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Superconductivity induced by a magnetic field
44
Physica 126B ( 1984 }44-50 North-Holland, Amsterdaln
SUPERCONDUCTIVITY INDUCED BY A MAGNETIC FIELD H.W. MEUL, C. ROSSEL, M. DECROUXand 9. FISCHER D~partement de Physique de la Mati~re Condens#e, Universit# de Gen~ve, CH - 1211Gen~ve 4, Switzerland G. REMENYI* Max-Planck-lnstitut f. Festkoerperforschung, Hochfeld-Magnetlabor, 166X, F - 38042 Grenoble C~dex, France A. BRIGGS Centre National de la Recherche S c i e n t i f i q u e , S.N.C.I. - C.R.T.D.T., 166X, F - 38042 Grenoble C#dex, France
A superconducting state, induced by a high external magnetic f i e l d , has been observed in the pseudo-ternary europium-tin-molybdenum s u l f i d e . The present state of experimental evidence f o r t h i s phenomenon is presented. The shape and the c~npositional dependence of the c r i t i c a l f i e l d temperature phase diagram is consistent with an explanation in terms of the Jaccarino-Peter compensation e f f e c t . I. INTRODUCTION The i n t e r p l a y of superconductivity and magnetism in ternary compounds has fascinated physicists for a long time. Since the discovery of ternary rare earth superconductors the coexistence of superconductivity and a n t i f e r r o magnetism as well as reentrant superconductivi t y have been observed and studied in d e t a i l (1). More recently the possible observation of p-wave superconductivity in heavy fermion systems has been considered by several groups (2). Here we present another novel phenomenon that has been discovered just recently (3): The magn e t i c - f i e l d - i n d u c e d superconducting state, which, contrary to the ordinary destructive e f f e c t of a magnetic f i e l d , needs a high ext e r n a l l y applied f i e l d to occur. That such an e f f e c t could take place in an ordered f e r r o magnetic metal, was considered in 1962 by Jaccarino and Peter (4). As a mechanism which might allow magnetic-field-induced superconduct i v i t y (MFIS), they proposed a spin-compensation e f f e c t in an applied f i e l d as a consequence of a negative exchange i n t e r a c t i o n between the conduction electrons and the magnetic ions. However, MFIS may equally well occur in the paramagnetic state, i f the exchange f i e l d Hj is l a r g e r than the paramagnetic l i m i t -
ing f i e l d Hp. The c r i t i c a l field-temperature phase diagram (H-T diagram) in this case contains two well separated superconducting domains, one at low f i e l d s , where the paramagnetic pairbreaking of the exchange f i e l d is s t i l l weak, and one at high f i e l d s , where superconductivity is possible due to the compensation e f f e c t . One necessary condition f or the existence of MFIS is a s u f f i c i e n t l y large o r b i t a l c r i t i c a l f i e l d , since o r b i t a l effects are not compensated in the Jaccarino-Peter model. The system in which MFIS has recently been observed is the pseudo-ternary compound EuxSnl_xMo6S8 containing small q u a n t i t i e s of Se and/or Br. The search f o r MFIS in this series was stimulated by the work of Fischer et a l. (5). They found an anomalous behavior of the c r i t i c a l f i e l d Hc2 versus temperature with a c h a r a c t e r i s t i c upturn in samples with high Eu-concentrations, which they interpreted as a r e s u l t of the Jaccarino-Peter compensation e f f e c t . The negative sign of the exchange interactions as well as i t s small value have been confirmed afterwards by NMR- and M6ssbauer-effect studies (Fradin et a l . (6)), by EPR measurements (Odermatt (7)), and by bandstructure calculations (Freeman and Jarlborg
* Permanent address: Deparbnent of Low Temperature Physics, Roland E~tv~s University, 1068 Budapest V I I I , Puskin U. 5 - 7, Hungary 0 3 7 8 - 4 3 6 3 / 8 4 / $ 0 3 . 0 0 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
H.W. Meul et al. / Superconductivity induced by a magnetic field
( 8 ) ) . L a t e r on Isino et a l . (9) have found a reduction of the resistance with increasing magnetic f i e l d at temperatures below the superconducting t r a n s i t i o n temperature Tc in a sample with nominal composition Euo.8Sno.2Mo6S7. A similar behavior has been reported by Wolf et al. (lO) in EUl.2Mo6S8 at a pressure of 14 kbar. However, in both cases wide superconducting transitions made the interpretation of this observation very d i f f i c u l t . The present paper is organized asfollows: After a short description of the sample preparation and the measuring procedure in Sec. 2, the experimental proof for the existence of the phenomenon of MFIS w i l l be presented in Sec. 3. The temperature-, f i e l d - , and compositional dependence of MFIS w i l l be discussed in Sec. 3 and 4. I t w i l l be shown in Sec. 5 that the Jaccarino-Peter effect, which is described there in more detail, accounts correctly for the shape and compositional dependence of the H-T phase diagram. 2. EXPERIMENTAL The samples investigated in this study were a l l prepared in the f o l l o w i n g way: In a pretreatment, the pseudo-ternary phase was formed by standard powder-metallurgical techniques. A very small amount of bromine (about 0.5 at-%) was added in order to promote the homogenization of the samples. In a second step the powdered reaction product was hot pressed at about 1500°C under u n i a x i a l pressure of 1.7 kbar f o r 2 hours with the use of a graphite matrix. X-ray analysis did not show any imp u r i t y phase. For the resistance measurements the samples were cut with the use of a low-speed diamond saw in the shape of small bars of about I0 mm length and 0.6 x 0.6 mm2 cross section. The resistance was measured by means of a standard four-terminal-ac technique (220 Hz) with a measuring current density of about I00 A/m2. The superconducting t r a n s i t i o n temperature Tc and the upper c r i t i c a l f i e l d Hc2 were determined by taking the midpoint of the res i s t i v e t r a n s i t i o n . The low-temperature and h i g h - f i e l d measurements were carried out e i t h e r in a He3-He4 d i l u t i o n r e f r i g e r a t o r combined with a superconducting coil (12 Tesla) or in a He3 cryostat inserted into a r e s i s t i v e polyh e l i x magnet ( I I ) of 25 Tesla. 3. TEMPERATUREAND FIELD DEPENDENCEOF MFIS The phenomenon of MFIS is now presented with the example of an appropriate sample whose composition w i l l be discussed in Sec. 4. In Fig. 1 the e l e c t r i c a l resistance R of the compound EUo.75Sno.25Mo6S7.2Seo.8 is shown as a function of the external magneti f i e l d at T = 370 mK.
45
Eu0.75 Sno.25 Mo 6 S 7.2 Se0.8 T : 370ink
z=
Z u'} bJ rr
5
10
15
20
25
APPLIED MAGNETIC FIELD I~oH ETESLA]
FIGURE 1 Resistance of Euo.75Sno.25Mo6S7.2Seo.8 versus magnetic f i e l d at T = 370 mK. RN is the resistance in the normal state. Tc of the sample in zero f i e l d is 3.89 K. Superconductivity is already destroyed at a r e l a t i v e l y weak magnetic f i e l d and a sharp t r a n s i tion into the normal state is observed. But then with increasing f i e l d the resistance starts to decrease again and disappears at I I Tesla. The field-induced state exists up to 17 Tesla, where a t h i r d t r a n s i t i o n starts to appear and MFIS is f i n a l l y destroyed by the action of the applied f i e l d . This superconducting-normal-superconducting-normal (S-N-S-N) m u l t i p l e t r a n s i t i o n behavior is c h a r a c t e r i s t i c of a paramagnetic metal which allows superconductivity to be induced by the compensation e f f e c t , and should be distinguished from the well-known peak e f f e c t which occurs in typell-superconductors only near Hc2. By measuring R(H) at various temperatures we obtain the H-T phase diagram, which is given in Fig. 2. We f i n d two separated superconducting domains, an ordinary one at low f i e l d s and a new field-induced one, which extends from 4 Tesla to 22 Tesla at T = 0 and from T = 0 to T = 1 K at H = 12 Tesla. 4. COMPOSITIONALDEPENDENCEOF MFIS I t appears that MFIS results from a very d e l i c a t e balance between the exchange f i e l d Hj and Tc (see discussion in Sec. 5). Experimentally the adjustment of Hj and Tc can be realized by suitable substitutions e i t h e r at the Eu-sites or at the s u l f u r sites. This l a t t e r type of s u b s t i t u t i o n is known to reduce the superconducting t r a n s i t i o n temperature (12) without changing much the other parameters of the system (13). In p a r t i c u l a r , the exchange f i e l d Hj remains unchanged in
H. W. Meul er al.
46
/ Superconductivity induced by a magnetic Jield
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FIGURE 3 C r i t i c a l ~emoerature T c versus S e - c o n c e n t r a t i o n in the s e r i e s Eu0 75Sn0 25Mo6S8_ySey. The shaded region is c o n s i s t e n t w i t q MFIS.
0
1
2 3 TEMPERATURE T [K]
4
FIGURE 2 H-T phase diagram of Euo.75Sno.25Mo6S7.2Seo. 8 f i r s t a p p r o x i m a t i o n . On the o t h e r hand, s u b s t i t u t i o n s o f the type EuxSnl_ x modify the exchange f i e l d ( ~ x ) w i t h o u t any n o t i c e a b l e i n f l u e n c e on Tc, as long as the E u - c o n c e n t r a t i o n is s m a l l e r than x = 0.8. At h i g h e r x - v a l u e s a s t r u c t u r a l phase t r a n s f o r m a t i o n takes p l a c e , which destroys s u p e r c o n d u c t i v i t y (14). We t h e r e f o r e chose a E u - c o n c e n t r a t i o n o f x = 0.75~ t h i s means t h a t the exchange f i e l d is f i x e d and by s u b s t i t u t i n g Se f o r S, Tc can be a d j u s t e d to the value necessary f o r MFIS to occur. In Fig. 3 the dependence o f Tc on the Sec o n c e n t r a t i o n in Eu0 755n0 25Mo6S8_ySey is shown. The r e g i o n c o n s i s t e n t w i t h MFIS is shaded in the f i g u r e . The boundaries of t h i s region have been determined e x p e r i m e n t a l l y by d e f i n i n g MFIS as the simultaneous appearance o f two separated superconducting domains in the H-T diagram. In the f o l l o w i n g , we w i l l discuss what happens, i f T c does not c o i n c i d e w i t h values i n s i d e the c r i t i c a l i n t e r v a l . Fig. 4 shows the c r i t i c a l f i e l d s o f two samples w i t h Tc-values l y i n g above the c r i t i cal r e g i o n . The temperature dependence o f Hc2 is s t i l l very anomalous w i t h a c h a r a c t e r i s t i c upturn and an i n f i n i t e slope a t 2.7 K f o r the
Euc 75 Sn025 Mo5 58
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5-
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FIGURE 4 C r i t i c a l f i e l d versus temperature of two samples of the s e r i e s EuN 7~SnN 2~Mo6S8_vSev w i t h Tc-values above the c r ~ L ~ c a ~ ' T n t e r v a l [ sample w i t h y = 0.25, but the phase diagram is only simply connected and MFIS is not p o s s i b l e any more. The anomaly becomes i n c r e a s i n g l y i n -
14. W. Meul et al. / Superconductivity induced by a magnetic field
47
Eu0.805SnQB5IvY6SB(BF)
EUo?55n0.25Mo6SB-ySey
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5 10 15 20 APPLIED M A G N E T I C FIELD I.ZoH [ T E S L A ]
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FIGURE 5 C r i t i c a l f i e l d versus temperature o f two samples o f the s e r i e s Euo.75Sno.25Mo6S 8_ySey w i t h Tc-values below the c r i t i c a l i n t e r v a l ]
FIGURE 7 Resistance o f Euo.805Sno.195Mo6S8 c o n t a i n i n g a small q u a n t i t y o f bromine, as a f u n c t i o n of the magnetic f i e l d a t various temperatures.
s i g n i f i c a n t the more T c is removed from the c r i t i c a l r e g i o n . A s i m i l a r behavior of the c r i t i c a l f i e l d w i t h a p o s i t i v e c u r v a t u r e has also been r e p o r t e d in o t h e r Chevrel phases EUxMl_xMo6S8 w i t h M = Pb,La,Yb ( 5 , 1 5 , 1 6 ) . I f on the o t h e r hand the superconducting t r a n s i t i o n temperature is below the c r i t i c a l i n t e r v a l , one f i n d s a r e e n t r a n t behavior w i t h a r e l a t i v e l y low c r i t i c a l f i e l d as shown in Fig. 5. There is no i n d i c a t i o n o f superconduct i v i t y in magnetic f i e l d s h i g h e r than 1 T e s l a o
The c r i t i c a l f i e l d s remain f i n i t e a t T = 0 due to a complex a n t i f e r r o m a g n e t i c o r d e r appearing below T : 0.5 K (17). MFIS may also be approached i n the s e r i e s EuxSnl_xMo6S 8 by way o f the s t r u c t u r a l phase t r a n s f o r m a t i o n , which causes a r a p i d drop o f Tc near x = 0.8 ( F i g . 6). As a consequence, Tc passes through a narrow i n t e r v a l c o n s i s t e n t w i t h MFIS. Using t h i s approach I s i n o e t a l . were the f i r s t who observed an i n d i c a t i o n of MFIS. However, the e f f e c t was smeared out by wide superconducting t r a n s i t i o n s making an i n t e r p r e t a t i o n in f a v o r of MFIS d i f f i c u l t . Indeed, the v a r i a t i o n o f Tc at x = 0.8 is so r a p i d , t h a t the p r e p a r a t i o n o f s u f f i c i e n t l y homogeneous samples i s not easy. Doping w i t h small amounts o f bromine has the e f f e c t o f l o w e r i n g the temperature of the s t r u c t u r a l phase t r a n s f o r m a t i o n in EuMo6S8 and makes the v a r i a t i o n o f T c w i t h x close t o x = 0.8 less steep and thus the superconducting t r a n s i t i o n s less wide ( F i g . 6). The R(H)-behavior of a sample w i t h nominal composition Euo.805Sno.195Mo6S8Bro. 1 at various temperat u r e s is shown in Fig. 7. The S-N-S-N m u l t i p l e t r a n s i t i o n at temperatures below 1 K i s c l e a r l y d i s p l a y e d . However, the t r a n s i t i o n w i d t h o f t h i s sample i s o f the o r d e r of the w i d t h o f the c r i t i c a l i n t e r v a l , so t h a t the e f f e c t of MFIS is more smeared out compared w i t h the samples c o n t a i n i n g Se. Note, t h a t in our f i r s t approach the region w i t h the strong v a r i a t i o n of T c has been avoided.
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FIGURE 6 C r i t i c a l temperature versus E u - c o n c e n t r a t i o n in the s e r i e s EuxSnl-xMo6S8 and the e f f e c t of adding small q u a n t i t i e s o f bromine.
ft. W. Meul et al. /' Superconductirit~ itMuced by u mugm'tic liHd
48
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MAGNETIC FIELD FIGURE 8 Schematic p l o t of the free energies of the normal and superconducting s t a t e s versus magnetic f i e l d f o r a paramagnetic superconductor w i t h a negative exchange i n t e r a c t i o n between the cond u c t i o n e l e c t r o n s and the magnetic ions. Spino r b i t e f f e c t s are n e g l e c t e d . 5. DISCUSSION The experimental f a c t s described in Sec. 3 and 4 are now i n t e r p r e t e d by t a k i n g the J a c c a r i n o - P e t e r compensation e f f e c t as the mechanism f o r MFIS. A q u a l i t a t i v e understanding can be obtained by c o n s i d e r i n g the free energy F as a f u n c t i o n of the a p p l i e d magnetic f i e l d , as shown s c h e m a t i c a l l y in Fig. 8. FN(H ) represents the normal s t a t e f r e e energy o f the conduction e l e c t r o n system w i t h i n c l u s i o n of the p o l a r i z a t i o n e f f e c t coming from both the a p p l i e d f i e l d and the i n t e r n a l exchange f i e l d a t low temperature T << Tc. The temperatureand f i e l d dependence o f the exchange f i e l d is described by the B r i l l o u i n f u n c t i o n . The free energy of the normal s t a t e is thus lowered very q u i c k l y according to the p o l a r i z a t i o n o f the conduction e l e c t r o n spins in the exchange f i e l d , which a l r e a d y reaches i t s s a t u r a t i o n value at low a p p l i e d f i e l d s of the o r d e r of kBT. Because o f the a n t i p a r a l l e l d i r e c t i o n of Hj r e l a t i v e to the e x t e r n a l f i e l d , the p o l a r i z a t i o n becomes weaker when H increases f u r t h e r , i . e . FN passes through a minimum and increases again up to the compensation p o i n t a t which the e x t e r n a l f i e l d e x a c t l y cancels the exchange f i e l d . In s t i l l higher f i e l d s the o r d i n a r y Pauli spin paramagnetism sets i n . The superconducting s t a t e is described by the Fs(H)-curve; a t y p e - I I - b e h a v i o r w i t h f i e l d p e n e t r a t i o n is assumed. I f Hj and Tc are a d j u s t e d c o r r e c t l y , we f i n d three i n t e r s e c t i o n p o i n t s Hl , H2, and H3 between FN and FS i n d i c a t i n g the various superconducting-normal t r a n s i t i o n s in the presence of the a p p l i e d f i e l d . I t can be seen e a s i l y t h a t there e x i s t s
only one s o l u t i o n , i f ] c , or e q u i v a l e n t l y , the superconducting condensation energy is too low (curve F~(H) in the f i g u r e ) or too high (curve Fs(H)). In the preceding discussion s p i n - o r b i t s c a t t e r i n g has been neglected. However, f o r ,~ q u a n t i t i v e a n a l y s i s o f the experimental res u l t s i t is inlportant to i n c o r p o r a t e t h i s e f f e c t i n t o the t h e o r y , lhe well-known microscopic theory of the superconducting c r i t i c a l f i e l d by Werthamer, Helfand, and Hohenberg ( l ' 3 i , which contains s p i n - o r b i t as well as paramagn e t i c e f f e c t s , has been extended by Fischer (19) to the case of a magnetic superconductor w i t h i n c l u s i o n of the compensation e f f e c t . The f i n a l formulas are q u i t e cumbersome, so t h a t we shall not w r i t e them out e x p l i c i t l y . An imp l i c i t equation f o r the c r i t i c a l f i e l d Hc2 is found, which contains as parameters tile supeYconducting t r a n s i t i o n temperature Tc, the
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TEMPERATURE T[K]. FIGURE g C r i t i c a l f i e l d s versus temperature of three d i f f e r e n t samples of the Euo.75Sno.25Mo6S8_ySey s e r i e s , compared w i t h c a l c u l a t i o n s ( s o l i ~ l i n e s ) using F i s c h e r ' s formula f o r the c r i t i c a l field.
H. W. Meul et al. / Superconductivity induced by a magnetic field
exchange f i e l d Hj, the Maki parameter ~, the magnetization M, the s p i n - o r b i t scattering parameter ~SO, and a magnetic scattering parameter ~m. I t turns out that magnetic scattering effects are unimportant in the series EuxSnl_xMo6S8 (20)~ we therefore take ~m = O. This means that the e f f e c t of MFIS presented here has nothing to do with magnetic scattering, whose influence on superconductivity has been studied by many authors (21). The c o n t r i bution of the magnetization to the magnetic induction B is also negligable in the present case. From the remaining parameters only Tc can be determined by experiment, so that there remain three f i t t i n g parameters. In Fig. 9 the c r i t i c a l f i e l d s of three samples, which are c h a r a c t e r i s t i c for the d i f f e r e n t types of behavior, are plotted together with the computed curves. We f i n d good agreement between experiment and theory. Remarkable is that these very d i f f e r e n t H-T diagrams can be obtained with one set of values for a, Hj, and the product Tc • ~SO (= 2~/3kB%s0)" The only q u a n t i t y that varies, is the superconducting t r a n s i t i o n temperature, whose value, however, is f i x e d by the measurements. Nevertheless, in order to get an optimum f i t , a s l i g h t v a r i a t i o n of the product Tc • ~SO has been admitted, which corresponds to an increase of the s p i n - o r b i t scattering time ~SO with increasing Se-concentration. The values of the three f i t t i n g parameters given in Fig. 9 are in good agreement with values obtained in other ternary molybdenum chalcogenides. In p a r t i c u l a r , the value for the exchange f i e l d Hj = -30 Tesla, which is equivalent to an exchange i n t e r a c t i o n of 20 meV, agrees well with EPR measurements by Odermatt (7). We therefore conclude that the observed MFIS is caused by the Jaccarino-Peter compensation e f f e c t . The anomalous transport prope r t i e s which have been found in EuMo6S8 at low temperature have p r a c t i c a l l y disappeared for Eu-concentrations x < 0.85 in EuxSnl_xMO6S8 and should be distinguished from the behavior reported here. In samples of the series Eu0 75Sn0 25Mo6S8_ySey we found no anomalous magnetoresistance j u s t above Tc, the Hall coe f f i c i e n t is p o s i t i v e and nearly temperature independent, and the e l e c t r i c a l resistance at low temperature is f l a t and m e t a l l i c - l i k e . In conclusion, we have observed a magneticfield-induced superconducting state in the series EuxSnl_xMO6S8, which can be explained in terms of the Jaccarino-Peter e f f e c t . This work answers a long standing question concerning the p o s s i b i l i t y of such an e f f e c t , but i t also raises several questions about the exact nature of t h i s novel state and i t s properties.
49
ACKNOWLEDGEMENTS We are very grateful to Prof. M. Peter for many stimulating discussions and his i n t e r e s t in t h i s work. We also thank Prof. R. Tournier for the support he has given to t h i s work. We acknowledge Dr. M. Karkut for helpful discussions and c r i t i c a l l y reading t h i s manuscript. Two of us (C.R. and H.W.M.) thank the MaxPlanck I n s t i t u t e and the low-temperature group of the Centre National de la Recherche S c i e n t i fique in Grenoble for the kind h o s p i t a l i t y . We thank A. Klaschka for help with the He3 measurements and A. S t e t t l e r for his technical assistance. REFERENCES ( I ) See for example: Superconductivity in Ternary Compounds, Vol. 2, eds. M.B. Maple and 9.Fischer (Springer, Berlin Heidelberg New York, 1982). (2) F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schaefer, Phys.Rev.Lett. 43 (1979) 1892. H.R. Ott, H. Rudigier, Z. Fisk, and J.L. Smith, Phys.Rev.Lett. 50 (1983) 1595. G.R. Stewart, Z. Fisk, J.O. Willes, and J.L. Smith, Phys. Rev.Lett. 52 (1984) 679. (3) H.W. Meul, C. Rossel, M. Decroux, ~. Fischer, G. Remenyi, and A. Briggs, Phys.Rev.Lett. 53 (1984) 497. (4) V. Jaccarino and M. Peter, Phys.Rev.Lett. 9 (1962) 290. (5) 9. Fischer, M. Decroux, S. Roth, R. Chevrel, and M. Sergent, J.Phys. C8 (1975) L474. (6) F.Y. Fradin, G.K. Shenoy, B.D. Dunlap, A.T. A l d r e t , and C.W. Kimball, Phys. Rev.Lett. 38 (1977) 719. (7) R. Odermatt, Helv.Phys.Acta 54 (1981) I . (8) A.J. Freeman and T. Jarlborg, in Superc o n d u c t i v i t y in Ternary Compounds, Vol.2, eds. M.B. Maple and 9. Fischer (Springer, B e r l i n Heidelberg New York, 1982) pp. 167 - 200. (9) M. I s i n o , N. Kobayashi, and Y. Muto, in Ternary Superconductors, eds. G.K. Shenoy, B.D. Dunlap, and F.Y. Fradin (North Holland, Amsterdam, 1981) p. 95. (I0) S.A. Wolf, W.W. F u l l e r , C.Y. Huang, D.W. Harrison, H.L. Luo, and S. Maekawa, Phys.Rev. B25 (1982) 1990. W.W. F u l l e r , S.A. Wolf, C.Y. Huang, D.W. Harrison, H.L. Luo, and S. Maekawa, J.Appl.Phys. 53 (1982) 2622. ( I I ) H.J. Schneider-Muntau, IEEE Trans.Mag., VoI.MAG-18 (1982) p. 1565. (12) M. Decroux and 0. Fischer, in Supercond u c t i v i t y in Ternary Compounds, Vol. 2, eds. M.B. Maple and ~. Fischer (Springer, B e r l i n Heidelberg New York, 1982) pp. 57.
50
ILLW. Meul et al. / SuperconductiviLv induced by a magnetic .field
(13) B. Lachal, A. Junod, and J. Muller, J. Low Temp. Phys. 55 (1984) 195. (14) M. Decroux, H.W. Meul, C. Rossel, 9. Fischer, and R. B a i l l i f , in Superconductivity in d- and f-Band Metals, eds. W. Buckel and W. Weber (KFK GmbH, Karlsruhe, 1982) p. 167. (15) M.S. T o r i k a c h v i l i , M.B. Maple, R.P. Guertin, and S. Foner, J. Low Temp. Phys. 49 (1982) 573. (16) M.S. T o r i k a c h v i l i , J. B e i l l e , S.E. Lambert, and M.B. Maple, in Superconduct i v i t y in d- and f-Band Metals, eds. W. Buckel and W. Weber (KFK GmbH, Karlsruhe, 1982) p. 241. (17) J. Bolz, G. Crecelius, H. Maletta, and F. Pobell, J. Low Temp.Phys. 28 (1977) 61. (18) H.R. Werthamer, E. Helfand, and P.C. Hohenberg, Phys. Rev. 147 (1966) 295. (19) 9. Fischer, Helv. Phys.Acta 45 (1972) 229. (20) H.W. Meul, M. Decroux, R. Odermatt, R. Noer, and 9. Fischer, Phys.Rev. B26 (1982) 6431. (21) A.A. Abrikosov and L.P. Gorkov, Sov. Phys.JETP 12 (1961) 1243. E. Mueller-Hartmann and J. Z i t t a r t z , Phys. Rev.Lett. 26 (1971) 428. I. Kirschner and A. Stark, Acta Phys.Hung. 30 (1971) 33. S. Maekawa and M. Tachiki, Phys. Rev. Bl8 (1978) 4688.
Physica 126B ( 1984 }44-50 North-Holland, Amsterdaln
SUPERCONDUCTIVITY INDUCED BY A MAGNETIC FIELD H.W. MEUL, C. ROSSEL, M. DECROUXand 9. FISCHER D~partement de Physique de la Mati~re Condens#e, Universit# de Gen~ve, CH - 1211Gen~ve 4, Switzerland G. REMENYI* Max-Planck-lnstitut f. Festkoerperforschung, Hochfeld-Magnetlabor, 166X, F - 38042 Grenoble C~dex, France A. BRIGGS Centre National de la Recherche S c i e n t i f i q u e , S.N.C.I. - C.R.T.D.T., 166X, F - 38042 Grenoble C#dex, France
A superconducting state, induced by a high external magnetic f i e l d , has been observed in the pseudo-ternary europium-tin-molybdenum s u l f i d e . The present state of experimental evidence f o r t h i s phenomenon is presented. The shape and the c~npositional dependence of the c r i t i c a l f i e l d temperature phase diagram is consistent with an explanation in terms of the Jaccarino-Peter compensation e f f e c t . I. INTRODUCTION The i n t e r p l a y of superconductivity and magnetism in ternary compounds has fascinated physicists for a long time. Since the discovery of ternary rare earth superconductors the coexistence of superconductivity and a n t i f e r r o magnetism as well as reentrant superconductivi t y have been observed and studied in d e t a i l (1). More recently the possible observation of p-wave superconductivity in heavy fermion systems has been considered by several groups (2). Here we present another novel phenomenon that has been discovered just recently (3): The magn e t i c - f i e l d - i n d u c e d superconducting state, which, contrary to the ordinary destructive e f f e c t of a magnetic f i e l d , needs a high ext e r n a l l y applied f i e l d to occur. That such an e f f e c t could take place in an ordered f e r r o magnetic metal, was considered in 1962 by Jaccarino and Peter (4). As a mechanism which might allow magnetic-field-induced superconduct i v i t y (MFIS), they proposed a spin-compensation e f f e c t in an applied f i e l d as a consequence of a negative exchange i n t e r a c t i o n between the conduction electrons and the magnetic ions. However, MFIS may equally well occur in the paramagnetic state, i f the exchange f i e l d Hj is l a r g e r than the paramagnetic l i m i t -
ing f i e l d Hp. The c r i t i c a l field-temperature phase diagram (H-T diagram) in this case contains two well separated superconducting domains, one at low f i e l d s , where the paramagnetic pairbreaking of the exchange f i e l d is s t i l l weak, and one at high f i e l d s , where superconductivity is possible due to the compensation e f f e c t . One necessary condition f or the existence of MFIS is a s u f f i c i e n t l y large o r b i t a l c r i t i c a l f i e l d , since o r b i t a l effects are not compensated in the Jaccarino-Peter model. The system in which MFIS has recently been observed is the pseudo-ternary compound EuxSnl_xMo6S8 containing small q u a n t i t i e s of Se and/or Br. The search f o r MFIS in this series was stimulated by the work of Fischer et a l. (5). They found an anomalous behavior of the c r i t i c a l f i e l d Hc2 versus temperature with a c h a r a c t e r i s t i c upturn in samples with high Eu-concentrations, which they interpreted as a r e s u l t of the Jaccarino-Peter compensation e f f e c t . The negative sign of the exchange interactions as well as i t s small value have been confirmed afterwards by NMR- and M6ssbauer-effect studies (Fradin et a l . (6)), by EPR measurements (Odermatt (7)), and by bandstructure calculations (Freeman and Jarlborg
* Permanent address: Deparbnent of Low Temperature Physics, Roland E~tv~s University, 1068 Budapest V I I I , Puskin U. 5 - 7, Hungary 0 3 7 8 - 4 3 6 3 / 8 4 / $ 0 3 . 0 0 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
H.W. Meul et al. / Superconductivity induced by a magnetic field
( 8 ) ) . L a t e r on Isino et a l . (9) have found a reduction of the resistance with increasing magnetic f i e l d at temperatures below the superconducting t r a n s i t i o n temperature Tc in a sample with nominal composition Euo.8Sno.2Mo6S7. A similar behavior has been reported by Wolf et al. (lO) in EUl.2Mo6S8 at a pressure of 14 kbar. However, in both cases wide superconducting transitions made the interpretation of this observation very d i f f i c u l t . The present paper is organized asfollows: After a short description of the sample preparation and the measuring procedure in Sec. 2, the experimental proof for the existence of the phenomenon of MFIS w i l l be presented in Sec. 3. The temperature-, f i e l d - , and compositional dependence of MFIS w i l l be discussed in Sec. 3 and 4. I t w i l l be shown in Sec. 5 that the Jaccarino-Peter effect, which is described there in more detail, accounts correctly for the shape and compositional dependence of the H-T phase diagram. 2. EXPERIMENTAL The samples investigated in this study were a l l prepared in the f o l l o w i n g way: In a pretreatment, the pseudo-ternary phase was formed by standard powder-metallurgical techniques. A very small amount of bromine (about 0.5 at-%) was added in order to promote the homogenization of the samples. In a second step the powdered reaction product was hot pressed at about 1500°C under u n i a x i a l pressure of 1.7 kbar f o r 2 hours with the use of a graphite matrix. X-ray analysis did not show any imp u r i t y phase. For the resistance measurements the samples were cut with the use of a low-speed diamond saw in the shape of small bars of about I0 mm length and 0.6 x 0.6 mm2 cross section. The resistance was measured by means of a standard four-terminal-ac technique (220 Hz) with a measuring current density of about I00 A/m2. The superconducting t r a n s i t i o n temperature Tc and the upper c r i t i c a l f i e l d Hc2 were determined by taking the midpoint of the res i s t i v e t r a n s i t i o n . The low-temperature and h i g h - f i e l d measurements were carried out e i t h e r in a He3-He4 d i l u t i o n r e f r i g e r a t o r combined with a superconducting coil (12 Tesla) or in a He3 cryostat inserted into a r e s i s t i v e polyh e l i x magnet ( I I ) of 25 Tesla. 3. TEMPERATUREAND FIELD DEPENDENCEOF MFIS The phenomenon of MFIS is now presented with the example of an appropriate sample whose composition w i l l be discussed in Sec. 4. In Fig. 1 the e l e c t r i c a l resistance R of the compound EUo.75Sno.25Mo6S7.2Seo.8 is shown as a function of the external magneti f i e l d at T = 370 mK.
45
Eu0.75 Sno.25 Mo 6 S 7.2 Se0.8 T : 370ink
z=
Z u'} bJ rr
5
10
15
20
25
APPLIED MAGNETIC FIELD I~oH ETESLA]
FIGURE 1 Resistance of Euo.75Sno.25Mo6S7.2Seo.8 versus magnetic f i e l d at T = 370 mK. RN is the resistance in the normal state. Tc of the sample in zero f i e l d is 3.89 K. Superconductivity is already destroyed at a r e l a t i v e l y weak magnetic f i e l d and a sharp t r a n s i tion into the normal state is observed. But then with increasing f i e l d the resistance starts to decrease again and disappears at I I Tesla. The field-induced state exists up to 17 Tesla, where a t h i r d t r a n s i t i o n starts to appear and MFIS is f i n a l l y destroyed by the action of the applied f i e l d . This superconducting-normal-superconducting-normal (S-N-S-N) m u l t i p l e t r a n s i t i o n behavior is c h a r a c t e r i s t i c of a paramagnetic metal which allows superconductivity to be induced by the compensation e f f e c t , and should be distinguished from the well-known peak e f f e c t which occurs in typell-superconductors only near Hc2. By measuring R(H) at various temperatures we obtain the H-T phase diagram, which is given in Fig. 2. We f i n d two separated superconducting domains, an ordinary one at low f i e l d s and a new field-induced one, which extends from 4 Tesla to 22 Tesla at T = 0 and from T = 0 to T = 1 K at H = 12 Tesla. 4. COMPOSITIONALDEPENDENCEOF MFIS I t appears that MFIS results from a very d e l i c a t e balance between the exchange f i e l d Hj and Tc (see discussion in Sec. 5). Experimentally the adjustment of Hj and Tc can be realized by suitable substitutions e i t h e r at the Eu-sites or at the s u l f u r sites. This l a t t e r type of s u b s t i t u t i o n is known to reduce the superconducting t r a n s i t i o n temperature (12) without changing much the other parameters of the system (13). In p a r t i c u l a r , the exchange f i e l d Hj remains unchanged in
H. W. Meul er al.
46
/ Superconductivity induced by a magnetic Jield
Euo';'5 Snc 25 Mo6S8-YSey
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-
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i
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-
Calculation Of HC2from multiple
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pair breaking theory
-
T ......
17
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FIGURE 3 C r i t i c a l ~emoerature T c versus S e - c o n c e n t r a t i o n in the s e r i e s Eu0 75Sn0 25Mo6S8_ySey. The shaded region is c o n s i s t e n t w i t q MFIS.
0
1
2 3 TEMPERATURE T [K]
4
FIGURE 2 H-T phase diagram of Euo.75Sno.25Mo6S7.2Seo. 8 f i r s t a p p r o x i m a t i o n . On the o t h e r hand, s u b s t i t u t i o n s o f the type EuxSnl_ x modify the exchange f i e l d ( ~ x ) w i t h o u t any n o t i c e a b l e i n f l u e n c e on Tc, as long as the E u - c o n c e n t r a t i o n is s m a l l e r than x = 0.8. At h i g h e r x - v a l u e s a s t r u c t u r a l phase t r a n s f o r m a t i o n takes p l a c e , which destroys s u p e r c o n d u c t i v i t y (14). We t h e r e f o r e chose a E u - c o n c e n t r a t i o n o f x = 0.75~ t h i s means t h a t the exchange f i e l d is f i x e d and by s u b s t i t u t i n g Se f o r S, Tc can be a d j u s t e d to the value necessary f o r MFIS to occur. In Fig. 3 the dependence o f Tc on the Sec o n c e n t r a t i o n in Eu0 755n0 25Mo6S8_ySey is shown. The r e g i o n c o n s i s t e n t w i t h MFIS is shaded in the f i g u r e . The boundaries of t h i s region have been determined e x p e r i m e n t a l l y by d e f i n i n g MFIS as the simultaneous appearance o f two separated superconducting domains in the H-T diagram. In the f o l l o w i n g , we w i l l discuss what happens, i f T c does not c o i n c i d e w i t h values i n s i d e the c r i t i c a l i n t e r v a l . Fig. 4 shows the c r i t i c a l f i e l d s o f two samples w i t h Tc-values l y i n g above the c r i t i cal r e g i o n . The temperature dependence o f Hc2 is s t i l l very anomalous w i t h a c h a r a c t e r i s t i c upturn and an i n f i n i t e slope a t 2.7 K f o r the
Euc 75 Sn025 Mo5 58
Se
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!%
L
Y=O Y=O 2S
5-
••
---~
-~-T T TEMPERATURET-~
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s
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FIGURE 4 C r i t i c a l f i e l d versus temperature of two samples of the s e r i e s EuN 7~SnN 2~Mo6S8_vSev w i t h Tc-values above the c r ~ L ~ c a ~ ' T n t e r v a l [ sample w i t h y = 0.25, but the phase diagram is only simply connected and MFIS is not p o s s i b l e any more. The anomaly becomes i n c r e a s i n g l y i n -
14. W. Meul et al. / Superconductivity induced by a magnetic field
47
Eu0.805SnQB5IvY6SB(BF)
EUo?55n0.25Mo6SB-ySey
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~O5o~
I
2
5 10 15 20 APPLIED M A G N E T I C FIELD I.ZoH [ T E S L A ]
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25
FIGURE 5 C r i t i c a l f i e l d versus temperature o f two samples o f the s e r i e s Euo.75Sno.25Mo6S 8_ySey w i t h Tc-values below the c r i t i c a l i n t e r v a l ]
FIGURE 7 Resistance o f Euo.805Sno.195Mo6S8 c o n t a i n i n g a small q u a n t i t y o f bromine, as a f u n c t i o n of the magnetic f i e l d a t various temperatures.
s i g n i f i c a n t the more T c is removed from the c r i t i c a l r e g i o n . A s i m i l a r behavior of the c r i t i c a l f i e l d w i t h a p o s i t i v e c u r v a t u r e has also been r e p o r t e d in o t h e r Chevrel phases EUxMl_xMo6S8 w i t h M = Pb,La,Yb ( 5 , 1 5 , 1 6 ) . I f on the o t h e r hand the superconducting t r a n s i t i o n temperature is below the c r i t i c a l i n t e r v a l , one f i n d s a r e e n t r a n t behavior w i t h a r e l a t i v e l y low c r i t i c a l f i e l d as shown in Fig. 5. There is no i n d i c a t i o n o f superconduct i v i t y in magnetic f i e l d s h i g h e r than 1 T e s l a o
The c r i t i c a l f i e l d s remain f i n i t e a t T = 0 due to a complex a n t i f e r r o m a g n e t i c o r d e r appearing below T : 0.5 K (17). MFIS may also be approached i n the s e r i e s EuxSnl_xMo6S 8 by way o f the s t r u c t u r a l phase t r a n s f o r m a t i o n , which causes a r a p i d drop o f Tc near x = 0.8 ( F i g . 6). As a consequence, Tc passes through a narrow i n t e r v a l c o n s i s t e n t w i t h MFIS. Using t h i s approach I s i n o e t a l . were the f i r s t who observed an i n d i c a t i o n of MFIS. However, the e f f e c t was smeared out by wide superconducting t r a n s i t i o n s making an i n t e r p r e t a t i o n in f a v o r of MFIS d i f f i c u l t . Indeed, the v a r i a t i o n o f Tc at x = 0.8 is so r a p i d , t h a t the p r e p a r a t i o n o f s u f f i c i e n t l y homogeneous samples i s not easy. Doping w i t h small amounts o f bromine has the e f f e c t o f l o w e r i n g the temperature of the s t r u c t u r a l phase t r a n s f o r m a t i o n in EuMo6S8 and makes the v a r i a t i o n o f T c w i t h x close t o x = 0.8 less steep and thus the superconducting t r a n s i t i o n s less wide ( F i g . 6). The R(H)-behavior of a sample w i t h nominal composition Euo.805Sno.195Mo6S8Bro. 1 at various temperat u r e s is shown in Fig. 7. The S-N-S-N m u l t i p l e t r a n s i t i o n at temperatures below 1 K i s c l e a r l y d i s p l a y e d . However, the t r a n s i t i o n w i d t h o f t h i s sample i s o f the o r d e r of the w i d t h o f the c r i t i c a l i n t e r v a l , so t h a t the e f f e c t of MFIS is more smeared out compared w i t h the samples c o n t a i n i n g Se. Note, t h a t in our f i r s t approach the region w i t h the strong v a r i a t i o n of T c has been avoided.
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~c bJ Q_ ~E lJJ l--
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,
,
,
I
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,
~
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oi
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FIGURE 6 C r i t i c a l temperature versus E u - c o n c e n t r a t i o n in the s e r i e s EuxSnl-xMo6S8 and the e f f e c t of adding small q u a n t i t i e s o f bromine.
ft. W. Meul et al. /' Superconductirit~ itMuced by u mugm'tic liHd
48
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......
I~ . . . .
MAGNETIC FIELD FIGURE 8 Schematic p l o t of the free energies of the normal and superconducting s t a t e s versus magnetic f i e l d f o r a paramagnetic superconductor w i t h a negative exchange i n t e r a c t i o n between the cond u c t i o n e l e c t r o n s and the magnetic ions. Spino r b i t e f f e c t s are n e g l e c t e d . 5. DISCUSSION The experimental f a c t s described in Sec. 3 and 4 are now i n t e r p r e t e d by t a k i n g the J a c c a r i n o - P e t e r compensation e f f e c t as the mechanism f o r MFIS. A q u a l i t a t i v e understanding can be obtained by c o n s i d e r i n g the free energy F as a f u n c t i o n of the a p p l i e d magnetic f i e l d , as shown s c h e m a t i c a l l y in Fig. 8. FN(H ) represents the normal s t a t e f r e e energy o f the conduction e l e c t r o n system w i t h i n c l u s i o n of the p o l a r i z a t i o n e f f e c t coming from both the a p p l i e d f i e l d and the i n t e r n a l exchange f i e l d a t low temperature T << Tc. The temperatureand f i e l d dependence o f the exchange f i e l d is described by the B r i l l o u i n f u n c t i o n . The free energy of the normal s t a t e is thus lowered very q u i c k l y according to the p o l a r i z a t i o n o f the conduction e l e c t r o n spins in the exchange f i e l d , which a l r e a d y reaches i t s s a t u r a t i o n value at low a p p l i e d f i e l d s of the o r d e r of kBT. Because o f the a n t i p a r a l l e l d i r e c t i o n of Hj r e l a t i v e to the e x t e r n a l f i e l d , the p o l a r i z a t i o n becomes weaker when H increases f u r t h e r , i . e . FN passes through a minimum and increases again up to the compensation p o i n t a t which the e x t e r n a l f i e l d e x a c t l y cancels the exchange f i e l d . In s t i l l higher f i e l d s the o r d i n a r y Pauli spin paramagnetism sets i n . The superconducting s t a t e is described by the Fs(H)-curve; a t y p e - I I - b e h a v i o r w i t h f i e l d p e n e t r a t i o n is assumed. I f Hj and Tc are a d j u s t e d c o r r e c t l y , we f i n d three i n t e r s e c t i o n p o i n t s Hl , H2, and H3 between FN and FS i n d i c a t i n g the various superconducting-normal t r a n s i t i o n s in the presence of the a p p l i e d f i e l d . I t can be seen e a s i l y t h a t there e x i s t s
only one s o l u t i o n , i f ] c , or e q u i v a l e n t l y , the superconducting condensation energy is too low (curve F~(H) in the f i g u r e ) or too high (curve Fs(H)). In the preceding discussion s p i n - o r b i t s c a t t e r i n g has been neglected. However, f o r ,~ q u a n t i t i v e a n a l y s i s o f the experimental res u l t s i t is inlportant to i n c o r p o r a t e t h i s e f f e c t i n t o the t h e o r y , lhe well-known microscopic theory of the superconducting c r i t i c a l f i e l d by Werthamer, Helfand, and Hohenberg ( l ' 3 i , which contains s p i n - o r b i t as well as paramagn e t i c e f f e c t s , has been extended by Fischer (19) to the case of a magnetic superconductor w i t h i n c l u s i o n of the compensation e f f e c t . The f i n a l formulas are q u i t e cumbersome, so t h a t we shall not w r i t e them out e x p l i c i t l y . An imp l i c i t equation f o r the c r i t i c a l f i e l d Hc2 is found, which contains as parameters tile supeYconducting t r a n s i t i o n temperature Tc, the
25~ Eu075Sn025M06SB YSev \,
•
Y = 0
.
~ =!8
25
20
k • LU 15
MultipLe p Q i r b r e a k i n g !
theory
H! - - 30 Tesitl t
9 _uJ
_ &79
T(
LL
e×D. v a l u e
kso
QS t n d l c a t e d
u_ ~0# rr 0 "
i
,:
k%
~SO = 8
0
kso- 7 3
I
2
3
L
E
TEMPERATURE T[K]. FIGURE g C r i t i c a l f i e l d s versus temperature of three d i f f e r e n t samples of the Euo.75Sno.25Mo6S8_ySey s e r i e s , compared w i t h c a l c u l a t i o n s ( s o l i ~ l i n e s ) using F i s c h e r ' s formula f o r the c r i t i c a l field.
H. W. Meul et al. / Superconductivity induced by a magnetic field
exchange f i e l d Hj, the Maki parameter ~, the magnetization M, the s p i n - o r b i t scattering parameter ~SO, and a magnetic scattering parameter ~m. I t turns out that magnetic scattering effects are unimportant in the series EuxSnl_xMo6S8 (20)~ we therefore take ~m = O. This means that the e f f e c t of MFIS presented here has nothing to do with magnetic scattering, whose influence on superconductivity has been studied by many authors (21). The c o n t r i bution of the magnetization to the magnetic induction B is also negligable in the present case. From the remaining parameters only Tc can be determined by experiment, so that there remain three f i t t i n g parameters. In Fig. 9 the c r i t i c a l f i e l d s of three samples, which are c h a r a c t e r i s t i c for the d i f f e r e n t types of behavior, are plotted together with the computed curves. We f i n d good agreement between experiment and theory. Remarkable is that these very d i f f e r e n t H-T diagrams can be obtained with one set of values for a, Hj, and the product Tc • ~SO (= 2~/3kB%s0)" The only q u a n t i t y that varies, is the superconducting t r a n s i t i o n temperature, whose value, however, is f i x e d by the measurements. Nevertheless, in order to get an optimum f i t , a s l i g h t v a r i a t i o n of the product Tc • ~SO has been admitted, which corresponds to an increase of the s p i n - o r b i t scattering time ~SO with increasing Se-concentration. The values of the three f i t t i n g parameters given in Fig. 9 are in good agreement with values obtained in other ternary molybdenum chalcogenides. In p a r t i c u l a r , the value for the exchange f i e l d Hj = -30 Tesla, which is equivalent to an exchange i n t e r a c t i o n of 20 meV, agrees well with EPR measurements by Odermatt (7). We therefore conclude that the observed MFIS is caused by the Jaccarino-Peter compensation e f f e c t . The anomalous transport prope r t i e s which have been found in EuMo6S8 at low temperature have p r a c t i c a l l y disappeared for Eu-concentrations x < 0.85 in EuxSnl_xMO6S8 and should be distinguished from the behavior reported here. In samples of the series Eu0 75Sn0 25Mo6S8_ySey we found no anomalous magnetoresistance j u s t above Tc, the Hall coe f f i c i e n t is p o s i t i v e and nearly temperature independent, and the e l e c t r i c a l resistance at low temperature is f l a t and m e t a l l i c - l i k e . In conclusion, we have observed a magneticfield-induced superconducting state in the series EuxSnl_xMO6S8, which can be explained in terms of the Jaccarino-Peter e f f e c t . This work answers a long standing question concerning the p o s s i b i l i t y of such an e f f e c t , but i t also raises several questions about the exact nature of t h i s novel state and i t s properties.
49
ACKNOWLEDGEMENTS We are very grateful to Prof. M. Peter for many stimulating discussions and his i n t e r e s t in t h i s work. We also thank Prof. R. Tournier for the support he has given to t h i s work. We acknowledge Dr. M. Karkut for helpful discussions and c r i t i c a l l y reading t h i s manuscript. Two of us (C.R. and H.W.M.) thank the MaxPlanck I n s t i t u t e and the low-temperature group of the Centre National de la Recherche S c i e n t i fique in Grenoble for the kind h o s p i t a l i t y . We thank A. Klaschka for help with the He3 measurements and A. S t e t t l e r for his technical assistance. REFERENCES ( I ) See for example: Superconductivity in Ternary Compounds, Vol. 2, eds. M.B. Maple and 9.Fischer (Springer, Berlin Heidelberg New York, 1982). (2) F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, and H. Schaefer, Phys.Rev.Lett. 43 (1979) 1892. H.R. Ott, H. Rudigier, Z. Fisk, and J.L. Smith, Phys.Rev.Lett. 50 (1983) 1595. G.R. Stewart, Z. Fisk, J.O. Willes, and J.L. Smith, Phys. Rev.Lett. 52 (1984) 679. (3) H.W. Meul, C. Rossel, M. Decroux, ~. Fischer, G. Remenyi, and A. Briggs, Phys.Rev.Lett. 53 (1984) 497. (4) V. Jaccarino and M. Peter, Phys.Rev.Lett. 9 (1962) 290. (5) 9. Fischer, M. Decroux, S. Roth, R. Chevrel, and M. Sergent, J.Phys. C8 (1975) L474. (6) F.Y. Fradin, G.K. Shenoy, B.D. Dunlap, A.T. A l d r e t , and C.W. Kimball, Phys. Rev.Lett. 38 (1977) 719. (7) R. Odermatt, Helv.Phys.Acta 54 (1981) I . (8) A.J. Freeman and T. Jarlborg, in Superc o n d u c t i v i t y in Ternary Compounds, Vol.2, eds. M.B. Maple and 9. Fischer (Springer, B e r l i n Heidelberg New York, 1982) pp. 167 - 200. (9) M. I s i n o , N. Kobayashi, and Y. Muto, in Ternary Superconductors, eds. G.K. Shenoy, B.D. Dunlap, and F.Y. Fradin (North Holland, Amsterdam, 1981) p. 95. (I0) S.A. Wolf, W.W. F u l l e r , C.Y. Huang, D.W. Harrison, H.L. Luo, and S. Maekawa, Phys.Rev. B25 (1982) 1990. W.W. F u l l e r , S.A. Wolf, C.Y. Huang, D.W. Harrison, H.L. Luo, and S. Maekawa, J.Appl.Phys. 53 (1982) 2622. ( I I ) H.J. Schneider-Muntau, IEEE Trans.Mag., VoI.MAG-18 (1982) p. 1565. (12) M. Decroux and 0. Fischer, in Supercond u c t i v i t y in Ternary Compounds, Vol. 2, eds. M.B. Maple and ~. Fischer (Springer, B e r l i n Heidelberg New York, 1982) pp. 57.
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ILLW. Meul et al. / SuperconductiviLv induced by a magnetic .field
(13) B. Lachal, A. Junod, and J. Muller, J. Low Temp. Phys. 55 (1984) 195. (14) M. Decroux, H.W. Meul, C. Rossel, 9. Fischer, and R. B a i l l i f , in Superconductivity in d- and f-Band Metals, eds. W. Buckel and W. Weber (KFK GmbH, Karlsruhe, 1982) p. 167. (15) M.S. T o r i k a c h v i l i , M.B. Maple, R.P. Guertin, and S. Foner, J. Low Temp. Phys. 49 (1982) 573. (16) M.S. T o r i k a c h v i l i , J. B e i l l e , S.E. Lambert, and M.B. Maple, in Superconduct i v i t y in d- and f-Band Metals, eds. W. Buckel and W. Weber (KFK GmbH, Karlsruhe, 1982) p. 241. (17) J. Bolz, G. Crecelius, H. Maletta, and F. Pobell, J. Low Temp.Phys. 28 (1977) 61. (18) H.R. Werthamer, E. Helfand, and P.C. Hohenberg, Phys. Rev. 147 (1966) 295. (19) 9. Fischer, Helv. Phys.Acta 45 (1972) 229. (20) H.W. Meul, M. Decroux, R. Odermatt, R. Noer, and 9. Fischer, Phys.Rev. B26 (1982) 6431. (21) A.A. Abrikosov and L.P. Gorkov, Sov. Phys.JETP 12 (1961) 1243. E. Mueller-Hartmann and J. Z i t t a r t z , Phys. Rev.Lett. 26 (1971) 428. I. Kirschner and A. Stark, Acta Phys.Hung. 30 (1971) 33. S. Maekawa and M. Tachiki, Phys. Rev. Bl8 (1978) 4688.