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Crystal field and magnetic moments of rare-earth ions in REBa2Cu3O-x (RE=Ce,,Yb)
% Solid State Communications, Vol.65,No.10, pp.1103-1106, 1988. ~8~_~4Printed in Great Britain.
0038-1098/88 $3.00 + .00 Pergamon Press plc
CRYSTAL FZELD AND HAGNETIC HOMENTS OF RARE-EARTH IONS IN REBa2Cu307.x (RE-Ca .....
V.
Znst£tute
Yb)
Nekvae£1
o f Phys£cs, C z e c h o s l . Acad. S c £ . , Na S l o v a n c e 2, 180 40 Praha 8, C z e c h o s l o v a k i a (Received23 november 1987byE. F. BERTAUT)
The s u p e r p o e i t £ o n model i s used to p r e d i c t t h e v a l u e s o f t h e f o u r t h - and s i x t h - o r d e r crystal-field p a r a m e t e r s and c o n s e q u e n t l y a l s o t h e n a t u r e of m a g n e t i c moments o f r a r e - e a r t h i o n s i n s u p e r c o n d u c t i n g o r t h o r h o m b l c phase o f REBa2Cu307.x(RE-Ce . . . . . Y b ) . A s i m i l a r i t y between t h e c o o r d i n a t £ o n dodecahedra o f r a r e - e a r t h i o n s i n REBs2Cu307. x and g a r n e t s i s used f o r t h i s p u r p o s e . The l o w - t e m p e r a t u r e m a g n e t i c moments o f r a r e - e a r t h i o n s a r e a n i e o t r o p i c and partially quenched. The q u a n t i t a t i v e c o n c l u s i o n s are i n g e n e r a l hampered by s t r o n g dependence o f the magnetic moments on the c r y s t a l - f i e l d p a r a m e t e r s o f second o r d e r . As t h e e u p e r p o s i t i o n model g i v e s no u s e f u l p r e d i c t £ o n f o r t h e s e p a r a m e t e r s , i t w£11 be n e c e s s a r y to d e t e r m i n e them by f £ t t i n g to s u i t a b l e e x p e r £ m e n t a l d a t a .
Zt a p p e a r s to be a w e l l e s t a b l i s h e d e x perimental fact that the superconductiv i t y and magnetism o f r a r e - e a r t h ( R E )
r e s p o n s i b l e f o r p a r t i a l q u e n c h i n g of t h e RE moments i n o r t h o r h o m b i c symmetr y l h s i t e s o f REBa2Cu307_ x . We s t a r t w i t h t h e CF h a m i l t o n i a n i n t h e u s u a l form o f e x p a n s i o n i n t e n s o r o p e r a t o r s
subsystem i n REBa2Cu307. x compound co.. exist without apparent correlation /1, 2/. This finding, itself extremely interesting, a l l o w s to s t u d y t h e s e two phenomena to a g r e a t e x t e n t s e p a r a t e l y . The RE i o n s r e t a i n t h e i r l o c a l moments which order antiferromagnetically at t e m p e r a t u r e s around one k e l v i n . The magn e t i c o r d e r was d i s c u s s e d i n terms o f both, the dipole-dipole / 3 / and RKKY i n t e r a c t i o n / 4 / . Zt f o l l o w s from t h e s p e c i f i c h e a t and m a g n e t i z a t i o n measurements t h a t t h e RE moments a t low temperatures in general differ considerably from t h e i r f r e e - i o n v a l u e s / 4 . 7 / . The p u r p o s e o f t h i s communication is
to e s t i m a t e
the crystal
field
cn
m
/e/: ~5-
n
T enm(Cn + C.m ) nm n-2,4,6;
m-0,2,6;
;
(1) m --= n
where the Bnm a r e s . c . CF p a r a m e t e r s , In o x i d e s t h e y a r e u s u a l l y t r e a t e d as phenomsnolog£cal q u a n t i t i e s to be d e t e r m i n e d by f i t t i n g to some r e l i a b l e experimental data (optical transitions, EPR s p e c t r a , e t c . ) . S i n c e such d a t a a r e n o t a v a i l a b l e f o r REBa2Cu307_x we p r o pose to e s t i m a t e t h e CF p a r a m e t e r s i n t h i s compound u s i n g the eemiemp£ricaZ
(CF) 1103
1104
RARE EARTH IONS IN REBa2Cu307_ x (RE=Ce,...,Yb)
superpos£t£on model / 9 / . sumes t h a t
The imdeZ p r e -
the CF o f RE i o n i s composed
of independent, axially tributions
s y m m e t r i c , con-
of individual
l£gands. This
e n a b l e s , among o t h e r s , to e x t r a p o l a t e the CF p a r a m e t e r s from one c r y s t a l compound to a n o t h e r , as long as the RE i o n
Vol. 65, No. 10
The r e s p e c t i v e exponents a r e t 4 = g . g , t 6 = 3 . 9 , the i n t r i n s i c parameters (in cm" I ) a r e supposed to be l i n e a r f u n c t i ons o f
the RE i o n r a d i i
r (in ~),
for
Ro = 2 . 3 8 ~ : B 4 ( 2 . 3 8 ~) - 4 4 7 0 r - 3 9 0 9 , B 6 ( 2 . 3 8 ~) = 20?Or -1706 / 9 / ° The l a t t i c e
parameters f o r
the s u -
i s i n both cases s u r r o u n d e d by e l m i l a r
p e r c o n d u c t i n g h i g h -T c o r t h o r h o m b i c
coordination
phase o f the REBa2CU3OT_x a r e w i d e l y a v a i l a b l e i n the l i t e r a t u r e , sog. / 1 2 / .
ty exists
p o l y h e d r o n . Such s l m i l a r £ -
between the c o o r d i n a t i o n
decahedra o f RE i n g a r n e t s / 9 /
do-
Only rarely,
and
REBa2Cu307. x / 1 0 / , presuming t h a t the 2 r , 2s s i t e s o f the l a t t e r compound a r e fuZZy o c c u p i e d / 1 1 /
by twovaZent o x y -
gens. The dodecahedra a r e i n both s y s -
however, a r e a l s o g i v e n a -
t o m i c p o s i t £ o n a Z p a r a m e t e r s f o r RE other
than Y / 1 1 ,
the s t r u c t u r a l with
13/o F u r t h e r m o r e , a l l
d a t a should be t r e a t e d
care as t h e y depend not o n l y on
tems formed by e i g h t 02- l i g a n d s l o c a -
the exper£mentaZ methods used to s t u d y
ted i n the c o r n e r s o f s l i g h t l y distorted cubes ( t h e d i s t o r t i o n is larger in
the s t r u c t u r e s ,
g a r n e t s ) a t two d i f f e r e n t
d i s t a n c e s R1
and R2 from the c e n t r a l RE l o n e . These d i s t a n c e s a r e c l o s e to 2 . 4 ~ . The s u perposition
model i s a p p l i e d here to
the n - 4,6 CF parameters electrostatic stant
contribution
o n l y as the o f more d i -
i o n s to second o r d e r p a r a m e t e r s
i s i n g e n e r a l c o n s i d e r a b l e . The CF a xes are taken i d e n t i c a l w i t h c r y s t a l l o g r a p h i c axes a , b , c / l O / . The s u p e r p o s i t i o n model a l l o w s to e x p r e s s the CF p a r a m e t e r s i n terms o f the " i n t r i n s i c Bnm =
i ~ knm B n ( R I )
l where knm is
most RE i o n s i n / 1 2 /
for
the purpose o f
o u r model c a l c u l a t i o n . For r e m a i n i n g lone the p a r a m e t e r s were e i t h e r l i n e a r Zy i n t e r p o l a t e d
(To) o r e x t r a p o l a t e d
( P r , Ce) from the v a l u e s f o r n e a r e s t - n e i g h b o u r RE compounds. F u r t h e r m o r e , we d i s r e g a r d the d i f f e r e n c e between the f r a c t i o n a l z - c o o r d i n a t e s of 02- l i g s n d e a t 2 r and 2s s i t e s , ses z = 0 . 3 8 ,
t a k i n g i n both c a -
for all
RE compounds. Zt
to be noted t h a t n e l t h e r
ve mentioned s i m p l i f i c a t i o n s ,
i = 1, 2 ,
the " c o o r d i n a t i o n
(2)
factor"
of pre-
p a r a t i o n . Having t h i s i n mind we have chosen the l a t t i c e p a r a m e t e r s g i v e n f o r
is
parameters" B n ( R i ) :
but a l s o on the c o n t e n t
of oxygen, g i v e n by c o n d i t i o n s
structure
affects
of
the abo-
concerning
the q u a l i t a t i v e
cZusions given below. The CF p a r a m e t e r s r e s u l t i n g
confrom
d e t e r m i n e d by a n g u l a r c o o r d i n a t e s o f
the s u p e r p o s i t i o n - m o d e l approach a r e
f o u r l l g a n d s a t the same d i s t a n c e R1
summarized i n Table 1. I t
/9/.
The i n t r i n s i c
p a r a m e t e r s a r e usu-
a l l y assumed to depend on the RE - 0 2 d i s t a n c e R as en(R ) . Bn(Ro)(Ro/R)
tn (3)
Taking the g a r n e t v a l u e s o f Bn and t n we can use e q u a t i o n s ( 2 , 3) to c a l c u l a t e the h i g h e r - o r d e r CF paramet e r s i n REBa2Cu307.x f o r any RE i o n presuming t h a t the s t r u c t u r e s o f the coordination
the CF symmetry i n REBa2Cu307. x i s c l o s e r to c u b i c one than i n g a r n e t s , i n accordance w i t h s t r u c t u r e s o f the c o r responding c o o r d i n a t i o n
,
dodecahedra a r e known.
i e seen t h a t
dodecahedra.
Zn f a c t , the p a r a m e t e r s B62, B66 can be put e q u a l to z e r o , f o r most p r a c t i c a l purposes. With the CF p a r a m e t e r s i n hand, one can i n p r i n c i p l e use the s t a n d a r d f o r m u l a e to c a l c u l a t e the magnetic moments o f RE i o n s i n a p p l i e d magnetic
Vol. 65, No. 10
1105
RARE EARTH IONS IN REBa2Cu307_x (RE=Ce,...,Yb)
Table 1
Crystal-field
p a r a m e t e r s ( i n cm" 1 )
f o r RE i o n s in
REBa2Cu307. x
,
fields. rature
i
i
•
•
i
i
i
i
i
,
i
i
,
RE
B40
B42
B44
B60
B62
B64
B66
Ce Pr
-3444 - 3267
275 223
195t 1847
1030 976
-3 -3
2129 2026
4 3
Nd
-3087
175
1742
922
-2
1923
2
Sm
-2737
115
1543
829
-1
1732
2
Eu
-2595
138
1463
791
-1
1651
2
To Dy
-2289 -2140
131 124
1289 1205
709 671
-1 -1
1486 1404
2 2
Ho
-1985
125
1115
629
-1
1324
2
Er
-1852
123
1039
595
-1
1254
2
Tm
-1723
119
965
562
-1
1188
2
Yb
-1627
115
907
531
-1
1135
2
Differentiating
the l o w - t e m p e -
magnetic moments o f all i o n s o f
the RE s e r i e s w i t h
r e s p e c t to i n d i v i -
model, o u r c o n c l u s i o n s c o n c e r n i n g the l o w - t e m p e r a t u r e m a g n e t i c momenta o f RE i o n s can be o n l y q u a l i t a t i v e :
(i)
d u a l CF p a r a m e t e r s we have f o u n d , how-
moments a r e a n i s o t r o p i c
ever,
ment w i t h e x p e r i m e n t a l d a t a / 5 ,
that while
very little ters
the moments v a r y but
with higher-order
in most cases,
parame-
they are generally
significantly their
the
and, i n a g r e e 6/,
l o w e r i n comparison w i t h
free-ion
values,
(li)
it should
parame-
be a s i m p l e t a s k to d e t e r m i n e the m i s -
ters B20, B22. This may be illustrated on the 4 . 2 K moment o f Oy3+ i n
s i n g p a r a m e t e r s B20, B22 by comparison o f the t h e o r y w i t h s u i t a b l e e x p e r i m e n -
DyBa2Cu307_ x . C o n s i d e r i n g the magnetic f i e l d o f 5 T a p p l i e d a l o n g the c r y s -
e.g.
very sensitive
tallographic
to second-order
axes a , , b ,
c, and k e e p i n g
the n = 4, 6 p a r a m e t e r s from Table 1
tal
d a t a . We e x p e c t t h a t such d a t a ,
tals,
the m a g n e t i z a t i o n o f s i n g l e will
be a v a i l a b l e
crys-
very probably
i n the n e a r e s t f u t u r e . F i n a l l y . we w i s h to note t h a t
the
c o n s t a n t , we v a r y B2O and B22. As t y p i c a l examples we show the r e s u l t s f o r
above mentioned i m p o r t a n c e o f
B20 = O, B22 = -100 c m ' l :
c o n d - o r d e r terms i n the CF h a m i Z t o n i a n
Ha = 1 o l ,
Hb = 8 . 7 , Hc = 1 . 6 p ." and f o r B20=100, B22 - 100 cm-Z: Ha = B 6 . 9 , Hb - 2 . 6 , Hc = 6 . 7 PB" B e s i d e s Dy, p a r t i c u l a r l y
has an a d d i t i o n a l
the s e -
consequence:although
the s t r u c t u r e s o f the c o o r d i n a t i o n dodecahedra a r e r a t h e r similar, the mag-
s e n s i t i v e to the v a l u e s o f B2O, B22 appear moments of Sm, Tb, Ho, E r , the
netic
least
REBa2Cu307_ x and i t s n o n s u p e r c o n d u c t i n g t e t r a g o n a Z phase / l O / can d i f f e r considerably.
s e n s i t i v e those o f Nd, Yb. Zt i s thus o b v i o u s t h a t , even i n
the c o n v e n i e n t
framework p r o v i d e d f o r
the CF c a l c u l a t i o n
by the a u p e r p o s i t i o n
moments o f
the i d e n t i c a l
RE i o n
i n the o r t h o r h o m b i c phase o f
1106
RARE EARTH IONS IN REBa2Cu307_x (RE=Ce,... ,Yb)
Vol. 65, No. 10
REFERENCES 1.
2.
3°
E.E. A l p , noy, D°G. K. Zhang, a l t t e d to
L. Sod.rheim, G.K. SheHtnk$, O.W. Capons ZZ, and 8.D. Ounlap, subPhys.Rev°Lett.
O.R° Thompson, D°K. C h r i s t e n , S°T. Sekula, B.C. SaZee, and LeA. Boatner, Phys.Rev. B 36, 836 (1987).
8.
9. 10°
B.D. Dunlap, H° Sleek1, Z. Sung a l l s , D.G. Hinkse K. Zhang, C. Segre, S.K. Hal¢k, and E°E.Alp, prepr£nt.
11.
4.
A.P. Ramtrez, L.F. Schneeleyer, and O°V. Waezczak, p r e p r £ n t .
12°
5.
F. H u l l t g e r , and H.R. O t t , Z. Phys. B 6~7, 291 (1987).
6.
O° ~ebek, O. Stehno, V. Nekvae£Z, 5. ~ a f r a t a , O. ~rdmek, Z. Hru~ks, L. Havela, V° Sechovek~, P° Svobode, and V. Valvoda, p h y e . s t a t . e e l . ( t o be p u b l i s h e d ) .
7.
S.E. Brown, O.D° Thompson, O.O. W i l l i e , R.H. Aik£n, E° Z i r n -
I3°
g i e b l , 3 . L . Sm£th, and Z . F£sk, Phys.Rev. B 3.~6, 2298 (1987). B.G, wybourne, Spectroecop£c Prop e r t i e s of Rare E a r t h s , X n t e r ec£ence P u b l . , New York, 1965. V. Nekvae£1, Czech.D.Phye. B 29.9, 785 (1979). Z. O£r~k, E. Po12ert, A. Tf£eka, and 5. V r a t £ e l a v , p h y s . . t a t . e e l . ( t o be p u b l i s h e d ) . H. Aeano, T. Zeh£gak£, K. Tak£ta, Opn.O.Appl.Phye. 2.~.6, L1064 (1987), end references c t t e d there£n. O.H. Tarascon, W.R. HcK£nnon, L.H. Greene, G.W. H u l l , and E.H. Vogel, Phye.Rev. B 36, 226 (1987). 8.D. Dunlap, H° Slaek£, D°G. Hinks, L° Sod.rheim, H. Bone, Ko Zhang, C. Segre, G.W° Crabtree, W°K. Kwok, S.K. HaZik, Zvan K. S c h u l l e r , O°D. Oorgeneen, and Z. Sungatla, O.Hagn.Hagn.Hat. ( t o be p u b l i s h e d ) .
0038-1098/88 $3.00 + .00 Pergamon Press plc
CRYSTAL FZELD AND HAGNETIC HOMENTS OF RARE-EARTH IONS IN REBa2Cu307.x (RE-Ca .....
V.
Znst£tute
Yb)
Nekvae£1
o f Phys£cs, C z e c h o s l . Acad. S c £ . , Na S l o v a n c e 2, 180 40 Praha 8, C z e c h o s l o v a k i a (Received23 november 1987byE. F. BERTAUT)
The s u p e r p o e i t £ o n model i s used to p r e d i c t t h e v a l u e s o f t h e f o u r t h - and s i x t h - o r d e r crystal-field p a r a m e t e r s and c o n s e q u e n t l y a l s o t h e n a t u r e of m a g n e t i c moments o f r a r e - e a r t h i o n s i n s u p e r c o n d u c t i n g o r t h o r h o m b l c phase o f REBa2Cu307.x(RE-Ce . . . . . Y b ) . A s i m i l a r i t y between t h e c o o r d i n a t £ o n dodecahedra o f r a r e - e a r t h i o n s i n REBs2Cu307. x and g a r n e t s i s used f o r t h i s p u r p o s e . The l o w - t e m p e r a t u r e m a g n e t i c moments o f r a r e - e a r t h i o n s a r e a n i e o t r o p i c and partially quenched. The q u a n t i t a t i v e c o n c l u s i o n s are i n g e n e r a l hampered by s t r o n g dependence o f the magnetic moments on the c r y s t a l - f i e l d p a r a m e t e r s o f second o r d e r . As t h e e u p e r p o s i t i o n model g i v e s no u s e f u l p r e d i c t £ o n f o r t h e s e p a r a m e t e r s , i t w£11 be n e c e s s a r y to d e t e r m i n e them by f £ t t i n g to s u i t a b l e e x p e r £ m e n t a l d a t a .
Zt a p p e a r s to be a w e l l e s t a b l i s h e d e x perimental fact that the superconductiv i t y and magnetism o f r a r e - e a r t h ( R E )
r e s p o n s i b l e f o r p a r t i a l q u e n c h i n g of t h e RE moments i n o r t h o r h o m b i c symmetr y l h s i t e s o f REBa2Cu307_ x . We s t a r t w i t h t h e CF h a m i l t o n i a n i n t h e u s u a l form o f e x p a n s i o n i n t e n s o r o p e r a t o r s
subsystem i n REBa2Cu307. x compound co.. exist without apparent correlation /1, 2/. This finding, itself extremely interesting, a l l o w s to s t u d y t h e s e two phenomena to a g r e a t e x t e n t s e p a r a t e l y . The RE i o n s r e t a i n t h e i r l o c a l moments which order antiferromagnetically at t e m p e r a t u r e s around one k e l v i n . The magn e t i c o r d e r was d i s c u s s e d i n terms o f both, the dipole-dipole / 3 / and RKKY i n t e r a c t i o n / 4 / . Zt f o l l o w s from t h e s p e c i f i c h e a t and m a g n e t i z a t i o n measurements t h a t t h e RE moments a t low temperatures in general differ considerably from t h e i r f r e e - i o n v a l u e s / 4 . 7 / . The p u r p o s e o f t h i s communication is
to e s t i m a t e
the crystal
field
cn
m
/e/: ~5-
n
T enm(Cn + C.m ) nm n-2,4,6;
m-0,2,6;
;
(1) m --= n
where the Bnm a r e s . c . CF p a r a m e t e r s , In o x i d e s t h e y a r e u s u a l l y t r e a t e d as phenomsnolog£cal q u a n t i t i e s to be d e t e r m i n e d by f i t t i n g to some r e l i a b l e experimental data (optical transitions, EPR s p e c t r a , e t c . ) . S i n c e such d a t a a r e n o t a v a i l a b l e f o r REBa2Cu307_x we p r o pose to e s t i m a t e t h e CF p a r a m e t e r s i n t h i s compound u s i n g the eemiemp£ricaZ
(CF) 1103
1104
RARE EARTH IONS IN REBa2Cu307_ x (RE=Ce,...,Yb)
superpos£t£on model / 9 / . sumes t h a t
The imdeZ p r e -
the CF o f RE i o n i s composed
of independent, axially tributions
s y m m e t r i c , con-
of individual
l£gands. This
e n a b l e s , among o t h e r s , to e x t r a p o l a t e the CF p a r a m e t e r s from one c r y s t a l compound to a n o t h e r , as long as the RE i o n
Vol. 65, No. 10
The r e s p e c t i v e exponents a r e t 4 = g . g , t 6 = 3 . 9 , the i n t r i n s i c parameters (in cm" I ) a r e supposed to be l i n e a r f u n c t i ons o f
the RE i o n r a d i i
r (in ~),
for
Ro = 2 . 3 8 ~ : B 4 ( 2 . 3 8 ~) - 4 4 7 0 r - 3 9 0 9 , B 6 ( 2 . 3 8 ~) = 20?Or -1706 / 9 / ° The l a t t i c e
parameters f o r
the s u -
i s i n both cases s u r r o u n d e d by e l m i l a r
p e r c o n d u c t i n g h i g h -T c o r t h o r h o m b i c
coordination
phase o f the REBa2CU3OT_x a r e w i d e l y a v a i l a b l e i n the l i t e r a t u r e , sog. / 1 2 / .
ty exists
p o l y h e d r o n . Such s l m i l a r £ -
between the c o o r d i n a t i o n
decahedra o f RE i n g a r n e t s / 9 /
do-
Only rarely,
and
REBa2Cu307. x / 1 0 / , presuming t h a t the 2 r , 2s s i t e s o f the l a t t e r compound a r e fuZZy o c c u p i e d / 1 1 /
by twovaZent o x y -
gens. The dodecahedra a r e i n both s y s -
however, a r e a l s o g i v e n a -
t o m i c p o s i t £ o n a Z p a r a m e t e r s f o r RE other
than Y / 1 1 ,
the s t r u c t u r a l with
13/o F u r t h e r m o r e , a l l
d a t a should be t r e a t e d
care as t h e y depend not o n l y on
tems formed by e i g h t 02- l i g a n d s l o c a -
the exper£mentaZ methods used to s t u d y
ted i n the c o r n e r s o f s l i g h t l y distorted cubes ( t h e d i s t o r t i o n is larger in
the s t r u c t u r e s ,
g a r n e t s ) a t two d i f f e r e n t
d i s t a n c e s R1
and R2 from the c e n t r a l RE l o n e . These d i s t a n c e s a r e c l o s e to 2 . 4 ~ . The s u perposition
model i s a p p l i e d here to
the n - 4,6 CF parameters electrostatic stant
contribution
o n l y as the o f more d i -
i o n s to second o r d e r p a r a m e t e r s
i s i n g e n e r a l c o n s i d e r a b l e . The CF a xes are taken i d e n t i c a l w i t h c r y s t a l l o g r a p h i c axes a , b , c / l O / . The s u p e r p o s i t i o n model a l l o w s to e x p r e s s the CF p a r a m e t e r s i n terms o f the " i n t r i n s i c Bnm =
i ~ knm B n ( R I )
l where knm is
most RE i o n s i n / 1 2 /
for
the purpose o f
o u r model c a l c u l a t i o n . For r e m a i n i n g lone the p a r a m e t e r s were e i t h e r l i n e a r Zy i n t e r p o l a t e d
(To) o r e x t r a p o l a t e d
( P r , Ce) from the v a l u e s f o r n e a r e s t - n e i g h b o u r RE compounds. F u r t h e r m o r e , we d i s r e g a r d the d i f f e r e n c e between the f r a c t i o n a l z - c o o r d i n a t e s of 02- l i g s n d e a t 2 r and 2s s i t e s , ses z = 0 . 3 8 ,
t a k i n g i n both c a -
for all
RE compounds. Zt
to be noted t h a t n e l t h e r
ve mentioned s i m p l i f i c a t i o n s ,
i = 1, 2 ,
the " c o o r d i n a t i o n
(2)
factor"
of pre-
p a r a t i o n . Having t h i s i n mind we have chosen the l a t t i c e p a r a m e t e r s g i v e n f o r
is
parameters" B n ( R i ) :
but a l s o on the c o n t e n t
of oxygen, g i v e n by c o n d i t i o n s
structure
affects
of
the abo-
concerning
the q u a l i t a t i v e
cZusions given below. The CF p a r a m e t e r s r e s u l t i n g
confrom
d e t e r m i n e d by a n g u l a r c o o r d i n a t e s o f
the s u p e r p o s i t i o n - m o d e l approach a r e
f o u r l l g a n d s a t the same d i s t a n c e R1
summarized i n Table 1. I t
/9/.
The i n t r i n s i c
p a r a m e t e r s a r e usu-
a l l y assumed to depend on the RE - 0 2 d i s t a n c e R as en(R ) . Bn(Ro)(Ro/R)
tn (3)
Taking the g a r n e t v a l u e s o f Bn and t n we can use e q u a t i o n s ( 2 , 3) to c a l c u l a t e the h i g h e r - o r d e r CF paramet e r s i n REBa2Cu307.x f o r any RE i o n presuming t h a t the s t r u c t u r e s o f the coordination
the CF symmetry i n REBa2Cu307. x i s c l o s e r to c u b i c one than i n g a r n e t s , i n accordance w i t h s t r u c t u r e s o f the c o r responding c o o r d i n a t i o n
,
dodecahedra a r e known.
i e seen t h a t
dodecahedra.
Zn f a c t , the p a r a m e t e r s B62, B66 can be put e q u a l to z e r o , f o r most p r a c t i c a l purposes. With the CF p a r a m e t e r s i n hand, one can i n p r i n c i p l e use the s t a n d a r d f o r m u l a e to c a l c u l a t e the magnetic moments o f RE i o n s i n a p p l i e d magnetic
Vol. 65, No. 10
1105
RARE EARTH IONS IN REBa2Cu307_x (RE=Ce,...,Yb)
Table 1
Crystal-field
p a r a m e t e r s ( i n cm" 1 )
f o r RE i o n s in
REBa2Cu307. x
,
fields. rature
i
i
•
•
i
i
i
i
i
,
i
i
,
RE
B40
B42
B44
B60
B62
B64
B66
Ce Pr
-3444 - 3267
275 223
195t 1847
1030 976
-3 -3
2129 2026
4 3
Nd
-3087
175
1742
922
-2
1923
2
Sm
-2737
115
1543
829
-1
1732
2
Eu
-2595
138
1463
791
-1
1651
2
To Dy
-2289 -2140
131 124
1289 1205
709 671
-1 -1
1486 1404
2 2
Ho
-1985
125
1115
629
-1
1324
2
Er
-1852
123
1039
595
-1
1254
2
Tm
-1723
119
965
562
-1
1188
2
Yb
-1627
115
907
531
-1
1135
2
Differentiating
the l o w - t e m p e -
magnetic moments o f all i o n s o f
the RE s e r i e s w i t h
r e s p e c t to i n d i v i -
model, o u r c o n c l u s i o n s c o n c e r n i n g the l o w - t e m p e r a t u r e m a g n e t i c momenta o f RE i o n s can be o n l y q u a l i t a t i v e :
(i)
d u a l CF p a r a m e t e r s we have f o u n d , how-
moments a r e a n i s o t r o p i c
ever,
ment w i t h e x p e r i m e n t a l d a t a / 5 ,
that while
very little ters
the moments v a r y but
with higher-order
in most cases,
parame-
they are generally
significantly their
the
and, i n a g r e e 6/,
l o w e r i n comparison w i t h
free-ion
values,
(li)
it should
parame-
be a s i m p l e t a s k to d e t e r m i n e the m i s -
ters B20, B22. This may be illustrated on the 4 . 2 K moment o f Oy3+ i n
s i n g p a r a m e t e r s B20, B22 by comparison o f the t h e o r y w i t h s u i t a b l e e x p e r i m e n -
DyBa2Cu307_ x . C o n s i d e r i n g the magnetic f i e l d o f 5 T a p p l i e d a l o n g the c r y s -
e.g.
very sensitive
tallographic
to second-order
axes a , , b ,
c, and k e e p i n g
the n = 4, 6 p a r a m e t e r s from Table 1
tal
d a t a . We e x p e c t t h a t such d a t a ,
tals,
the m a g n e t i z a t i o n o f s i n g l e will
be a v a i l a b l e
crys-
very probably
i n the n e a r e s t f u t u r e . F i n a l l y . we w i s h to note t h a t
the
c o n s t a n t , we v a r y B2O and B22. As t y p i c a l examples we show the r e s u l t s f o r
above mentioned i m p o r t a n c e o f
B20 = O, B22 = -100 c m ' l :
c o n d - o r d e r terms i n the CF h a m i Z t o n i a n
Ha = 1 o l ,
Hb = 8 . 7 , Hc = 1 . 6 p ." and f o r B20=100, B22 - 100 cm-Z: Ha = B 6 . 9 , Hb - 2 . 6 , Hc = 6 . 7 PB" B e s i d e s Dy, p a r t i c u l a r l y
has an a d d i t i o n a l
the s e -
consequence:although
the s t r u c t u r e s o f the c o o r d i n a t i o n dodecahedra a r e r a t h e r similar, the mag-
s e n s i t i v e to the v a l u e s o f B2O, B22 appear moments of Sm, Tb, Ho, E r , the
netic
least
REBa2Cu307_ x and i t s n o n s u p e r c o n d u c t i n g t e t r a g o n a Z phase / l O / can d i f f e r considerably.
s e n s i t i v e those o f Nd, Yb. Zt i s thus o b v i o u s t h a t , even i n
the c o n v e n i e n t
framework p r o v i d e d f o r
the CF c a l c u l a t i o n
by the a u p e r p o s i t i o n
moments o f
the i d e n t i c a l
RE i o n
i n the o r t h o r h o m b i c phase o f
1106
RARE EARTH IONS IN REBa2Cu307_x (RE=Ce,... ,Yb)
Vol. 65, No. 10
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