E. Agostinelli, P. Filaci, D. Fiorani and E. Paparazzo. I.T.S.E, Area della Ricerca di Roma, C.N.R., Casella Postale 10, 00016 Monterotondo Stazione, Roma, Italy.
Solid State Communications, Vol. 56, No. 6, pp. 541-543, 1985. Printed in Great Britain.
0038-1098/85 $3.00 + .00 Pergamon Press Ltd.
SPIN-GLASS LIKE BEHAVIOUR IN A CONCENTRATED CHROMIUM SPINEL: Zno.sCdo.sCr2S4 E. Agostinelli, P. Filaci, D. Fiorani and E. Paparazzo I.T.S.E, Area della Ricerca di Roma, C.N.R., Casella Postale 10, 00016 Monterotondo Stazione, Roma, Italy
(Received 15 June 1985 by G.F. Bassani) Low field d.c. and a.c. susceptibility measurements are reported for the non magnetically diluted spinel Zno.sCdo.sCr2S4. A spin-glass like behaviour is observed at low temperature (TF = 15.4 K at g = 198 Hz). This is the result of the presence of competing interactions (ferromagnetic between nearest-neighbours and antiferromagnetic between higher order neighbours) and of the disorder of their distribution due to the substitution between non-magnetic zinc and cadmium ions in the tetrahedral sites of the spinel lattice. INTRODUCTION IT IS WELL-KNOWN that frustration and disorder are the essential ingredients for obtaining a spin-glass state. The disorder in the distribution of magnetic interactions may be either topological, as in amorphous materials, or may arise from a random magnetic dilution in crystalline materials. A spin-glass behaviour has been observed in nonmagnetically diluted crystalline insulating systems as well, but only few examples are known (i.e. EuSo.lSeo.9) [ 1 - 3 ] . In this context, the magnetically concentrated spinel system Zno.sCdo.sCr2S4, the object of the present investigation, offers a peculiar example, as in this case the disorder of the magnetic interactions is due to the substitution between non magnetic ions (Zn and Cd). In this system magnetic chromium ions occupy the octahedral (B) sites, while non-magnetic zinc and cadmium ions occupy the tetrahedral (A) sites of the spinel structure. The frustration arises from the coexistence of short-range interactions of opposite sign: ferromagnetic super-exchange between first neighbours (J1) ( C r - S - C r chain) and antiferromagnetic superexchange between higher-order neighbours (K) through different paths involving more than one sulphur atom [4]. The value of K is very sensitive to the type of nonmagnetic ion occupying the A sites. The J1/K ratio depends therefore on the substitution between zinc and cadmium. A ferromagnetic phase is stabilized in CdCr2S4 (Tc = 84.5 K; O = 152K) [5] and, conversely, the magnetically stable phase is antiferromagnetic (at low temperature there is a superposition of helimagnetic and modulated phase) [6] in ZnCr2S4 (Tlv = 18K; 0 = lSK) [5,7]. The Jl/K ratio is expected to vary continuously with the composition x in the system ZnxCdx_l Cr2S4 and it will be very sensitive to fluctuations of
concentration. A critical value R = --0.25 [8] (when K correspond only to the third neighbours interactions) has been theoretically predicted, above which a helimagnetic state replaces the ferromagnetic one. We report preliminary results of low-field d.c. and a.c. susceptibility measurements indicating that for the intermediate composition x = 0.5 a spin-glass state is established at low temperature ( T = 1 5 . 4 K at p = 198 Hz) induced by frustration and disorder of magnetic interactions. EXPERIMENTAL The sample was synthesized as a powder by direct reaction of ZnS, CdS and Cr2Sa at T = 900°C in a sealed quartz tube. X-ray diffraction shows that the sample is composed of single phase spinel (a = 10.023 + 0.001 A). Low-field susceptibility measurements were performed in the temperature range 4.2 K ~ T ~ 250K. a.c. susceptibility measurements were performed at v = 198 Hz using a mutual inductance bridge. Low-field d.c. ( H = 400Oe) susceptibility measurements were performed using a Faraday balance described elsewhere [9]. The d.c. measurements were performed in two runs: (i) after cooling in zero field to the lowest temperature the field was applied and was held constant during the measurements with increasing temperature (XZFC);(ii) the sample was cooled down again at the same constant field and the measurements were made with increasing temperature (XFc)RESULTS AND DISCUSSION The temperature dependence of low-field d.c. and a.c. susceptibility measurements exhibits a typical spinglass behaviour (Figs. 1,2). The a.c. susceptibility (X'a.c.) (Fig. 1) shows a sharp
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CONCENTRATED CHROMIUM SPINEL: Zno.sCdo.sCr2S4
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:3
d
I
I
I
10
20
30 T (K)
Fig. 1. Temperature dependence of a.c. susceptibility (×'~.c.) at v = 198 Hz.
F.C. 18
E
15
I
I
I
Fig. 2. Temperature dependence of d.c. susceptibility (eXzFc and OXFC) measured applying a field of 400 Oe. maximum at T = 15.4K for v = 198Hz. The d.c. susceptibility curve (Fig. 2) also shows a maximum, when measured after cooling in a zero field (XzFc), at T = 14.5 K. Below this temperature, magnetic irreversibility appears: the susceptibility measured after field-cooling from 250 K splits from the ×zvc curve remaining constant down to 4.2K. The low-temperature plateau of XFC the sharp maximum of XZFC and the appearance of irreversibility just below this maximum suggest the occurrence of a cooperative freezing at Tv. This behaviour has been found in other insulating spin-glasses for high concentrations of the magnetic ions (i.e. CdCr2xIn2-2xS4) [I0, 11], and Fel-xMgxC12
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[12] as well as in diluted metallic alloys (i.e. CuMn [13], where a small maximum of Xrc at TF is also observed). On the other hand, a continuous slow increase of XFC with decreasing temperature below TF and the appearance of irreversibility above TF has been found in other diluted insulating materials [11,12] and in metallic spin-glasses like La~_xGdxAl2 (where the amplitude of the RKKY interaction is much smaller than in canonical spin-glasses, like CuMn), whose properties are better explained in terms of a progressive freezing of clusters [ 14]. The temperature dependence of Xvc was measured up to 250K and is reported in Fig. 3. At high temperature ( T > 100K) a Curie-Weiss behaviour X = Co/(T--do) is followed with Co = 1.78 and 0o = + 45 K. The positive value of do indicates a predominance of ferromagnetic interactions. Below 100K the susceptibility starts to deviate from the Curie-Weiss law and this indicates a progressive development of short-range correlations between chromium spins. Below about 60K down to TF there is another region of linearity. A Curie-Weiss like law X = C/(T-- O) is therefore followed in this temperature range with a Curie constant value C larger than the Co value corresponding to the high-temperature paramagnetic region (C/Co = 2.1) and a negative 0 value (-- 7 K), indicating a predominance of antiferromagnetic interactions. This paramagnetic-like behaviour at low temperature, resembling to that of superparamagnetic clusters, should be associated with rigid clusters with predominant intracluster ferromagnetic interactions (because of the higher strength of the n.n. ferromagnetic interactions) coupled among them by antiferromagnetic interactions. In the hypothesis of strictly ferromagnetic clusters n = C/Co represents the average number of spin per cluster (in the case of canted ferromagnetic clusters this number should be lower). The same kind of behaviour has been observed in other magnetically diluted systems, like ZnCr2x Al2-2x $4 [ 11], CdCr2xIn2-2xS4 [11] and FexMgx-~Cl2 [15], where the mean number of spin per cluster was found to increase with the concentration x. In our concentrated system x is equal to 1 and the low value of n, mediated by fluctuations of concentration between Zn and Cd, gives an idea of the effect of the frustration between competing interactions. CONCLUSIONS Low-field d.c. and a.c. susceptibility curves for the non-magnetically diluted Zno.sCdo.sCr2S4 system exhibit a behaviour characteristic of a spin-glass like state at low temperature. This is induced by the
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Acknowledgements - We thank Dr. J.L. Dormann and Dr. M. Nogues for useful discussions.
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xatl(ern U/at )-1
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0
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T(K)
Fig. 3. Inverse of F.C. susceptibility (Xv~.) as function of the temperature.
competition between n.n. ferromagnetic interactions and higher-order neighbours antiferromagnetic interactions, due to the substitution between Zn and Cd ions, which produces local fluctuation of the Jx/K ratio. The high-temperature behaviour of the susceptibility shows that magnetic correlations are established far above TF and lead to the growth of rigid clusters, which exhibit a superparamagnetic-like behaviour down to TF, where they freeze cooperatively in an infinite cluster.
