Spin current generation via magnetic skyrmion, bimeron, and meron crystals

TL;DR

This work shows that spin currents can be efficiently generated by 2D topological spin textures—skyrmion, bimeron, and meron crystals—through the interplay of exchange coupling, topology, and Rashba SOC. Using a Kondo-lattice framework, the authors compute electronic structures and linear-response transport, revealing that SkX and BmX produce spin currents aligned with their magnetizations without SOC, while MX yields no spin current unless SOC is present, where enhanced spin Berry curvature drives a large out-of-plane spin current at certain fillings. Symmetry analysis via spin-space and magnetic-space groups explains the allowed spin-current components and the role of degeneracies, particularly along zone boundaries in MX, which amplify the spin Hall response. These findings extend the design space for spintronic devices by enabling spin current generation without net magnetization and highlight the potential of BmX and MX textures in topological magnetic metals for robust, multifunctional spin transport.

Abstract

Spin current offers a promising route toward energy-efficient and high-speed information processing. Developing efficient methods for their generation remains a central challenge in spintronics. Here, we investigate spin current generation via two-dimensional topological spin textures: a skyrmion crystal (SkX) with out-of-plane magnetization, a bimeron crystal (BmX) with in-plane magnetization, and a meron crystal (MX) with zero net magnetization. We show that these distinct spin textures generate spin currents with characteristic spin polarization directions. In the absence of spin--orbit coupling, the SkX and BmX generate spin currents polarized along their magnetization directions, whereas the MX yields no spin current. Upon introducing spin--orbit coupling, while the behavior of the SkX does not qualitatively change, the BmX generates nonzero spin currents in multiple polarization directions. Notably, the MX, despite its zero net magnetization, exhibits a pronounced spin current with out-of-plane spin polarization, driven by an enhanced spin Berry curvature associated with characteristic band degeneracy. We further demonstrate that the electronic and spin transport properties of each texture are governed by their magnetic symmetries. Our results highlight the topological spin textures as efficient sources of spin current even without net magnetization, expanding the design for spintronics devices based on topological magnetic metals.

Figures (8)

• Figure 1: Spin configurations of three topological spin textures and corresponding electronic band structures. (a)--(c) Schematic illustrations of the spin configurations on a square lattice for (a) SkX ($\gamma=0$), (b) BmX ($\gamma=0$), and (c) MX ($\gamma=\pi/2$). The green-shaded squares represent the magnetic unit cell, which consists of $4 \times 4$ sites. The directions of the emergent magnetic field $\mathbf{B}_{\mathrm{em}}$ and the net magnetization $\mathbf{M}$ are also shown. (d)--(f) Electronic band structures on the high-symmetry lines (see the right inset) for (d) SkX, (e) BmX, and (f) MX. The model has 32 bands in total, and the four lowest-energy ones are shown. The gray dashed lines represent the results without SOC, while the magenta lines show the results with SOC, where the strength of SOC is set to $\lambda_{\mathrm{R}}=0.1t$. In (f), the left inset shows an enlarged view around the $\mathrm{X}$ point. The blue horizontal line indicates the Fermi energy at $n_\mathrm{e} = 1$ in the presence of SOC, which crosses the bands at the $\mathrm{X}$ point.
• Figure 2: Spin-projected electronic band structures in the presence of SOC. The left, center, and right columns correspond to SkX, BmX, and MX, respectively. In each panel, the surface color indicates the spin expectation value $s_a(\mathbf{k};n)$, where $a=x,y, \mathrm{and}\ z$ for panels (a)--(c), (d)--(f), and (g)--(i), respectively.
• Figure 3: Electron filling dependencies of the charge and spin conductivities for three spin textures. The left, center, and right columns correspond to SkX, BmX, and MX, respectively: (a)--(c) charge Hall conductivity $\sigma_{xy}$ (intrinsic, plotted as the dimensionless quantity $h\sigma_{xy}/e^2$), and the spin Hall conductivities $\sigma^{s_a}_{xy}$ (intrinsic, left axes) and $\sigma^{s_a(\tau)}_{xy}$ (dissipative, right axes), and (d)--(f) longitudinal charge conductivity $\sigma^{(\tau)}_{yy}$ (dissipative, plotted as the dimensionless quantity $h^2\sigma^{(\tau)}_{yy}/e^2t\tau$), and spin conductivities $\sigma^{s_a}_{yy}$ (intrinsic, left axes) and $\sigma^{s_a(\tau)}_{yy}$ (dissipative, right axes). In each panel, the charge conductivity is plotted in gray, while the spin conductivities are plotted in different colors according to the spin polarization direction $a=x,y,z$ and the type of contribution (intrinsic or dissipative), as shown in the legend below the panels. For both the charge and spin conductivities, the open circles indicate the results without SOC, and the filled circles represent the results with SOC. The inset in (f) shows an enlarged view of $\sigma^{s_z(\tau)}_{yy}$ for $2\leq n_{\mathrm{e}}\leq4$.
• Figure 4: Berry curvature and spin Berry curvature for each spin texture in the presence of SOC. The left, center, and right columns correspond to SkX, BmX, and MX, respectively. (a)--(c) Momentum-space distributions of the Berry curvature $B_{xy}$ [Eq. \ref{['eq:Berry']}] for the lowest-energy band. (d)--(l) Spin Berry curvature $B^{s_a}_{xy}$ [Eq. \ref{['eq:SpinBerry']}] for the lowest-energy band for the spin components: (d)--(f) $a=x$, (g)--(i) $a=y$, and (j)--(l) $a=z$. The black squares indicate the magnetic Brillouin zone boundary.
• Figure 5: Temperature dependence of the spin Hall angle $\theta_{xy}^{s_z}$ for the MX at several electron fillings $n_{\mathrm{e}}$ in the presence of SOC.