Positive Temperature Coefficient of Anisotropy due to $d^{6}L$ Groundstate in $\epsilon$-Fe${}_2$O${}_3$

Abstract

Positive anisotropy temperature coefficients ($dK/dT>0$) usually arise from hybridization between magnetic 3d states and strongly spin-orbit-coupled (SOC) subsystems. Yet $\epsilon$-Fe${}_2$O${}_3$ shows $dK/dT>0$ (125-200~K) without an obvious SOC partner. We study pure and Cr-doped (with weakened Fe-O hybridization) $\epsilon$-Fe${}_2$O${}_3$ across the transition from low temperature incommensurate to high-anisotropy magnetic phases. We identify a $d^{6}L$ groundstate in $\epsilon$-Fe${}_2$O${}_3$ while reduced hybridization yields $d^6+d^6{L}^2$ in the Cr-doped system, highlighting metal-ligand hybridization as a route to tune magnetic, electronic and orbitronic properties.