Model of phase transitions in copper spinel on Sn alloying

A theoretical study of the properties of the copper spinel Cu1+[Cr1+x3+Cr1+2x4+Sbx5+]S42- is carried out in the framework of the spin Hamiltonian. Only the cation sublattice B, containing the ions Cr3+ (S3=3/2), Cr4+ (S4=1) and the diamagnetic sites Sb5+ (S=0), is considered. Nearest magnetic ions are coupled by effective exchange interactions via the intermediate anions: J34>0 (double exchange), J44>0, J33<0 (superexchange), where J34>>J33 perpendicular, J44. For a random distribution of ions the general physical behavior pattern of the system as a function of the concentration x of the alloying element is as follows. In the region x>xcr 0.3 there exists an infinite ferromagnetic cluster of intercoupled ionsCr3+-Cr4+ (percolation via strong 3-4 ferromagnetic bonds). At x>xcr finite ferromagnetic clusters appear, oriented 'up' and 'down' and coupled by antiferromagnetic bonds J33. The total magnetization vanishes, and a spin separation or a state of the cluster spin-glass type is realized. At x 0.5 percolation via antiferromagnetic bonds J33 appears, and practically only simple isolated ferromagnet clusters in an antiferromagnetic matrix remain, oriented 'up' and 'down' in equal numbers. The limit compound (x=0.5) consists 1/4 of 'holes'-diamagnetic sites with broken bonds-and 3/4 of Cr3+ cations with antiferromagnetic bonds. Percolation via 3-4 bonds leads not only to ferromagnetism but also simultaneously to a metallic state owing to the double-exchange mechanism (the formation of a ferromagnetic half metal). In the absence of percolation via 3-4 bonds the system is an insulator. Thus as the copper spinel is alloyed with antimony (0≤x≤0.5), concentration phase transitions occur: a metallic ferromagnet (x<xcr) is transformed to an insulator with spin separation (xcr∼0.3), which in the limit x=0.5 becomes an antiferromagnetic insulator