Magnonic analog of the Edelstein effect in antiferromagnetic insulators

Here we investigate the nonequilibrium spin polarization due to a temperature gradient in antiferromagnetic insulators, which is the magnonic analog of the inverse spin-galvanic effect of electrons. We derive a linear-response theory of a temperature-gradient-induced spin polarization for collinear and noncollinear antiferromagnets, which comprises both extrinsic and intrinsic contributions. We apply our theory to several noncentrosymmetric antiferromagnetic insulators, i.e., to a one-dimensional antiferromagnetic spin chain, a single layer of kagome noncollinear antiferromagnet, e.g., ${\text{KFe}}_3{\left(\text{OH}\right)}_6{\left({\text{SO}}_4\right)}_2$, and a noncollinear breathing pyrochlore antiferromagnet, e.g., ${\mathrm{LiGaCr}}_4{O}_8$. The shapes of our numerically evaluated response tensors agree with those implied by the magnetic symmetry. Furthermore, assuming a realistic temperature gradient of $10\text{K/mm}$, we find two-dimensional spin densities of up to $~{10}^6\hslash /{\text{cm}}^2$ and three-dimensional bulk spin densities of up to $~{10}^{14}\hslash /{\text{cm}}^3$, encouraging an experimental detection.