ANISOTROPY OF Hc2 IN THE CHEVREL PHASES

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ANISOTROPY OF Hc2 IN THE CHEVREL PHASES

M. Decroux, B. Seeber, Ø Fischer, R. Delesclefs, R. Flükiger

To cite this version:

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JOURNAL DE PHYSIQUE

_{Colloque C6, supplkment au}

_no

_8,

_{Tome 39, aolit}

_1978,

_page

_C6-363

ANISOTROPY O F

H c 2

IN T H E

CHEVREL

PHASES

M. Decroux, B. Seeber,

0

F i s c h e r , R . D e l e s c l e f s and R. ~ l ~ k i ~ e r *

Departement de Physique de Za Matidre CondensBe, UniversitB de GenBve, 32 Bd drYvoy 1211 GenBve 4, SwitzerZand.

I

Massachussets I n s t i t u t e of Technology, Supercond. Materials Group, Cambridge, Mass. 021139, U.S.A.

Rlsum6.- Nous avons mesure l ' a n i s o t r o p i e du champ c r i t i q u e s u r un m o n o c r i s t a l Mo6Se8. Ce composs montre une a n i s o t r o p i e d ' environ 12 %

.

Le champ c r i t i q u e Hc2 e s t maximum l o r s q u e H e s t p a r a l l e l e 1 l ' a x e t e r n a i r e . L'accord e n t r e nos r Q s u l t a t s e t l e s p r 6 d i c t i o n s b a s s e s s u r l e modlle d e masse e f f e c t i v e e s t e x c e l l e n t . Nous d i s c u t o n s Qgalement ce nouveau r d s u l t a t a i n s i que l e s prSc6dents s u r l a base des r g c e n t s c a l c u l s de bande.

A b s t r a c t . - The a n i s o t r o p y of t h e upper c r i t i c a l f i e l d of Mo6Se8has been measured. This compound shows an a n i s o t r o p y of about 12 %, w i t h t h e maximum Hc? v a l u e when H i s p a r a l l e l t o

t h e t e r n a r y a x i s . The e f f e c t i v e mass model w i t h t h e mass r a t i o E~

2

1.25 f i t s our r e s u l t s w e l l . We d i s c u s s t h i s new r e s u l t and p r e v i o u s ones on t h e b a s i s of band s t r u c t u r e s c a l c u l a - t i o n s .

The high c r i t i c a l f i e l d s of t h e Chevrel phases / I / ( M ~ M O ~ X ~ M = m e t a l ,

x

= S, Se, Te) a r e b e l i e v e d t o r e s u l t from t h e p a r t i c u l a r s t r u c t u r e of t h e s e compounds. These m a t e r i a l s have a rhombohedral hexagonal c r y s t a l s t r u c t u r e w i t h t h e space group R?

.

The otlly symmetry element i s t h e t h r e e f o l d in- v e r s i o n a x i s i n t h e rhombohedral

[I

1

I]

d i r e c t i o n . The Mo6X8 c l u s t e r s a r e elongated along t h e t e r n a r y a x i s by a few p e r c e n t s depending on t h e oxydation s t a t e of t h e t h i r d element M 121.

The l a t t i c e b e i n g almost c u b i c we do n o t I expect any a n i s o t r o p y t o occur.However i n s i n g l e c r y s t a l s of PbMo6S8 PbMo6Sea and SnMo6Se8 we found t h e same a n i s o t r o p y of H of about 20 % 1 3 1 . For

c2

SnMo6Se8, t h e e f f e c t i v e mass model w i t h t h e mass r a t i o c 2 = 0.69 f i t s our d a t a w e l l , t h e r e f o r e we do n o t e x p l a i n t h i s b i g a n i s o t r o p y w i t h t h e s m a l l rhombohedral deformation. I n o r d e r t o check whether t h e r e i s any c o r r e l a t i o n between t h e a n i s o t r o p y and t h e rhombohedral a n g l e aR ( s e e t a b l e I) we have measured a Mo6Se8 s i n g l e c r y s t a l . A t h r e e a x i s gonio- meter allows u s t o t u r n t h e c r y s t a l i n any d i r e c -

t i o n . We measured t h e r e s i s t i v e t r a n s i t i o n by a f o u r probe method. I n our measurements we chose a c u r r e n t of 2.5 mA a f t e r having checked t h a t t h e r e i s no change i n t h e t r a n s i t i o n form up t o 4 mA.

The c r i t i c a l f i e l d was d e f i n e d a s t h e midpoint of

F i g u r e 1 shows t h e c r i t i c a l f i e l d dependence of Mo6Se8 w i t h t h e a n g l e 8 between H and t h e t e r n a r y a x i s a t 4.2 K . For t h i s compound Hc2 h a s a maximum v a l u e when t h e t e r n a r y a x i s i s p a r a l l e l t o H , un-

l i k e t h e t h r e e t e r n a r y compounds mentioned b e f o r e , which show a minimum of Hc2 f o r t h e same o r i e n t a -

t i o n .

I

experimental pant

Mo6

-.-

theoret~cal curve

41 ,

1

current 1 H

I

angle ( degree ) F i g . I : Angular dependence of H a t 4.2 K.8 i s c2 t h e a n g l e between t h e t e r n a r y a x i s and t h e e x t e r - n a l f i e l d . t h e r e s i s t i v e t r a n s i t i o n . We measured t h e a n g u l a r

and temperature dependence of Hc2 w i t h a pulsed I n f i g u r e 2 we have p l o t t e d t h e temperature f i e l d magnet. The r a t e of change of H up t o dependence of Hc2 f o r MogSe8. The experimental 5500 kG/s has no i n f l u e n c e on t h e t r a n s i t i o n . data does n o t f o l l o w t h e t h e o r e t i c a l p r e d i c t i o n of

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WHH w i t h o u t paramagnetic l i m i t a t i o n . The almost l i n e a r dependence of Hc2 (T) h a s been observed i n many superconducting Chevrel phases.

TEMPERATURE ( K )

F i g . 2 : Temperature dependence of Hc2. The f u l l l i n e s a r e t h e WHH's t h e o r e t i c a l p r e d i c t i o n f o r H 0 ) and Hc2

1

('0. c2

I t

I f we suppose t h a t t h e gap i s i s o t r o p i c , t h e o r b i t a l c r i t i c a l f i e l d i s g i v e n by t h e e f f e c - t i v e mass model Hc2 (8) = H c211 (cos2 8 + 'E s i n 2 8)-: w i t h c 2 = m/M where M i s t h e e f f e c t i v e mass i n t h e [ I I I

]

and m the one p e r p e n d i c u l a r t o t h i s d i r e c t i o n . I n f i g u r e 1 we s e e t h a t Hc2 (9) w i t h H -

c211 - 40.4 kG and c2 = 1.25 f i t s our e x p e r i m e n t a l d a t a w e l l i n s p i t e of v e r y s m a l l d e v i a t i o n s . However s l i g h t d e v i a t i o n s were a l r e a d y found on Snbfo6Se8.

Recent band s t r u c t u r e c a l c u l a t i o n s /4/ f o r Mo6Se8 show t h a t two bands c r o s s t h e Fermi l e v e l , a n E band of n e a r l y cubic symmetry and an

g

AU band coming from t h e s p l i t t i n g of t h e T2U band. The p o s i t i o n of t h e AU band a t t h e Fermi Level may be t h e r e a s o n of t h e a n i s o t r o p y of Hc2 and i s per- haps c o r r e l a t e d w i t h t h e c l u s t e r deformation / 2 / . The e l o n g a t i o n of t h e c l u s t e r can be s e e n through t h e two Mo-Mo i n t r a - c l u s t e r d i s t a n c e s ( s e e t a b l e I ) .

The disagreement of Hc2 (T) w i t h WHH's t h e o r y could be e x p l a i n e d by t h e presence of two bands a t t h e Fermi l e v e l . I n t h a t c a s e we cannot e l i m i n a t e t h e p o s s i b i l i t y of a n i s o t r o p i c s p i n - o r b i t i n t e r a c t i o n

141.

Table I

Table I : Rhombohedral l a t t i c e parameters, Mo-Mo i n t r a c l u s t e r d i s t a n c e s and e f f e c t i v e mass r a t i o of t h e f o u r i n v e s t i g a t e d compounds. Sample PbMo6S8 PbMo6Seg SnMo6Seg Mosses

I n s p e c t i n g Table I i t seems t h a t t h e degree of a n i s o t r o p y i s c o r r e l a t e d w i t h t h e rhombohedra1 a n g l e b u t we cannot e x p l a i n i t .

I n conclusion i t is p o s s i b l e t h a t t h e a n i - s o t r o p y of Hc2. found i n t h e s e compounds i s t h e consequence of two d i f f e r e n t phenomenae : aniso- t r o p i c s p i n o r b i t i n t e r a c t i o n and a n i s o t r o p i c or- b i t a l c r i t i c a l f i e l d . References Rhombohedra1 lat- tice parameters aR = 6.542 i t 1 aR = 8 g 0 1 4 '

+

0 . 6 ' aR = 6.719 f l r 3 aR = 89O 9 ' -t 1.8' a R = 6 . 7 6 8 f l . ? 2 OR = 8g018'

+

1 . 2 ' aR = 6.660 i 2 2 aR = 91°43' + 1 . 5 '

/ I /

F i s c h e r ,

0,

Proceeding of LT 14

5

(1975) 172.

/ 2 / Yvon, K., Current Top. Mat. S c i .

3

(1978). /3/ Decroux, M . , F i s c h e r ,

0 .

,

F l i i k i g e r , R., Seeber, B., D e l e s c l e f s , R. and S e r g e n t , M. S o l i d S t a t e Commun

5

(1978) 393. dintra (1) MO-MO 2.732

fl

2.734

g

2 . 7 7 5 ; 2.836

2

/4/ Andersen, O . , Klose, W. and Nohl, H., t o b e published i n Phys. Rev.