Validating mean field theory in a complex disordered high-entropy spinel oxide

The advent of unique high-entropy oxides has sparked substantial research interest due to their exceptional functional properties, which often surpass the mere sum of their constituent elements' characteristics. This paper introduces a complex high-entropy spinel oxide with composition (${\mathrm{Ni}}_{0.2}{\mathrm{Mg}}_{0.2}{\mathrm{Co}}_{0.2}{\mathrm{Cu}}_{0.2}{\mathrm{Zn}}_{0.2})({\mathrm{Mn}}_{0.66}{\mathrm{Fe}}_{0.66}{\mathrm{Cr}}_{0.66}){\mathrm{O}}_{4}$. We performed comprehensive structural (x-ray and neutron diffraction), microstructural, magnetic, and local electronic structure investigations on this material. Despite the material's high degree of disorder, detailed magnetization measurements and low-temperature neutron powder diffraction studies reveal long-range ferrimagnetic ordering beginning at 293 K. The sample exhibits a high saturation magnetization of 766 emu/$\mathrm{cm}{}^{3}$ (at 50 K), a low coercivity (${H}_{C}$) of 100 Oe (50 K), a high transition temperature (${T}_{C}$) around room temperature, and high resistivity value of 4000 ohm-cm at room temperature, indicating its potential for high-density memory devices. The magnetic structure is determined using a collinear-type ferrimagnetic model with a propagation vector k = 0,0,0. Various analytical techniques, including modified Arrott plots, Kouvel-Fischer analysis, and critical isotherm analysis, are employed to investigate the phase transitions and magnetic properties of this complex system. Our results indicate a second-order phase transition. Remarkably, despite the complex structure and significant disorder, the critical exponents obtained are consistent with the mean field model. The high entropy leads to a remarkably homogeneous distribution of multiple cations, validating the approximation of average local magnetic environments and supporting the mean field theory.