Topological transverse spin transport in a canted antiferromagnet/heavy metal heterostructure

We theoretically study the conditions under which a spin Nernst effect - a transverse spin current induced by an applied temperature gradient - can occur in a canted antiferromagnetic insulator, such as $\mathrm{L}\mathrm{a}\mathrm{F}\mathrm{e}{\mathrm{O}}_3$ and other materials of the same family. The spin Nernst effect may provide a microscopic mechanism for an experimentally observed anomalous thermovoltage in $\mathrm{L}\mathrm{a}\mathrm{F}\mathrm{e}{\mathrm{O}}_3$/Pt heterostructures, where spin is transferred across the insulator/metal interface when a temperature gradient is applied to $\mathrm{L}\mathrm{a}\mathrm{F}\mathrm{e}{\mathrm{O}}_3$ parallel to the interface [W. Lin $etal$, Nat. Phys. $\mathbf{18}$, 800 (2022)]. We find that $\mathrm{L}\mathrm{a}\mathrm{F}\mathrm{e}{\mathrm{O}}_3$ exhibits a topological spin Nernst effect when inversion symmetry is broken on the axes parallel to both the applied temperature gradient and the direction of spin transport, which can result in a spin injection across the insulator/metal interface. Our work provides a general derivation of a symmetry-breaking-induced spin Nernst effect, which may open a path to engineering a finite spin Nernst effect in systems where it would otherwise not arise.