Exchange Integrals in the Helimagnetic Phase of ZnCr_2xAl_2−2xS₄ (0.85 ≦ x ≦ 1)

Abstract

The spinel solid solutions ZnCr,,Al, -,,S4 are studied by neutron diffraction experiments. They show a helimagnetic phase in the concentration range 0.85 5 x 5 1. The helix angle decreases as x is decreased. The three first exchange integrals and their evolution with x are obtained. The disappearance of the long-range order is shown to be due to the large decrease of the ferromagnetic in-plane interaction. The results are extended to obtain the fourth exchange integral.

Magnetic Properties and Critical Behaviour of the B-Spinel CdCr2xIn2?2xS4 (0.9 ? x ? 1)

“…The critical temperature T c AE3 and the critical exponents g AE0X002 for the magnetic susceptibility and n AE0X001 for the correlation length deduced by applying different MY N Pade  approximant method. The values are calculated by considering the values of J 1 and J 2 given in Table 1 x T c (K) g [1,4] …”

“…In the same table we give also the values of the intra-plane and inter-plane interactions J aa Y J ab and J ac , respectively, 404 M. Hamedoun, M. Houssa, Y. Cherriet, and F. Z. Bakkali Ta b l e 1 Critical temperature T c , Curie-Weiss temperature q p , values of the first, second, intraplane and inter-plane exchange integrals of CdCr 2x In 2À2x S 4 as a function of dilution x which have been calculated adopting the probability distribution described in [1,2],…”

“…Using the mean-field theory [7] and the probability distribution of interaction between chromium ions on the B sites of the spinel lattice [1,2], the variation of the intra-plane and inter-plane interactions with the ratio of dilution x is obtained in the range of concentration 0X9 x 1.…”

Magnetic phase diagram of diluted spinel Zn1−xCuxCr2Se4 system

“…The Zn 1Àx Cu x Cr 2 Se 4 is normal spinel with strong preference of Cr ions to locate in the octahedral (B) positions. Substitution of Zn with Cu ions gives a structural solid solution of the normal spinel structure [9] and causes fundamental changes of both magnetic and electrical properties. These systems are still the subject of extensive experimental and theoretical studies [10][11][12][13][14].…”

Phase Diagram of ZnCr2pAl2—2pS4 and Zn1—pCdpCr2Se4

“…Thus among these spinel compounds ZnCr 2 S 4 is antiferromagnetic (AF) (T N = 18 K) [2,5], ZnCr 2 Se 4 is AF (T N = 20 K) [3,6] and CdCr 2 Se 4 is ferromagnetic (F) (T C = 128 K) [2,7].…”