We have computationally studied the properties of higher-order magnetic anisotropy constants in an $L{1}_0/A1\text{−}\mathrm{FePt}$ 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 $R\approx 0.50$. 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.

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• Magnetic anisotropy
• Magnetic coupling
• Magnetic interactions
• Magnetic order
• Magnetic phase transitions