Magnetism and superconductivity in the Chevrel phase HoMo6S8

PHYSICA ELSEVIER

Physica B 215 (1995) 127- 133

Magnetism and superconductivity in the Chevrel phase H o M o 6 S 8 P. Burlet a'*, J. Flouquet a, J.L. Genicon b, R. Horyn ~, O. Pena ~, M. Sergent c C~A, Dbpartement de Recherche Pbndarnentale sur la Matikre Condense,e. SPSMS-MDN, 38054 Grenoble Cedex 9, France b CRTBT-C~VRS, 166)( 38042 Grenoble Cedex, France c Chimie du Solide et lnorganique Molbculaire, Universitb de Rennes, Campus de Beaulieu, 35042 Rennes Cedex, France

Received 25 November 1994

Abstract

We summarise the results of a neutron scattering study of the magnetic ordering in a single crystal of HoMo6S 8. An in situ measurement of the sample resistance allows to correlate the magnetic state with the resistive behaviour. A bulk superconductivity is associatcd with any magnetic ordering if the magnetic Ho moment is small enough to keep the induction below the critical field B¢2. A partial superconductivity occurs in ferromagnetic states; it is interpreted by superconducting walls in lamellar domain structures. A bulk superconducting phase observed in a single domain ferromagnetic state is explained by the effcct of the demagnetising field.

I. Introduction

The Chevrel phases MMo6Xs, in which X = S, Se, Te, exist with metal M going from light alkaline metals towards heavy transuranium metals through in particular the magnetic transition series (3d,41). Many of these phases are superconducting with Tc reaching rather high values (15 K for PbM06Ss) and good superconducting properties [1]. In the case of rare-earth-based Chevrel phases the presence of a paramagnetic ion and the occurrence of long-range magnetic ordering has stimulated experimental as well as theoretical studies of the interplay of magnetism and superconductivity [2]. The Chevrel phase HoMo6Ss, which exhibits superconductivity and ferromagnetic ordering, is certainly one of the best systems for such studies. HoMo6S 8 is superconducting below the critical temperature Tel = 1.8 K and undergoes a reentrance in the * Corresponding author.

normal state of Tc2 = 0.700 K. At around the same temperature it develops long-range magnetic ordering. Neutron experiments on powder samples [3] have shown that a modulated long period structure (k = [0.03, - 0.03, 0]) occurs at the ordering transition down to the temperature T,,,2 whcre a ferromagnetic state is stabilised. Thc Ho magnetic moments are oriented along the unique rhombohedral axis of the crystal structure (space group R3) In this paper we summarise the results of a single crystal neutron diffraction study of the magnetic behaviour of HoMo6Ss [4,5]. This work was undertaken to determine precisely the magnetic transition temperatures Tin1 and Tin2 and compare them with the superconducting transition temperature Tcz because it is not established that the reentrance into the resistive state coincides strictly with the modulated to ferromagnetic phase transition. Moreover it has been shown through resistivity and magnetisation measurements [6,7] that superconducting states can be induced at low temperature, in

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128

P. Burlet et aL / Physica B 215 (1995) 127-133

the ferromagnetic state either by warming a single crystal from a saturated ferromagnetic state or during a magnetisation cycle. The neutron-diffraction technique, which measures the ionic magnetic moment, whatever the domain state of the sample, obviously gives complementary information to the results of macroscopic measurements. After a description of the experimental conditions the magnetic phases occurring in the phase diagram of HoMo6S s will be described, and the parameters describing the field and temperature dependence will be defined. The temperature dependence of the magnetic ordering and of the sample resistance in zero field will then be described. Results concerning the superconducting phases occurring at low temperature will be presented and discussed.

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Depending on the temperature and field conditions several well-defined magnetic phases are observed. They can be distinguished from each other by a few parameters. The scans corresponding to the main phases encountered in this study are shown in Fig. 1 and the relevant parameters are given in Table 1. The paramagnetie state observed at any temperature above Tin1 corresponds to the value of the pure nuclear intensity of the [00 1] Bragg peak with the resolution limited full width at half maximum (FWHM) F = 2.6 x 10 -a r.l.u. Away from this peak only the background is observed. In this state the sample resistance is R. = 900 gf~ and 0 above and below T~I, respectively. The ferromagnetic phases are characterised by the intensity of the [00 1] reflection which is the superposition of the nuclear intensity (independent of T and H)

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2. Experimental

3. Magnetic phases of HoMo6S8

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To realise this experiment we used a single crystal of HoMo6S 8 of 15 mg set on the neutron spectrometer DN3 of the Siloe reactor in a cryomagnet equipped with a 3He-4He insert. The crystal was oriented with the [1 1 0] axis vertical in order to have a significant field component along the rhombohedral easy axis [1 1 1] and to set the magnetic propagation vector k = [k, - k, 0] in the horizontal plane. The neutron wavelength (2 = 2.4 A) and collimation conditions have been chosen to have enough resolution and sufficient intensity. Neutron scans along the [-1, -- 1, 0] direction around the (0 0 1) Brillouin zone centre allow a characterisation of the magnetic state for any field and temperature. To correlate the magnetic properties with the electrical behaviour an in situ measurement of the resistance was performed.

,

Fig. 1. Neutron scans characteristic of the magnetic states of HoMo6Ss.

Table 1 I(00 1) •(0.005, 0.005, 1)

FWHM (10 -3 r.l.u.)

Paramagnetic Modulated Microdomain 1 Microdomain 2

1200 1400 1600 2000

2.6 3.0 4.4 3.2

Ferro saturated

2700

0 0-80 50 0 0

2.6

and of a magnetic contribution proportional to the square of the ferromagnetically ordered moment. The half width at half maximum, after subtraction of the nuclear contribution and deconvolution for the experimental resolution, gives the size of the magnetic domains (up and down along the [1 1 1] direction). Three phases in which magnetic intensity is only observed on the [1, -- 1,0] peak have been observed. The single domain ferromagnetic state induced by magnetic field is characterised by a resolution limited Bragg peak and a sample resistance equal to the normal resistance R,. Two other ferromagnetic phases with F W H M significantly larger than the resolution are observed. They correspond to antiphase domains of size L given in Table 2. At low temperature, when the Ho moment is saturated, these phases, called mierodomain 1 and microdomain 2, are characterised by well-defined sample resistance values of 0.66Rn and 0.92Rn, respectively.

P. Burlet et al. / Physica B 215 (1995) 127 133 Table 2 Low temperature normalised resistance and width of the ferromagnetic domains

Modulated (quenched) Microdomain 1 Microdomain 2 Ferro single domain

R/R.

L(,~,)

0.4 0.7 0.9 1

285 800 2900 oc

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4.4

0.15 The modulated phase gives a magnetic intensity away from the [00 1] peak but, due to a limited resolution, some overlap between the nuclear Bragg peak and the magnetic contribution occurs• However the intensity at the point Q = [0.005, - 0.005, 1], at which only a small contribution of the microdomain 1 phase is observed, can be considered as characteristic of the modulated phase. This modulated phase, observed only on slow cooling between Tin1 and "/'m2, corresponds to a transverse spin wave modulation of wave vector k = [k, - k , 0 ] , with k decreasing with temperature from k = 0 . 0 1 2 at 7"=1 down to k = 0.008 at Tr,2. The sample resistance keeps a zero value in the stability range of this modulated phase. This phase can also be observed at the lowest temperature if the sample is rapidly cooled (quenched) from above T,,~. Then the sample resistance amounts to half of the normal resistance R,.

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TEMPERATURE Fig. 2. Temperature dependence of the sample resistance, the FWHM and the neutron counts at Q = (0.005,0.005, 1) in the cooling procedure.

:Q to 1000 800

4. Z e r o field b e h a v i o u r

The thermal dependencies of the relevant quantities characterising the magnetic state and of the sample resistance are given in Figs. 2 and 3 for a slow cooling process and on warming from the quenched modulated phase, respectively. O n cooling, below Tin1 = 0.750 + 0.005 K the modulated phase develops down to Tin2 = 0.700 + 0.005 K below which the microdomain 1 phase is observed. These transitions are well defined by the jumps of F W H M and the intensity variation. The sample resistance keeps a zero value down to T¢2 = 0.685 + 0.005 K, and further increases continuously to reach a saturated value of 0.66R, below 0.5 K, when the Ho magnetic m o m e n t saturates. AC susceptibility measurements [7], Fig. 4, show a diamagnetic contribution at low temperature, which proves the presence of a residual superconductivity in the microdomain 1 phase. O n warming the quenched modulated phase of wave vector k = [k, - k, 0] with k = 0.008 r.l.u., wlfich correspond to up and down regions of size L = 285 A along the wave vector direction, no change is observed up to

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TEMPERATURE Fig. 3. Temperature dependence of the sample resistance, the FWHM and the neutron counts at Q = (0.001,0.001, 1) in the warming procedure.

0.3 K. This modulated state transforms into the microdomain 1 phase which remains stable up to T,,I = 0 . 7 5 0 + 0 . 0 0 5 K . For 0 . 3 K < T < 0 . 4 5 K the sample resistance increases from the value characteristic of the modulated phase tR,/2) to that characteristic of the

P. Burlet et al. / Physicu B 215 (1995) ]27-133

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Fig. 4. AC susceptibility of H o M o 6 S a at low temperature (from Ref. 17]). cr,,

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microdomain 1 state (0.66R,) and decreases continuously at higher temperature to vanish at T~2 = 0.685 K. F r o m these experimental results it appears unambiguously that the reentrance transition in a resistive state is not linked to the transition from the modulated and ferromagnetic states since it occurs inside the ferromagnetic microdomain state. Moreover it is clear that the normal state is not recovered even at the lowest temperature but rather a mixed state with a well-defined value of

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MAGNETIC FIELD (kOe)

Fig. 5. Magnetic field dependence at T = 0.07 K of the sample resistance and of the (001) intensity. The sample is initially in the quenched modulated phase.

5. Low temperature superconductivity A superconducting state can be obtained at low temperature ( < 0.1 K) during a magnetisation cycle. As seen in Fig. 5, on increasing the applied field the ferromagnetic microdomain state transforms into a fully aligned ferromagnet for H = 1.8 kOe with resistance R = Rn. O n decreasing the field this state remains stable down to H = 0 and, after inversion of the field direction, the magnetic contribution and the resistance vanish at It = 0.8 kOe before further increasing and reaching the ferromagnetic saturation for H = - 1.8 kOe. During this measurement a temperature instability was observed at H = 0.8 kOe, with a rise of sample temperature above 0.7 K. This can be explained because for H = 0.8 kOe and rn = 9.6 #n the energy corresponding to the magnetisation reversal reaches 5.4 J/mol which is enough to warm the sample considering the nuclear specific heat ( ~ 6 J / m o l - ~ K -~). It is then possible that a superconducting, magnetically disordered state was quenched by a very fast cooling. Similar phenomena have also been observed in magnetisation studies [7]. More interesting is the low temperature superconducting state obtained on warming a saturated ferromagnetic

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Fig. 6. Temperature dependence of the sample resistance, the integrated (00 1) magnetic intensity and the FWHM obtained on warming from a ferromagnetic single domain state. state. This state is reached by application of an external field H > 2 kOe and is conserved if the field is switched off. Fig. 6 shows the variation of R/R., of the magnetic

P. Burlet et aL /Physica B 215 (1995) 127-133

contribution to the integrated intensity, and of the F W H M of the [00 1] peak. At T = 0.100 K the sample resistance drops to zero and the magnetic intensity decreases to reach about 1/3 of its saturated value at 0.2 K whereas the F W H M keeps the resolution limited value (2.6 × 10- 3 r.l.u). This implies a reduction of the ordered Ho moment. This state with a zero resistance and a resolution limited and low intensity magnetic contribution persists up to 0.2 K where the resistance as well as the intensity and F W H M increase. In between 0.3 K < T < 0.5 K a microdomain ferromagnetic state is recovered with F = 3.2 x 10 -3 r.l.u, a magnetic contribution to the [0 0 1] intensity similar to that observed in the saturated state and a resistance of 0.92R,. Above 0.5 K the magnetic signal thermally decreases continuously and vanishes at Tin1 = 0.750 K whereas the resistance vanishes at T~2 = 0.685 K.

6. Discussion First the occurrence, just below Trnl, of a modulated phase results from the influence of the superconductivity on the exchange interactions. This point has already been fully studied and is well understood [8, 9] so that we will focus on the other results presented here. At low temperature, when the Ho magnetic moment reaches saturation, the normal state with a resistance R, equal to that observed above Tel is only obtained if a magnetic field is applied, large enough to induce a single domain ferromagnetic state. All the other magnetically ordered states (microdomains I and 2, quenched modulated phases) are characterized by a well-defined size L of up and down domains and correlated with a well-defined low temperature resistance value. At higher temperature, near the ordering transition, the reentrance in a finite resistance state with R < R~ occurs in the ferromagnetic microdomain phases at the temperature T~2 = 0 . 6 8 5 K definitively lower than Tin2 = 0.700 K. On warming from the saturated single domain ferromagnetic state a zero resistance state associated with a single domain ferromagnetic state with a reduced magnetic moment value of the Ho ion is stabilised at low temperature. These findings can be interpreted by considering that the pertinent parameters for the superconducting behaviour and the magnetic one are different. Superconductivity is dependent on the macroscopic magnetic induction B whereas the magnetic ordering is driven by the local induction B1o~. Both depend on the external field B = Bo, the magnetisation M = m / V and the demagnetising field coefficient n (m an V are the Ho ordered moment and the unit cell volume, respectively)

131

and they are given by the following expressions: B = Bo + 4zrM(1 -- n), Bloc = Bo + 2m -- 4 n n M ,

where 2m is the internal field due to exchange and dipolar interactions. Concerning the superconductivity a bulk superconducting state (R = 0) will be observed if anywhere in the crystal the induction B is lower than the critical field Be2. This is the case of the high temperature modulated phase and of the microdomain 1 and 2 phases in the range Tee < T < TreE.Indeed at Tez the Ho magnetic moment amounts to 7.6/zB which corresponds to B = 3170 G, in agreement with the value B~a = 3200 G obtained by resistivity measurement under applied field just above

T~I [7]. A normal state with R = Rn will be obtained if B is homogeneously larger than B¢2; this is the case for the ferromagnetic single domain phase. A mixed state with R < R, can be reached if in some parts of the sample B is on the average vanishing on a scale length larger than the coherence length 4. This is the case of the microdomains and quenched modulated phases. These phases, due to the huge anisotropy of HoM06S8, must be considered as lamellar antiphase structures with domain shape such as n = 0. In zero field the induction B is, inside a domain, 4 ~ m / V but it vanishes around the domain walls allowing partial superconductivity. In an intermediate temperature range (typically from To2 down to 0.5 K) where the Ho moment still thermally increases, the width e of the superconducting region decreases down to e = ~ and the sample resistance increases to saturate at lower temperature when the widths of the superconducting parts are equal to the coherence length 4. Such a mixed state is shown schematically in Fig; 7. At low temperature the size of the domains as well as the sample resistance are well defined. These two quantities can be related by considering that the resistive volume Vr is given by vr = v(1 -

i/L)

(here V is the volume of the crystal and L the width of the magnetic domains) and hence the sample resistance by R = R,(1 -- UL).

The values of L and R / R . observed for the different phases are given in Table 2. The plot of R / R , as a function of 1/L shown in Fig. 8 gives a width ~ = 180 A for the superconducting regions. This last value is in good agreement with the coherence length ~ = 200/~ and strongly supports the hypothesis of a wall superconductivity.

132

P. Burlet et al. / Physica B 215 (1995) 127-133 e--~ i qi

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TEMPERATURE (K) Fig. 8. Sample resistance versus the inverse of the domain size at low temperature.

T o interpret the b e h a v i o u r observed o n w a r m i n g from a single d o m a i n n o r m a l state one m u s t consider t h a t in this state the demagnetising coefficient n has a finite value a n d this modifies the i n d u c t i o n B a n d the local i n d u c t i o n B l o c. It has been p o s t u l a t e d t h a t the reduction of B by the demagnetising field c a n induce a s u p e r c o n d u c t i n g ferr o m a g n e t i c state [10], b u t in the case of H o M o 6 S s the i n d u c t i o n B = 4~M(1 -- n) is still a b o v e Be2 because the m e t a s t a b l e single d o m a i n state presents at low T the n o r m a l resistance Rn. O n w a r m i n g this single d o m a i n state we experimentally observe t h a t while still keeping the single d o m a i n state the ordered H o m o m e n t decreases. This leads to a reduction of B below Bo2 a n d then to b u l k superconductivity. W h a t remains to be explained is the r e d u c t i o n of the o r d e r e d H o m o m e n t . T h e H o ions n o w experience a reduced local i n d u c t i o n Bloc = 2m -- 4nnM, which c a n lead to a n ordered m o m e n t value smaller t h a n t h e s a t u r a t e d value. F o r a given value of n one can define a critical t e m p e r a t u r e

5000 ~-, 4 0 0 0 CD o z 3000

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0.2

0.3

0.4

0.5

0.6

0.7

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TEMPERATURE (K)

Fig. 9. (a) Ho magnetic moment versus the reduced temperature T/T.,. (b) Demagnetising coefficient as deduced from the experimental moment values in the microdomain domain state. (c) Temperature dependence of the induction B obtained on warming a ferromagnetic single domainstate.

4K

k T * = moBlo~ = mo(Z -- - ~ n ) m ,

P. Burlet et al. / Physica B 215 (1995) 12~133 less than Tml and the thermal dependence of m is now a function of t = T / T * instead of t = T/Tml. The function re(t) is known from the thermal dependence of m in zero field (Fig. 9(a) ) and n and T * can be deduced from the experimental value of re(T) . F o r instance at T = 0.15 K one measures m = 0.65 m0 corresponding to T / T * = 0.95, T * = 0.158 K and n = 0.2. The variation of n(T) and B deduced from the experimental values m(T) are given in Figs. 9(b) and (c), respectively. The demagnetising field extrapolates at low temperature to n = 0.26 a value similar to that deduced from magnetisation measurements on the same crystal. The decrease of n on increasing temperature is certainly a consequence of closure domains at the surface of the sample and the drop of n to zero corresponds to the formation of volumic domains. In conclusion, the occurrence of a resistive state in HoMo6S8 is not linked to the modulated to ferromagnetic transition but it depends only on the value of the magnetic induction B, a bulk superconductivity being observed as long as B < Bo2. However, B depends on the nature of the magnetic phase through the demagnetising field. In the microdomain phases the demagnetising field vanishes and not any bulk superconductivity is possible below Tm2 whereas a partial superconductivity occurs around the domain walls leading to a resistance smaller than the normal state resistance. In the single domain

133

ferromagnetic state the demagnetising coefficient has a finite value and the magnetic induction B and the local induction Bloc are reduced so that a low temperature bulk superconductivity associated to a low ordered m o m e n t of the H o ions is possible.

References [1] O. Pefia and M. Sergent, Progr. Solid State Chem. 19 (1989) 165, and references therein. [2] O. Fisher, in: Ferromagnetic Materials, Vol. 5, eds. K.H.J. Bushow and E.P. Wohlfarth (North-Holland, Amsterdam, 1990) p. 465-550, and references therein. [-3] J. Lynn, J.L. Ragazzoni, R. Pynn and J. Joffrin. J. Physique Lett. 42 (1981) L45. [4] P. Burlet, A. Dinia, S. Quezel, W.A.C. Erkelens, J. Rossat-Mignod, R. Horyn, O. Pefia, C. Geantey, M. Sergent and J.L. Genicon, Physica B 148 (1987) 99. [-5] A. Dinia, These, Universit+ de Grenoble (1987). [-6] M. Giroud, J.L. Genicon, R. Tournier, C. Geantet, O. Pefia, R. Horyn and M. Sergent, J. Low Temp. Phys. 69 (1987) 419; Physica B 148 (1987) 113. [-7] M. Giroud, These, Universit6 de Grenoble (1987). [-8] M. Tachiki, J. Magn. Magn. Mater. 31 34 (1983) 484. [-9] L.N. Bulaevskii, A.I. Buzdin, S.V. Panjukov and M.L. Kulic, Phys. Rev. 28 (1983) 1370. [10] V.L. Ginzburg, Sov. Phys. JETP 4 (1957) 153.