Magnon transport in noncollinear spin textures: Anisotropies and topological magnon Hall effects

We analyze signatures of noncollinear spin textures in the magnon transport of both spin and heat by means of atomistic spin dynamics. The influence of the spin texture is demonstrated for a spin spiral and for a skyrmion lattice on a frustrated antiferromagnet. Spin spirals show an anisotropy in the longitudinal transport, whereas skyrmion lattices exhibit transverse transport, which is interpreted in terms of topology and establishes skyrmion-induced versions of magnon Hall effects. The conductivities depend sensitively on the spiral pitch and on the skyrmion size; we predict magnon Hall angles as large as 60%.

Figure 1

Topological charge $w$ per skyrmion for $\lambda =4$ versus external magnetic field $B$. A topological phase transition from the ${\mathrm{Sp}}^2$ phase to the SkX phase takes place at $B\approx 1\mathrm{meV}$. Insets show the respective static structure factor in the structural Brillouin zone. $J_1=1.171572875\mathrm{meV}, J_3=-1\mathrm{meV}, T=3\mathrm{K}$, and $N\times N=1600$.

Figure 2

Time dependence of the longitudinal (blue: $C_{\mathrm{th},\mathrm{th}}^{xx}$, red: $C_{\mathrm{th},\mathrm{th}}^{yy}$) and transverse (green: $C_{\mathrm{th},\mathrm{th}}^{xy}$, brown: $C_{\mathrm{th},\mathrm{th}}^{yx}$) thermal current correlation functions in the ${\mathrm{Sp}}^2$ (a) and in the SkX phase (b). The CCFs are normalized to their value at $t=0$. Vertical arrows indicate signatures unique to the respective magnetic phase. Parameters as in Fig. 1 with $B=0.6\mathrm{meV}$ and $B=1.2\mathrm{meV}$ in the ${\mathrm{Sp}}^2$ and SkX phase, respectively.

Figure 3

Spin conductivity ${\sigma }_{\mu \nu }$ (a), magnetothermal conductivity ${\xi }_{\mu \nu }$ (b), and thermal conductivity ${\kappa }_{\mu \nu }$ (c) versus external magnetic field for $\lambda =4$ ($\mu ,\nu =x,y$). Parameters as in Fig. 1, Gilbert damping $\alpha =0.05, \sigma$ multiplied by $\hslash$. Lines are guides to the eye; vertical arrows indicate signatures unique to the respective magnetic phase.

Figure 4

(a) Longitudinal transport anisotropy ${\kappa }_{xx}/{\kappa }_{yy}$ in the ${\mathrm{Sp}}^2$ phase. The ordering vector is along the $x$ direction. (b) Magnon Hall angle ${\kappa }_{xy}/{\kappa }_{xx}$ in the SkX phase versus $J_1/J_3$ ($J_1>0$). Three magnetic phases are indicated: collinear ferromagnetic phase (blue, “ferro”), ${\mathrm{Sp}}^2$/SkX phase (red), and the antiferromagnetic phase (green, “antiferro”). For $-4<J_1/J_3<0$ the ratio $J_1/J_3$ translates into the ${\mathrm{Sp}}^2$ pitch $\lambda$ and the corresponding skyrmion size. Cluster sizes were chosen such that the magnetic textures are commensurate. $B$ and $T$ had to be varied for the formation of the SkX phase; $\alpha =0.05$. For the ${\mathrm{Sp}}^2$ phase the magnetic field is half as large as in the SkX phase.