Magnetically induced polarization in centrosymmetric bonds

Abstract

We reveal the microscopic origin of electric polarization $\vec{P}$ induced by noncollinear magnetic order. We show that in Mott insulators, such $\vec{P}$ is given by all possible combinations of position operators ${\hat{\vec{r}}}_{ij}=({\vec{r}}_{ij}^0,{\vec{\mathbf{r}}}_{ij}^{})$ and transfer integrals ${\hat{t}}_{ij}=(t_{ij}^0,{\mathbf{t}}_{ij}^{})$ in the bonds, where ${\vec{r}}_{ij}^0$ and $t_{ij}^0$ are spin-independent contributions in the basis of Kramers doublet states, while ${\vec{\mathbf{r}}}_{ij}^{}$ and ${\mathbf{t}}_{ij}^{}$ stem solely from the spin-orbit interaction. Among them, the combination $t_{ij}^0{\vec{\mathbf{r}}}_{ij}^{}$, which couples to the spin current, remains finite in the centrosymmetric bonds, thus yielding finite $\vec{P}$ in the case of noncollinear arrangement of spins. The form of the magnetoelectric coupling, which is controlled by ${\vec{\mathbf{r}}}_{ij}^{}$, appears to be rich and is not limited to the phenomenological law $\vec{P}\sim {\mathbf{\epsilon }}_{ij}\times [{\mathbf{e}}_i\times {\mathbf{e}}_j]$ with ${\mathbf{\epsilon }}_{ij}$ being the bond vector connecting the spins ${\mathbf{e}}_i$ and ${\mathbf{e}}_j$. Using density-functional theory, we illustrate how the proposed mechanism work in the spiral magnets CuCl${}_2$, CuBr${}_2$, CuO, and $\alpha$-Li${}_2$IrO${}_3$, providing consistent explanation to available experimental data.

arXiv comment6 pages, 3 figures

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• Linear Response Based Theories for Dzyaloshinskii-Moriya Interactions
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