Strain-Induced Magnetic Anisotropy in Epitaxial Thin Films of the Spinel CoCr₂O₄

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We show that the magnetic anisotropy in spinel-structure CoCr₂O₄ thin films exhibits a strain dependence in which compressive strain induces an out-of-plane magnetic easy axis and tensile strain an in-plane easy axis, exactly opposite to the behavior reported for the related compound CoFe₂O₄. We use density functional theory calculations within the LSDA+U approximation to reproduce and explain the observed behavior. Using second-order perturbation theory, we analyse the anisotropy tensor of the Co²⁺ ions in both octahedral and tetrahedral coordination, allowing us to extend our results to spinels with general arrangements of Co²⁺ ions.