Evolution from a ferromagnetic to a spin-glass regime in the spinel-type image

Successive changes from ferromagnetic, re-entrant mixed, to spin-glass regime have been manifestly found with increasing Ti-composition x in the quaternary spinel-type Cu(Cr1-xTix)2S4Cu(Cr1-xTix)2S4 system. The Curie temperature TcTc decreases steeply with increasing x and this transition becomes ill-defined around x=0.47x=0.47. Two distinct transitions appear below TcTc over the range x=0.40–0.47x=0.40–0.47. Coexistence of the ferromagnetism and spin-glass order would be observed below the Gabay and Toulouse transition (TGTTGT), owing to freezing of the transverse-spin components without changing of the ferromagnetic order parameter. Finally, at a yet lower temperature de Almeida–Thouless transition (TATTAT), the longitudinal-spin component freezes randomly at which an irreversibility arises between zero-field-cooled (ZFC) and field-cooled (FC) magnetizations. Over the range of 0.47⩽x⩽0.850.47⩽x⩽0.85, a cusp of the ZFC magnetization is seen at TgTg like conventional spin-glass. Specimens with x⩾0.90x⩾0.90 remain paramagnetic down to 2.0 K. A magnetic phase diagram between T versus x has been obtained experimentally. The values of the multicritical point in 100 Oe is detected to be x=0.47x=0.47 and View the MathML sourceT=7.40K. The low-field magnetization and the phase diagram are satisfactorily explained by the theory of Gabay and Toulouse on the basis of Heisenberg isotropic vector spin model rather than the Ising spin model.