Physica 148B (1987) 113-116 North-Holland, Amsterdam

MAGNETIC-FIELD-INDUCED SUPERCONDUCTIVITY IN THE F E R R O M A G N E T I C STATE OF HoMo6S s

M. G I R O U D , J.L. G E N I C O N and R. T O U R N I E R Centre de Recherches sur les Tr~s Basses Temperatures, C.N.R.S, BP 166X, 38042 Grenoble-Cgdex, France

C. G E A N T E T , O. PErT, IA, R. H O R Y N and M. S E R G E N T Laboratoire de Chimie Min~rale, Universitd de Rennes, Avenue du Gdn&al Leclerc, 35042 Rennes-CYdex, France

Received 20 July 1987

We present new results obtained by simultaneous magnetization and resistance measurements on a HoMo6S 8 single crystal, in the whole temperature range 30 mK ~< T ~< 4.2 K and for several orientations of the easy magnetization axis with respect to the applied field. Field-induced superconductive transitions are observed in the ferromagnetic state of that re-entrant superconductor. They are described as the first experimental realization of an electromagnetic effect earlier suggested by Ginzburg, which requires a negligible effect of the exchange field. Our results concerning the anisotropy of H¢2 are consistent with that requirement. We also notice the possible existence of Ising wall superconductivity in HoMorSs.

1. Introduction

Since the discovery in 1977 of two ferromag- netic re-entrant superconductors HoMo6S 8 [1] and ErRhaB 4 in the primitive tetragonal struc- ture [2], extensive studies of the mutual influence of superconductivity and magnetic ordering have been carried out [3]. The importance of ex- change interactions [4], the possible change in the nature of the transition at Hc2 [5, 6], the existence of a modula ted magnetic order in the superconducting state [7, 8] and the supercon- ductivity of domain walls [9, 18] have been theoretically investigated.

HoMo6S 8 is superconductive between Tc~ = 1.78 K and Tee ~ 0.65 K, and becomes ferromag- netically ordered below T m = 0.75 K, with a long wavelength modulat ion between 0.69 and 0.75 K [10]. The resistance of the ferromagnet ic state after zero-field cooling is only 50 to 85% of the residual resistance R. at T > T c l . The most strik- ing proper ty of UoMo6S 8 is the occurrence of a zero-resistance state produced in the ferromag- netic state [11] by applying a reverse field on a crystal or by heating it to T = 0.1 K after having saturated its magnetization. In order to deter- mine the origin of that behaviour, we per formed simultaneous resistance and magnetizat ion mea-

surements on a 15 mg single crystal, in the tem- perature range 30 m K < T < 4.2 K and for sever- al orientations of the easy magnetization axis with respect to the applied field - HoMo6S 8 is an Ising fer romagnet [12]. A detailed report about these new results will be published elsewhere [131.

2. Experimental results

In the lowest tempera ture range (30 to 80 mK) , important resistance drops are observed on the first magnetizat ion branch of the hys- teresis cycle, and the resistance vanishes when applying a reverse field after having saturated the crystal magnetization. Magnetization jumps are simultaneously observed, releasing magnetic energy in amounts of 0.8 to 5 J / tool ; in the latter case, the crystal may be heated to T > To2 and the superconductive state may be quenched in through the first order transition at T ~ 0 . 7 K . But it is not the only relevant mechanism, since we also produce a zero-resistance state by h e a t - ing the crystal to T ~ 0.1 K only, in zero applied field after having saturated its magnetizat ion at T ~ 40 mK.

At slightly higher temperatures , we show it is

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114 M. Giroud et al. / Magnetic-field-induced superconductivity in HoMo6S ~

R/R~ r-

-20o -I00 0 100 200 (roT)

p~M

100 1

- 1 0 0 .

- ~ T:95mK -~ " HJIc J -300 ~ r~tm j

- 5 0 0 t , , , , , , , , -200 -i00 i00 200

IJ, o HO (mT)

Fig. 1. Resistance ratio R / R , (upper curve) and magnetiza- tion ~z0M (lower curve) of a HoMo6S s single crystal at T = 95 mK, versus applied field p,0Ha parallel to the easy axis. The "abrupt" decrease of M for H, < 0 is a time effect.

possible to induce superconductive transitions without heating. Fig. 1 depicts R and M, simulta- neously measured, versus the applied magnetic field H a parallel to the easy axis c, at T = 95 mK. On increasing Ha, starting from a demagnetized state, R rapidly rises from 0.45-0.80 R, (value after zero-field cooling) to its normal state value R, in fields of about 20 roT, while M increases by only 2% of its saturation value M S. The be- haviour in such weak fields is reversible and nearly isotropic, on the contrary of what is ob- served for higher applied fields. In higher fields, an important resistance drop occurs during the first magnetization, between /~0Ha = 130 and 180roT, the magnetization in that field range being ~0 M ~ 200 mT, i.e. about 45% of its satu- ration value. When coming back to reverse fields ~0Ha < 0 after saturation of M, a zero-resistance state is observed. The "steps" in fig. 1 are due to time effects on the magnetization and on the resistance in a constant field.

When the angle between the applied field and the easy axis is increased, the resistance drops are smeared out and no decrease of R is possible

in fields perpendicular to the easy axis. At higher temperatures T > 0.15 K, important time effects have a dramatic influence and we do not observe field-induced transitions above 0.2 K, where M becomes nearly reversible.

We performed a systematic study of the phase diagram between Tc2 and Tc~. In fig. 2a, we plot

a

the internal upper critical field Hc2 = (He2 - n M ) versus temperature, n being the demagnetization factor measured from the Curie-Weiss law for the susceptibility (n = 0.26 for that crystal):

M M C - - - ( 1 )

Xa H. H + nM T - T m + nC '

where H~ is the applied field and H the internal field, both parallel to the c-axis. Since the macro- scopic average of the local dipolar field is in fact the induction, we also plot in fig. 2b, the critical induction Oc2 = p.O(/-/ca2 + (1 - n)M) versus tem- perature. On decreasing the angle (Ha, c), M

p . o H c 2

(mr) 30O

200

I 0 0

0

B e 2

a

1 1.5 T ( K )

(roT) 3Eli]

O *,m

200 % @

1 0 0 m I " ~ o

0 . . . . 0 .~5 " -~ - - -1 1 . 5

T ( K )

Fig. 2. a) Internal upper critical field P, oHc2 versus tempera- ture. (O) a = ( H . , c ) = 0 ° ; (A) a = 3 5 ° ; ( I ) o t=90 ° . b) Critical induction Be2 = ~,olln~2 + (1 - n)M][. (O) a = (Ha, C) = 0°; (&) o~ = 35°; ( n ) a = 90 °, [same data as in (a)].

M. Giroud et al. / Magnetic-field-induced superconductivity in HoMorS 8 115

increases and He2 becomes weaker; the maxi- mum in Hc2(T ) shifts towards higher tempera- ture. On the contrary, Be2 ,is isotropic and "peaks" at T ~ 0.75 K = T m before falling down to zero between T m and Tc2. The critical field nc l is too low to be measured in our experiment (He1 ~< 1 mX).

In addition, we observed a change in the nature of the transition below Tin0.75 K, where M increases discontinuously in the (internal) field where R starts to be non-zero.

3. Discussion

Our results for T > Tc2 show that exchange effects on the superconductivity of HoMo6S 8 are particularly weak: there is no clear deviation from the Curie-Weiss law

3.06 (S.I. units)

Xa T - 0.75 + 3.06 n

below Tel (except in very weak fields of order of Hcl , which is below 1 mT); that would not be the case if the Ho 3÷ magnetic moments were strong- ly interacting with conduction electrons. The absence of anisotropy in Bc2 proves that the anisotropy of He2 originates in the dipolar field created by the H o 3+ Ising magnetic moments. In fact, the "effective" field acting on electrons is

bef f : ~ bdipola r) q- hex = B + AexM ,

where AexM is the anisotropic exchange field, which is known to produce an important aniso- tropy of Be2 in ErRh4B 4 crystals [14,15]. Moreover, the fact that the transition appears to be of first order only below T m is also indicative of weak exchange effects [4, 6]. The reason therefore must be the existence of an important spin-orbit scattering in HoM06S 8 (the spin-orbit mean free path /so must be appreciably shorter than the B.C.S. coherence length ~0 ~ 1400/~), together with a relatively low exchange energy (0ex ~< 0.15 K per Ho ion in the normal state).

Dipolar interactions being dominant in HoM06S8, we can describe the low-temperature ( T < Tc2 ) field-induced transitions as the first experimental observation of an electromagnetic

effect earlier suggested by Ginzburg [16]. We define B_+ as the induction in up (resp. down) ferromagnetic domains:

B_+ ~ ~z0mlH a - n M +-- Msr I , (2)

where H a is the applied field, M the average sample magnetization which we measure, - n M a reasonable approximation for the demagnetizat- ing field, and -+M~ the spontaneous magnetiza- tion of Ho ions in each type of domains. When the field H is antiparallel to the magnetization in a ferromagnetic domain, the induction may be reduced below its critical value Bc2.

We show in fig. 3 the resistance ratio R / R , versus B_+ (B+ for the down scale, B_ = B + - 2/x0M s for the upper scale). B+ or B are calcu- lated using formula (2), the magnetization M and the normalized resistance R / R n being simul- taneously measured. On the left-hand side curve of fig. 3, superconducting transitions are induced under zero external field by heating the crystal from 40 to 120mK after saturation of its mag- netization at 40 mK. The up ferromagnetic do- mains become superconducting at B+ = 370 mT. On the right-hand side curve of fig. 3, the resist- ance drop observed on the first magnetization branch of the hysteresis cycle at T = 95 mK (see fig. 1) has been plotted versus B_. The down ferromagnetic domains become superconducting in a positive external field when B_ = 360 mT.

R / R n _ _

.75

.5

0 20[

.25

i

4

3oo 400 B+(mT)

B-(mT) -400 -300

Fig. 3. Resistance ratio R / R n versus induction B+ in up or down domains (see text). ( I , 0 , &): superconductive transi- tion induced by heating from 40 to 120 mK a monodomain crystal (3 different runs): B+ ~ Be2(0 ). (@): resistance drop observed on the first magnetization branch of the hysteresis cycle at T = 9 5 m K : IB I = Be2(0).

116 M. Giroud et al. / Magnetic-field-induced superconductivity in HoMo6Ss

T h e s u p e r c o n d u c t i v e t r ans i t ions p r o d u c e d e i the r by sl ightly hea t ing up to 0.12 K a m o n o d o m a i n crysta l ( l e f t -hand side curve) , or on increas ing the field ( r igh t -hand side curve , first magne t i za - t ion) bo th occur when I B+I o r I B_l is a b o u t 3 7 0 m T , which co inc ides wi th the e x t r a p o l a t i o n to ze ro t e m p e r a t u r e of Bc2(T) . No te tha t the res i s tance m a y not vanish if the d o m a i n s which a re a l lowed to b e c o m e s u p e r c o n d u c t i n g r ep re - sent a minor i ty of the s amp le vo lume .

As a c o n s e q u e n c e of tha t e x p l a n a t i o n , and in a g r e e m e n t with ou r resul ts , no f i e ld - induced supe r conduc t i ve t r ans i t ion should occur if the m a g n e t i z a t i o n is r evers ib le (M = H a / n for T > 0 . 2 K ) since IB+l then r ema ins close to p,0M~ > Be2. [B+I < Bc2 can ne i the r be fulfi l led for high

angles ( H a, c). F ina l ly we brief ly come back to the b e h a v i o r

of R in very w e a k fields: the absence of aniso- t r o p y in the m a g n e t o r e s i s t a n c e ind ica tes tha t it is not due to a bu lk p r o p e r t y . A b r a n c h e d super - conduc t ing sur face layer of ze ro ave rage mag- ne t i za t ion might be invo lved , but we wou ld ex- pec t it to be much less sensi t ive to fields app l i ed p e r p e n d i c u l a r to the easy axis. The low va lue of R m a y r a the r be due to Ising wall supe rconduc - t ivity: the wall s u p e r c o n d u c t i n g cri t ical f ield Hcw may be h igher than the bu lk Be2 [9], a l lowing the ex is tence of s u p e r c o n d u c t i n g shee ts pa ra l l e l to the easy axis c. I t wou ld be cons i s ten t with an o b s e r v e d d e p e n d e n c e on the s amp le qual i ty , on the o r i e n t a t i o n of the e lec t r ica l con tac t s and on the coo l ing ra te [13, 17]: the res i s tance is lower in the q u e n c h e d m o d u l a t e d phase , c o r r e s p o n d i n g to a sma l l e r in te r -wal l spacing.

4. Conclusion

We o b s e r v e d magne t i c - f i e ld - i nduced supe rcon- duc t ive t rans i t ions in the f e r r o m a g n e t i c s ta te of H o M 0 6 S s. The s tudy of the u p p e r cr i t ical field revea ls tha t d ipo la r i n t e rac t ion is d o m i n a n t in H o M 0 6 S s , ind ica t ing tha t the l o w - t e m p e r a t u r e f i e ld - induced t rans i t ions a re due to the r educ t i on of the magne t i c induc t ion b e l o w its cr i t ical va lue when H and M are an t ipa ra l l e l [16]. Is ing wall

supe rconduc t iv i t y m a y be r e spons ib l e for the low value of the res i s tance af te r zero- f ie ld cool ing.

Acknowledgements

This work was s u p p o r t e d by the D i rec t ion des R e c h e r c h e s et E t u d e s Techn iques . J. Rossa t - M ignod , P. Bur le t , A . Din ia and coworke r s a re a c k n o w l e d g e d for f rui t ful discussions .

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