Magnon Spin Nernst Effect in Antiferromagnets

We predict that a temperature gradient can induce a magnon-mediated spin Hall response in an antiferromagnet with nontrivial magnon Berry curvature. We develop a linear response theory which gives a general condition for a Hall current to be well defined, even when the thermal Hall response is forbidden by symmetry. We apply our theory to a honeycomb lattice antiferromagnet and discuss a role of magnon edge states in a finite geometry.

Figure 1

Left: Magnon spectrum of a single layer antiferromagnet with DMI $D=0.1J$ (black arrows correspond to $\nu$ sign convention of DMI), with schematics of the lattice and order in $z$ direction in the bottom. Right: Magnon spectrum of antiferromagnet on a bilayer honeycomb lattice. Parameters are chosen to be $J^{\prime }=J$ and $D=0.1J$. In both cases the distribution of the Berry curvature over the Brillouin zone is plotted by the color distribution on top of the spectrum for one of the degenerate subbands.

Figure 2

Spin Nernst conductivity ${\alpha }_{xy}^{\mathrm{s}}$, defined after expression (15). Left: a single layer honeycomb antiferromagnet. Right: double layer honeycomb antiferromagnet. Plots are given for different values of DMI.

Figure 3

Magnon spectrum of 80 atoms wide strip of honeycomb lattice antiferromagnet. Strip is in the $x$ direction, while the $y$ direction is assumed infinite. The edges of the system are of the zigzag type. Left: Single layer with DMI, $D=0.2J$. Right: Double layer. Protected magnon edge states occur in the high energy band gap. Parameters are chosen to be $J^{\prime }=1.3J$ and $D=0.2J$.