a t 3 0 0 K) i s s p l i t
( a t 1 6 0 K) i n t o t w o l i n e s
w h o s e gz c o m p o n e n t s l i e + 45 ° f r o m t h e b a x i s
i n t h e "~c* p l a n e .
Rotation
of the crystal
around the [011] direction
gives us the gxx and
gvy components of the g tensor at low temperathre (Table I).
m
gl =1.9~89
(I)
g2(e)-glfCOS2(e)+g~sln2(e).
cosines
0.7071, 0.7071, 0
s11-1.9539
Because the spectrum
has axial
symmetry
for
rotation
around the g]] principal
axis of the
crystal
field,
the g parameter
is described
by
the expression
O~
direction
I
At room t e m p e r a t u r e ,
after measuring anisotropy
in the three perpendicular
planes,
we
found that the principal
a x i s g ] ] l i e s i n t h e ab
p l a n e a n d m a k e s a n a n ~ l e o f 45 ° w i t h t h e ~ axi-~.
O n l y o n e t y p e o f Cr 5 i s o b s e r v e d a t r o o m t e m perature.
The spin-Hamiltonian
used in describing the
EPR s p e c t r u m h a s t h e f o r m
H
I
4O
AH
(G)
2O
,'-o_ o_.O"
× ;" 300 K
Figure 1
EPR s p e c t r u m a n i s o t r o p y a t room t e m p e r a t u r e
( f u l l l l n e ) a n d 160 K ( b r o k e n l i n e ) .
B e c a u s e of
s y ~ , a e t r y t h e EPR s p l i t t i n g
c a n be o b s e r v e d
only
in the ! rotation.
Tc
I
Jl
15o T(K)
20o
250
Figure 2
The EPR l i n e s p l i t t i n g
AH v_~s. t e m p e r a t u r e
f o r e x t e r n a l f i e l d Ho d i r e c t e d a l o n g [ 1 1 0 ] .
T
Vol. 52, No. 8
FERROELECTRIC
CESIUM DIHYDROGEN PHOSPHATE
gives their
width.
When
F<5
the singlet
llne change into a doublet.
The j u m p f r e q u e n c y o b t a i n e d f r o m Eq. (3) i s
F=0.S[(26)2-(A~)2]
I/2,
(4)
or
F = ( g p B l 2 k ) [ ( A H o ) 2 - ( A H t ) 2 ] 112 ,
(5)
w h e r e AHo i s t h e m a x i m u m d o u b l e t s p l i t t i n g
value
in gauss
a n d AH t t h e
splitting
at given
temperature.
Taking into consideration
t h e g=1.967 v a l u e
of the center
o f t h e d o u b l e t we h a v e t h e f o l lowing expression for the jump frequency in our
experiment:
r =8.65xI06[AHo)2-(AHt)2] I/2 .
(6)
The p l o t o f i n F v s . 1 0 3 / T s h o w n i n F i g .
d e s c r i b e d by t h e s i m p l e A r r h e n i u s l a w
3 can be
(7)
l/~c=(l/~co)exp(U/kT).
w h e r e 1 / ~ c = F , 1 / ~ c o = 1 . 3 8 x 1 0 1 3 s a c a n d AU=0.215
eV e x c e p t i n t h e n a r r o w r e g i o n a b o u t 5 K b e l o w
T*. The c r i t i c a l
s l o w i n g down e f f e c t i n CDP w a s
m e a s u r e d C by K a n d a e t a l . 11 i n t h e f r e q u e n c y
region
b e l o w 1 GHz.
The independent-dipole
relaxation
time, which is governed by the hopping of protons between the double well potential minim~ in the high temperature region, was
~o=1.9 10- 3 sac.
They get the • value of the
ferroelectric
relaxation
mode by the following
expression
which is valid for a pseudo-one
dim e n s i o n a l I s i n g s y s t e m a b o v e Tc:
~
O
cosh(2~3
)T
(S)
#c3I(1-2#JII)?T-T c)
F o r CDP t h e o b s e r v e d t e m p e r a t u r e
d e p e n d e n c e of
the relaxation
time was fitted
with :he following parameters:
J[[/k=234
K is the intrachain interection
constant,
3~/k=6.78 K is the
interchain
interaction
constant,
~=I/kT,
and
~ c = I / k T c . By u s i n g Eq. (9) we o b t a i n i n t h e 200
t o 245 K t e m p e r a t u r e
region the range of values
5
~c-1=(0.58-1.?0)x1011
sac -1 to co,pare with our
experimental
value
range
~c~ =(~,~-4.6)x10 ~
sec -1 .
The change of the gzz directions
b y +_ 45 °
from
the b axis
requires
a corresponding
reorientatlon
of the Cr0 4 tetrahedron
qr
reorientatlon
o f t h e dx2 ~2 o r b i t a l
o f t h e Cr 5+
Ion.
Such dx2__2 orbltalplvoting
seems more
reasonable
andYhas been well establ~shed
by
ENDOR a n d EPR d a t a f o r Cr 5+ i n KII2As04 . g ' 1 2
Fig. 4 shows the hypothetical
pivoting
of
the d 2 2 orbital
due to interaction
of the
negatively
charged orbital
with the positive
protons.
The relation
g~l<gJ_ between
the experimental values of the g-tensor components
leads
t o t h e c o n c l u s i o n t h a t t h e dx2___2 o r b i t a l
of the
Cr 5+ i o n h a s l o w e s t e n e r g y 8 a n d Y l s p e r p e n d i c u l a r
to t h e gll d i r e c t i o n a b o v e T:. Above T: t h e g/J.
axis lles along the [II0] directlon
b u t b e l o w Tc
it lies along the [011] and [011] directions.
Such changing of the principal
axes requires
pivoting
of the y2 lobe around the c e axis due
to the
interaction
with the protons in c-axis
b o n d s w h i c h a r e o r d e r e d a b o v e T c.
Due t o c o u p l i n g
of the dx2_v2 orbital
to
the nearest
t w o p r o t o n s we o b s e r v e i n t h e EPR
spectrum a symmetry breaking
effect
when the
frequency
of reorientatton
o f t h e Cr 5+ c e n t e r s
associated
with b-bond proton jumping is lower
t h a n o u r EFR f r e q u e n c y .
Discussion
Much i n t e r e s t
has recently
centered on the
possible
existence
of a dynamic central
peak
(CP) n e a r s t r u c t u r a l
and ferroelectric
phase
transitions.
There are two points
o f v i e w on
the physical
origin
o f CP p h e n o m e n a ,
First,
some have ascribed
t h e CP d y n a m i c s t o a p u r e
lattice
excitation,
13"14 that is, an intrinsic
phenomenon.
In accord with this view, when the
transition
i s a p p r o a c h e d f r o m a b o v e T c, r e g i o n s
/~./=
~
02
4
i
0
I
I
4.2
I
I
4.4
IO~/T (K)
Figure 3
The I n F v__ss. 1 0 3 / T p l o t .
I~ 0
4.~
~ z-axis
dx2 2
0 -y
03
2
0t
OleO02
-r
oo
4.0
711
bl~
a~
c,I,
z-oxis
• =protons
Figure 4
Schematic
reorientations
o f dx2_y2 o r b i t a l
due t o m o v i n g i n h y d r o g e n b o n d s .
712
FERROELECTRIC CESIUM DIHYDROGEN PHOSPHATE
,with the short range order and symmetry of the
low temperature
phase start
to appear.
The
other possibility
i s t h a t t h e CP mode i s due t o
presence of impurities
or o t h e r d e f e c t s . 15
Halperin
and Varma 9 considered
a model in
which the distortion
in a defect unit cell may
Jump between orientations
which break symmetry,
s situation
they describe
as a relaxing
defect
cell.
The f i r s t EPR i d e n t i f i c a t i o n
of this kind
o f c e n t e r w a s made b y M u l l e r e t a~l. 8 f o r Cr 5+ i n
a KII2AsO 4 c r y s t a l .
Within the relaxing
Halperln-Vsrma
model
the reorientational
correlatlon
time • of the
defect is related to the central peak width~
by
the relation
= 2
2+ 2
F Ws/~(m s b )
(9)
w h e r e w~=A(T-Tc) i s t h e s o f t mode f r e q u e n c y a n d
b2 is proportional
to the defect concentration
A defect
concentration
o f o r d e r 10 - 5 i s s u f f i cient for
explaining
t h e CP w i d t h
in this
model. 9
In oar experiment
the fractional
Cr 5+
concentration
w a s a b o u t 10 - 3 .
However, r cannot
be fitted
b y Eq. ( i 0 ) b u t r a t h e r
by a simple
activation
process for which r =I/~.
On t h e o t h e r h a n d t h e p r e s e n c e
of ferroelectric
clusters
f a r a b o v e T_ w i t h a s i z e o f
o r d e r 102 A° i n CDP h a s b e e n w e ~ l e s t a b l i s h e d
by
a neutron scattering
experiment. 1
It is our opinion
that the ferroelectric
clusters
far above Tc are 'tpinned"
and stabilized by the defect center and by the height of
Vol. 52, No. 8
the barrier
for the b-bond protons
which are
c o u p l e d w i t h t h e dx2_V2 o r b i t a l .
As a r e s u l t
th6jump
frequency
for th~
protons interacting
w i t h t h e d e f e c t i s a b o u t 10
times lower than in undisturbed
parts
of the
crystal.
The defect
center
and associated
pinned cluster
are switched
by the arrival
of
clusters
of an opposite polarity
and not by the
s o f t mode f l u c t u a t i o n
A similar
explanation
has been ~ade by
G o n z a g a e~t a_~1.I 0 f o r b e h a v i o r
of (As04)~- cent e r s i n ADA-ADP m i x e d c r y s t a l s .
The values
obtained
f o r ~ a n d AU f o r
CDP:Cr 5+ a s w e l l a s t h e f l a t t e n i n g , o f t h e I n 1 / z
versus 103/T plot near T: are quite similar
to
the results
obtained
b y L a m o t t e e_.tt a l . 1 6 f o r
(As0a) 4- radicals
i n KDA. T h e f l a t p o r t i o n
of
the In F curve in our case with the activation
e n e r g y AU=0.05 eV and t y p i c a l ~o=10 - 1 2 s e c v a l u e
g i v e s ~=I0 - 1 1 s e c a n d c a n be c o n n e c t e d w i t h o f f center
m o t i o n o f Cr 5+ i o n s a l o n g t h e ~ a x i s
w~ich can explain
the nonaxlal
8 tensor below
Tc •
It follows
that the cooperative
dynamics
a r o u n d Cr 5+ c a n n o t b e i n t r i n s i c .
Acknowledgements--We
thank Professor
J.
E.
Drumheller
f o r t h e u s e o f h i s EPR a p p a r a t u s .
This work was supported
in part by National
S c i e n c e F o u n d a t i o n G r a n t DMR-8205280.
References
1.
2.
3.
4.
5.
6.
7.
8.
B.C.
Frazer,
D. S e m m i n g s e n , W.D. E 1 1 e n s o n
a n d G. S h l r a n e ,
Phys.
Rev.
B 20,
2745
(1979).
Y. U e s n a n d T. K o b a y a s h l , P h y s . S t a t . S o l .
( a ) ~ , 475 (1976).
H. M a t s u n a g a ,
K. I t c h and E. N a k a m n r a , J .
P h y s . S o c . J a p a n ~ 8 , 2011 ( 1 9 8 0 ) .
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