Pure spin current in antiferromagnetic insulators

We theoretically investigate the transport properties of the two coupled antiferromagnon modes in a uniaxial antiferromagnetic insulator. The exchange-induced magnon-magnon scattering is found to give rise to strong mode splitting and confluence processes, which conserve the total angular momentum but change the magnon number. These processes can dramatically affect the antiferromagnon dynamics by driving the two oppositely polarized antiferromagnon species to opposite chemical potentials, resulting in a counterflow of the two species with the net magnon current being significantly suppressed. Our results suggest that the antiferromagnetic insulators could be a suitable platform for studying bosonic pure spin currents in insulators.

Figure 1

Diagrams of the exchange-induced magnon-magnon scatterings. The magnon number is conserved in (A) and (B), whereas it is changed in (C).

Figure 2

Nonlocal transport setup with NM bars on top of an AFI film. The spin Hall effect of the source bar creates spin accumulation and injects magnon into the AFI. The diffusion builds up the spatial profiles of the nonequilibrium magnon densities, which injects spin currents into the metallic detector and drain bars.

Figure 3

Spatial profile of the chemical potentials of the two magnon species at steady state driven by ${\mu }_s={\mu }_{\uparrow }-{\mu }_{\downarrow }=0.5$. The red squares and blue dots are obtained from calculations for a compensated interface with and without damping, respectively. The orange solid curve represents the sum of the two chemical potentials (solid and open triangles) for a purely polarized surface in the limit of $g^{\beta }\simeq 0$.

Figure 4

(a) Spatial profile of the magnon chemical potentials in the presence of a detector between the source and drain. The red squares correspond to the results without detectors. (b) The readout of the spin chemical potential in the detector as a function of the location of the detector. The red solid curve in (b) represents the fitting curve with a single exponential function in the long-distance region. The blue dashed and green dotted curves are fittings with Eq. (35) with nonperfect and perfect magnon sink models, respectively.

Figure 5

(a) The local magnon chemical potentials of $\alpha$ magnons (solid symbols) and $\beta$ magnons (open symbols) in the presence of temperature gradient ${\partial }_{x}T=-0.02$ due to the Joule heating effect of the source bar (${\mu }_s=0.01$). The inset shows the results in an isolated AFI channel without any metallic bars. $L$ represents the length of the AFI channel. (b) The same calculation with a detector on the right end.

Figure 6

Spatial profile of the chemical potentials of the two magnon species at steady state for ${\mu }_s={\mu }_{\uparrow }-{\mu }_{\downarrow }=2$ with (a) compensated and (b) purely polarized surfaces. The gray area represents the region of Bose-Einstein condensation.