Magnetic octupole tensor decomposition and second-order magnetoelectric effect

DOI10.1016/J.AOP.2022.168964zbMATH Open1504.78006arXiv2206.00522OpenAlexW4283276942WikidataQ114209496 ScholiaQ114209496MaRDI QIDQ2103189

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Publication date: 13 December 2022

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Abstract: We discuss the second-order magnetoelectric effect, in which a quadratic or bilinear electric field induces a linear magnetization, in terms of the ferroic ordering of magnetic octupoles. We present the decomposition of a general rank-3 tensor into its irreducible spherical tensors, then reduce the decomposition to the specific case of the magnetic octupole tensor, $mathcal{M}_{ijk}=intm{u}_i(mathbfr)r_j{r}_k{d}^{3}mathbfr$. We use first-principles density functional theory to compute the size of the local magnetic multipoles on the chromium ions in the prototypical magnetoelectric Cr${}_2$O${}_3$, and show that, in addition to the well established local magnetic dipoles and magnetoelectric multipoles, the magnetic octupoles are non-zero. The magnetic octupoles in Cr${}_2$O${}_3$ have an anti-ferroic arrangement, so their net second-order magnetoelectric response is zero. Therefore they form a kind of hidden order, which could be revealed as a linear magnetic (antiferromagnetic) response to a non-zone-center (uniform) quadratic electric field.

Full work available at URL: https://arxiv.org/abs/2206.00522

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