Disentangling the contributions of individual cations to magnetic order in a spinel high entropy oxide

High entropy oxides (HEOs) can possess long-range ordered magnetic states despite their extreme chemical disorder. Very little is known about how the different chemical constituents in HEOs contribute to the emergence of these magnetic states. In this work, we leverage element-specific magnetometry attained via x-ray magnetic circular dichroism (XMCD) to understand how magnetic order is driven in two ferrimagnetic spinel-structured HEOs with compositions (Cr,Mn,Fe,Co,Ni)$_3$O$_4$ and (Cr,Mn,Fe,Co,Ni)$_{2.4}$Ga$_{0.6}$O$_4$. We find that while the magnetic transition is simultaneous for all chemical species, the rate at which their magnetic moments grow is strongly cation dependent. This behavior is explained by the varying $\textit{3d}$ crystal field level fillings of the magnetic cations, which in turn determine their ability to participate in the different magnetic exchange pathways available in the spinel structure. Dominant $A$-$B$ sublattice exchange enables some species to harden rapidly ($\textit{e.g.}$ tetrahedral Fe$^{3+}$ and octahedral Ni$^{2+}$) while others exhibit a sluggish transition due to frustration from competing interactions ($\textit{e.g.}$ octahedral Fe$^{3+}$ and Cr$^{3+}$). Non-magnetic substitution suppresses these differences, introducing broken magnetic linkages that relieve frustration. Tailoring the magnetism of HEO spinels therefore requires detailed knowledge of both their site selectivities and their exchange pathways.