Magnon thermal Hall effect in collinear ferrimagnets

Abstract

In this paper we theoretically discuss thermal Hall effect of magnons in insulating Néel ordered antiferromagnets at zero external magnetic field. We show that for compensated Néel order the non-zero thermal Hall effect will occur inthe absence of any symmetry between the two magnetic sublattices, thus making the system ferrimagnetic. The thermal Hall effect of magnons will be non-zero by a virtue of the spin-momentum splitting of the magnon spectrum due to the Dzyaloshinskii-Moriya interaction as well as anisotropic second-nearest exchange interaction different in the two magnetic sublattices, both corresponding to the broken symmetry. We construct a theoretical model in which an external electric field may change the symmetry of the antiferromagnetic system thus altering the thermal Hall effect of magnons.

Figures (3)

• Figure 1: The models of two antiferromagnetic systems are depicted. The red and blue sites represent the spin-up and spin-down magnetic sublattices of the Néel order. The systems include a nearest-neighbor Heisenberg exchange interaction (HEI, $J>0$) and Dzyaloshinskii-Moriya interaction (DMI). Further-neighbor HEI and DMI are indicated by dashed lines. In a simplifying assumption, we exclude any interactions across the green atom. The arrows on the bonds denote the sign of the DMI. The left model possesses a symmetry connecting the two magnetic sublattices, whereas this symmetry is absent in the right model.
• Figure 2: Spectrum defined in Eq. (\ref{['spectrum']}) of the two antiferromagnetic magnon modes, plotted for $\theta = -0.2$ and $t=\zeta=0$ values. Left/right plots correspond to the model I/II. The plots are shown to emphasize the role of DMI in splitting of the magnon modes in momentum at the ${\bf \Gamma}$ point.
• Figure 3: LEft: THE of magnons for the model B for $\theta = 0.2$, $t=0.4$, $\zeta =0$. We checked that $\theta \rightarrow -\theta$ will change the sign of the THE. Right: evolution of the sign of the THE with the position of the green atom.