Role of trivalent substitution at octahedral side on ferromagnetism and transport properties of ZnX₂S₄ (X = Ti, V, Cr) spinels

The electronic, magnetic, and thermoelectric properties of ZnX₂S₄ (X = Ti, V, Cr) are addressed for spintronic. The more released in ferromagnetic (FM) states than antiferromagnetic (AFM) states report the stable ferromagnetism. The formation and cohesive energies ensure the FM states are thermodynamically favorable. The Heisenberg classical model computations have been applied for Curie temperature. The band structures (BS) and density of states (DOS) are computed to describe half-metallic ferromagnetism, spin polarization, spin–orbit coupling, and exchange mechanism. The ferromagnetism is further interpreted in terms of crystal field energy (E_crys), direct exchange energy Δ_x(d), exchange constants (N₀α and N₀β), magnetic moments, and exchange splitting energy Δ_x (pd). The thermoelectric response is elaborated in terms of thermoelectric parameters including electrical and thermal conductivities, and Seebeck coefficient dependent power factor.