Critical behavior of multiferroic sulpho spinel compounds: MCr2S4 (MÂ =Â Co & Fe)

Near the paramagnetic to ferrimagnetic transition temperature, the dc magnetization data of two sulpho spinels, CoCr2S4 and FeCr2S4, are analyzed by the modified Arrott plot, the Kouvel-Fisher method, log M vs log H, and the scaling analysis. Critical exponents β = 0.3946±0.0064, 0.421±0.04, γ = 1.101±0.004, 1.041±0.015, and δ = 3.77±0.06, 3.512±0.14 are obtained around the critical temperature ∼ 224.4 K and 166.5 K for CoCr2S4 and FeCr2S4, respectively. Scaling analysis indicates that calculated critical exponents, as well as critical temperatures, are intrinsic to the systems. The values of critical exponents of CoCr2S4 are between those predicted for a three dimensional Heisenberg model and those predicted by mean field theory. Probably, the observed large spin-phonon coupling and magnetocrystalline anisotropy caused by Co ion may play the key role in this critical behavior of CoCr2S4. The critical exponents of FeCr2S4 are close to the mean field theory except for δ, which is higher than the theoretical value. The higher value of δ may arise due to the incomplete ferrimagnetic transition and presence of short range magnetic ordering above TC for FeCr2S4.