Investigation of cation distribution, electrical, magnetic properties and their correlation in Mn_2-xCo_2xNi_1-xO ₄ films

X-ray photoelectron spectroscopy was performed on Mn_{2- x}Co_2xNi_1-xO₄ (x=0.2, 0.4, 0.5, 0.6, and 0.8) series spinel films to determine their cation distributions. The results show that both Ni and Co ions exhibit bivalence, while Mn ions exhibit coexisting multivalence. The hopping frequency ν₀ of each sample was obtained by combining cation distribution results and electrical measurement data. Analysis of the divergence at Neel temperature between field cooling and zero-field cooling magnetization curves revealed that the ferromagnetic coupling between octahedral site ions first leads to spontaneous magnetization at T_C, after which a second spontaneous magnetization arises from the antiferromagnetic couple between tetrahedral and octahedral sites at a lower temperature T_N. The correlation between hopping conductivity and magnetic transition temperature is discussed. We propose that the strength of the ferromagnetic couple between octahedral sites is subject to the product term of Nc(1-c)ν₀, which determines the ferromagnetic transition temperature (T_C) of the system. Our results provide an avenue to understand the origin of magnetic interaction in small-polaron hopping semiconductors.