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SUPERCONDUCTIVITY AND MAGNETIC ORDER
M. Maple
To cite this version:
M. Maple. SUPERCONDUCTIVITY AND MAGNETIC ORDER. Journal de Physique Colloques,
1978, 39 (C6), pp.C6-1374-C6-1378. �10.1051/jphyscol:19786574�. �jpa-00218065�
JOURNAL DE PHYSIQUE Colloque C6, suppldment au no 8, Tome 39, aoiir 1978, page C6- 1374
SUPERCONDUCTIVITY AND MAGNET1 C ORDER
"
M.B. Maple
I n s t i t u t e for Pure and Applied Physical Sciences, University o f California, San Diego La JoZZa, California 92093, U. S.A.
Rdsum6.- Les composds supraconducteurs terres rares (TR) ternaires et pseudoternaires sont des candidats excellents pour une dtude de la coexistence de la supraconductivitd et l'ordre 2 longue portde des moments magndtiques des terres rares. Nous prdsentons un bref rdsumd des investigations rdcentes sur l'interaction entre la supraconductivitd et l'ordre magn6tique P longue portse dans les composds ternaires et pseudoternaires des TR molybdPne cha1cogCni.de et rhodium boride.
Abstract.- Superconducting ternary and pseudoternary rare earth (RE) compounds are excellent candi- dates in which to study the coexistence of superconductivi'ty and long-range ordering of W3 magnetic moments. Recent investigations of the interaction between superconductivity and long-range magnetic order in ternary and pseudoternary RE molybdenum chalcogenide and RE rhodium boride compounds are briefly reviewed.
1. INTRODUCTION.- Superconductinp ternary compounds of rare earth (RE) ions with partially-filled 4f electron shells provide a unique opportunity to study the coexistence of superconductivity and ma- gnetic order. Since the RE ions in these ternary compounds are distributed periodically throughout the lattice, ordering of the RE magnetic moments via the RKKY interaction is long-range in nature and characterized by a sharp magnetic ordering tempera- ture TM and well-defined features in the physical properties at TM. In many of these ternary RE com- pounds, the exchange interaction between the conduc- tion electron spins and RE magnetic moments is weak (the exchange interaction parameter
3
is Q 0.01 eV).This enables the compounds to retain their supercon- ductivity even in the presence of relatively large concentrations of RE ions and results in low values of TM that are comparable to the superconducting transition temperature T
.
Two systems of isostructural ternary RE compounds, therhombohedral RE molybdenum chalcogenides, RExMo S /I/ and R E 2 0 Se /2/ (x = 1.0 or 1.2),
6 8 6 8
and the tetragonal RE rhodium borides,
mhLBL
/3,4/, have been found to exhibit superconductivity
.
Ternary and pseudoternary RE compounds within these two crystal structure types have been the focus of recent investigations of the interaction between superconductivity and long-range magnetic order which are briefly reviewed. A more extensive review of
- -
'Research supported by the U.S. Department of Ener- gy under Contract No E(04-3)-34PA227.
some of the material discussed herein can be found elsewhere 151.
2. COEXISTENCE OF SUPERCONDUCTIVITY AND ANTIFERROlfA- GNETIC ORDER.- Coexistence of superconductivity and long-range order that is antiferromagnetic in nature has been reported for several of the rhombohedra1 RE molybdenum chalcogenide compounds RExMo S /6/
6 8 and RExMo6Se8 (X = 1.0 or 1.2)
.
/7-1 I/.With the exception of Ce and Eu, all of the RExMo6S8 /I/ and REXMo6Se8 /2/ compounds are super- conducting. The superconducting transition tempera- ture T of both series of compounds exhibits a cha- racteristic variation with RE that can be accounted for in terms of superconducting electron depairing via the exchange interaction between the conduction electron spins and the RE magnetic moments / 12,13/.
The Ce and Eu compounds apparently remain normal to 50 mK because of extremely large depressions of their transition temperatures due to anomalous exchange scattering associated with the Kondo effect /12/.
The onset of antiferromagnetlc order in the saperconducting state for RE Mo S compoundswith
1.2 6 8
RE = Tb, Dy and Er was recently inferred by Ishikawa and Fischer from a feature at the magnetic ordering temperature TM in the curve of the upper critical field vs temperature /7/. The occurrence of antifer- romagnetic order in the superconducting state for RExMo6Se8 (x = 1.0 or 1.2) compounds with RE = Cd, Tb and Er was deduced from the simultaneous presence o.f a pronounced lambda-type anomaly in the specific heat and a cusp-like feature in the magnetic suscep-
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786574
-tibility at TM 17-111. Magnetic susceptibility measurements in the superconducting state are possi- ble in many of the RExMo6Se8 compounds because they are extreme type I1 superconductors / 1 4 / that per- mit nearly complete penetration of the magnetic fields in which the magnetization measurements were made. The types of behavior observed are exemplified by the plots of specific heat C and inverse molar magnetic susceptibility
X-h
vs temperature for..
Er Mo Sea that are displayed in figure 1 and 2 1.2 6
respectively /lo/. The specific heat data of figure
TEMPERATURE ( K l
Fig. 1 : Specific heat C vs temperature for Er Mo Se (from Ref. 1101).
1.2 6 8
1 exhibit a jump near 6 K which is associated with the superconducting transition and a remarkable lambda-type anomaly at a temperature TI = 1.07 K that appears to be due to long-range ordering of the
~r3' magnetic moments in the superconducting state.
This is borne out by the cusp-like feature near T X in the magnetic susceptibility data of figure 2 which indicates that the long-range magnetic order is an- tiferromagnetic in nature. The entropy of ordering of the ~ r magnetic moments conforms closely with ~ +
the value corresponding to the gaound state degene- racy of the ~ r ~ions in Er + Mo Se and the ma-
1.2 6 8 '
gnetic field dependence of the lambda-type anomaly is consistent with antiferromagnetic order /lo/
Er,
,
Mo6 See745 4 F ~ e l d , powdered sample
TEMPERATURE (K)
Fig. 2 : Inverse molar suceptibility
X-i
vs tempera-ture T for Erl.,Mo6Se8 (solid and powdered samples) between 0.8 and 12 K. A plot of
x
vs T in the vici- nity of tbe Ndel temperature at 1.05 M K is displayed in the inset (from Ref. / 101).Recent powder neutron diffraction data on ErxMo Se
6 8
verify that long-range ordering of the ~ rmagnetic ~ + -moments develops at TM but it has not yet been pos-
sible to index themagnetic Bragg reflections and thereby determine the ~ rmagnetic structure ~ + / 151.
Calorimetric evidence for a magnetic transition in the superconducting state for Yb Mo S was recen-
1.0 6 8 tly reported by Alekseevski et al. 1161.
3. REENTRANT SUPERCONDUCTIVITY DUE TO THE ONSET OF FERROMAGNETIC ORDER.
-
3.1. Ternary rare earth compounds.- Destruction of superconductivity at a second lower critical tempe- rature by the onset of long-range magnetic order was reported recently for two ternary RE compounds, Ho,.,Mo,S, 1171 and ErRh4B4 1181. Neutron scattering
experiments on H o ~ . ~ Y o ~ S , 1191 and ErRh4B4 /20/
have shown that the long-range magnetic order that develops in both compounds is ferromagnetic. The compound ErRh4B4 belongs to a series of tetragonal RE rhodium borides RERh4B4 which were originally re- ported by Matthias and coworkers /3,4/ to have ground states that, with increasing 4f electron shell occu- pation number, switched from superconducting for RE = Sm and Nd, to ferromagnetic for RE = Gd, Tb, Dy and Ho, and back to superconducting for RE = Er, Tm and Lu.
C6-1376 JOURNAL DE PHYSIQUE
Shown i n f i g u r e 3 a r e p l o t s of t h e a c magne- t i c s u s c e p t i b i l i t y
xac
and e l e c t r i c a l r e s i s t a n c e of ErRh,B, a s f u n c t i o n s of temperature 1181.TEMPERATURE (KI
Fig. 3 : a c magnetic s u s c e p t i b i l i t y
x
and a c e l e c - t r i c a l r e s i s t a n c e v s temperature f o r %R~,+B,, (from Ref. 1181).Both measurements r e v e a l a t r a n s i t i o n t o t h e super- conducting s t a t e a t T = 8.7 K , followed by a t r a n -
C1
s i t i o n back t o t h e normal s t a t e a t TC2 = 0.9 K which i s t h e r m a l l y h y s t e r e t i c . I n addition,Xac e x h i b i t s a l a r g e p o s i t i v e v a l u e j u s t below Tc2 and r a p i d l y be- comes l e s s paramagnetic w i t h d e c r e a s i n g temperature.
The l a t t e r behavior i n d i c a t e s t h a t a t r a n s i t i o n t o a m a g n e t i c a l l y ordered s t a t e accompanies t h e super- conducting t o normal s t a t e t r a n s i t i o n a t T
.
Simi-c2
l a r behavior or t h e magnetic s u s c e p t i b i l i t y and e l e c - t r i c a l r e s i s t a n c e i s e x h i b i t e d by Ho Mo S . / 1 7 / .
1.2 6 8 A p l o t of t h e s p e c i f i c h e a t C of ErRh B and
4 4 i t s nonmagnetic c o u n t e r p a r t LuRh B a s a f u n c t i o n of
4 4
temperature T between 0.5 and 18 K i s d i s p l a y e d i n f i g u r e 4 1211. The ErRh B d a t a r e v e a l a s p e c i f i c
4 4
h e a t jump a t t h e upper c r i t i c a l temperature T = 8.7 K followed by a pronounced lambda-type anomaly w i t h a peak a t 0.93 K n e a r t h e lower c r i t i c a l tempe- r a t u r e Tcz. Shown i n t h e i n s e t of f i g u r e 4 i s a C v s T p l o t i n t h e v i c i n i t y of T which r e v e a l s t h e
c2
presence of a s h a r p spike-shaped f e a t u r e a t t h e peak of t h e lambda-type anomaly. T h i s f e a t u r e appears t o be due t o t h e coupled superconducting-ferromagne- t i c t r a n s i t i o n which t a k e s p l a c e a t T
.
The e n t r o p yc 2
a s s o c i a t e d w i t h t h e lambda-type anomaly i s
*
kB I n 4, i n d i c a t i n g t h a t t h e degeneracy of t h e Er 3+ J = 15/2 Hund's r u l e m l t i p l e t i s p a r t i a l l y l i f t e d by t h e c r y s t a l l i n e e l e c t r i c f i e l d , and t h a t t h e ground s t a t e i s a q u a r t e t o r a d o u b l e t s e p a r a t e d froma few d e g r e e s Kelvin. The remainder of t h e kB I n 16 e n t r o p y of t h e E r + J = 1512 Hundf s r u l e m u l t i p l e t
r e s i d e s i n a Schottky anomaly w i t h a peak n e a r 1 1 K.
Mijssbauer e f f e c t 1221 h i g h f i e l d m a g n e t i z a t i o n and thermal expansion 1231 measurements have a l s o been c a r r i e d o u t on ErRh4B4.
T(K)
F i g . 4 : S p e c i f i c h e a t C v s temperature T f o r ErRh,B, and LuRh,B,: A p l o t of C v s T i n t h e v i c i n i - t y of T i s shown i n t h e i n s e t (from Ref. 1211).
c2
3.2.Pseudoternary r a r e e a r t h compounds.-The pseudo- t e r n a r y RE systems t h a t havebeen i n v e s t i g a t e d t o d a t e belong t o t h e c l a s s of t e t r a g o n a l RE rhodium b o r i d e compounds and i n c l u d e (Erl -xC,dx)Rh4B4, 1241 (Y -x Gdx)Rh4B4, 1241 (Erl-xHox)Rh4B4, /25/ (Lul -xHox)Rh4 B 4 , 1261 and (Er l-xTmx)Rh4Bq/27/.
The ( L U ~ - ~ H O ~ ) R ~ B pseudoternary system, 4 4
whose low temperature phase diagram i s shown i n f i g u r e 5, 1'261 e x h i b i t s many of t h e f e a t u r e 4 t h a t a r e common t o a l l of t h e RERh4B4 p s e u d o t e r n a r y sys- tems t h a t have been s t u d i e d . F i g u r e 5 shows t h a t t h e upper and lower c r i t i c a l t e m p e r a t u r e s T and T
C 1 C2
and t h e magnetic o r d e r i n g temperature TM converge a t a c r i t i c a l c o n c e n t r a t i o n x = 0.92 below which a n o t h e r low-lying d o u b l e t e x c i t e d s t a t e by l e s s t h a n cr
re-entrant superconductive behavior occurs and above which only magnetic ordering occurs.
PARAMAGNETIC
T(K1 -
6 -
SUPERCONDUCTING 4 -
2 -
.
' J,,'0 I I I
0 0 0 2 0 4 0 6 0 8 10
Fig. 5 : Low temperature phase diagram for the pseudoternary system (Lu Hox)Rh4B4 (from Ref. 1264
1 -x
The ac magnetic susceptibility measurements that were employed to establish the low temperature phase diagram for (Lu Ho )Rh4B4 do not revealwhe-
1-X X
ther the curve of T vs x actually coincides with C 2
the curve of T vs x for x < x However, low tempe-
M cr'
rature heat capacity data for a (Luo.,Ho,.,)Rh4B4 compound indicate that T and TM for x < xcr are
c2
coincident, or nearly so. The low temperature heat capacity data for (Lu Ho )Rh B and the end-mem-
0 ' 5 0 ' 5 4 4
ber LuRh B and HoRh B compounds are shown in figure 4 4 4 4
6 1261. The data for (Lu Ho )Rh B exhibit a
0.5 0 . 5 4 4
T ( K I
Fig. 6 : Specific heat C vs temperature T for LuRh4B,, Hokh,B, and (Lu,,. 5Ho,. 5 ) Rh,B, (from kf./2q)
two features are similar to those that appear in the heat capacity of the ferromagnetic HoRh B com-
4 4 pound. An additional feature of the heat capacity data for (Lu Ho )Rh B is the spike-shaped ano-
0 - 5 0 . 5 4 4
maly at TM = T that is superimposed on the sawtooth
'3
shaped feature 726,281. The spike-shaped anomaly re- sembles that observed for ErRh B and, similarly, is
4 4
apparently due to the coupled superconducting-ferro- magnetic transition since it does not appear in the heat capacity data for HoRh B
.
Since T and TM4 4 c2
are coincident, the reduction of the curve of T c2 vs x relative to the linearly extrapolated curve of TM vs x for x < x (indicated by the dashed line in
cr
figure 5), is consistent with a reduced value of the conduction electron susceptibility
x
(q) for q x kF in the superconducting state (kF is the Fermi momen- tum) 1291.
4.CONCLUDING REMARKS.- Superconducting ternary and pseudoternary compounds of RE ions with partially- filled 4f electron shells are excellent candidates in which to study the interaction between supercon- ductivity and long-range ordering of RE magnetic mo- ments. The experiments have thus far revealed the development of long-range magnetic order in the su- perconducting state, the coexistence of superconduc- tivity and long-range antiferromagnetic order, the destruction of superconductivity at a second lower critical temperature T by the onset of long-range
c2
ferromagnetic order, and a new spike-shaped specific heat anomaly at T which is apparently associated
c2
with the coupled superconducting-ferromagnetic tran- sition. It can be anticipated that the experiments reviewed herein and future investigations on super- conducting ternary and pseudoternary RE compounds will make it possible to establish the criteria for,
and critically test theories of /29/, the coexistence of superconductivity and various types of orderad magnetic structures.
specific heat jump at T a sawtooth-shaped feature
~ 1 '
associated with long-range magnetic order that oc- curs at a temperature T T and a low tempera-
M c2'
ture tail which is apparently the high temperature portion of Ho nuclear Schottky anomaly. The latter
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JOURNAL D E PHYSIQUE
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