Higher-order magnetic anisotropy in soft-hard magnetic materials

Abstract

We have computationally studied the properties of higher-order magnetic anisotropy constants in an $L{1}_{0}/A1\text{\ensuremath{-}}\mathrm{FePt}$ core-shell system which is characterized by a strong second-order two-ion Fe-Pt anisotropy component. We show that the core-shell structure induces an unexpected fourth-order anisotropy constant ${K}_{2}$, the magnitude of which varies nonmonotonically with the core-size ratio $R$ reaching a peak at $R\ensuremath{\approx}0.50$. Furthermore, we find that ${K}_{2}$ scales with the normalized magnetization by ${(M/{M}_{s})}^{2.2}$ at temperatures below the Curie temperature, a remarkable deviation from the established Callen-Callen theory which instead predicts a scaling exponent of 10. We construct an analytic model which demonstrates ${K}_{2}$ arises from the canting of the core and shell magnetization, and successfully reproduces and justifies the scaling exponent obtained from numerical simulation.