Spin-transfer torques in antiferromagnetic textures: Efficiency and quantification method

We formulate a theory of spin-transfer torques in textured antiferromagnets, which covers the small to large limits of the exchange coupling energy relative to the kinetic energy of the intersublattice electron dynamics. Our theory suggests a natural definition of the efficiency of spin-transfer torques in antiferromagnets in terms of well-defined material parameters, revealing that the charge current couples predominantly to the antiferromagnetic order parameter and the sublattice-canting moment in, respectively, the limits of large and small exchange coupling. The effects can be quantified by analyzing the antiferromagnetic spin-wave dispersions in the presence of charge current: in the limit of large exchange coupling the spin-wave Doppler shift always occurs, whereas, in the opposite limit, the only spin-wave modes to react to the charge current are ones that carry a pronounced sublattice-canting moment. The findings offer a framework for understanding and designing spin-transfer torques in antiferromagnets belonging to different classes of sublattice structures such as, e.g., bipartite and layered antiferromagnets.

Figure 1

(a) Schematic of the easy-axis (EA) AMF. (b) The spin-wave dispersions of the EA-AFM in the absence (${\omega }_{\mathit{q},\pm }^{\mathrm{EA}}$) and presence (${\omega }_{\mathit{q}{\mathit{u}}_J,\pm }^{\mathrm{EA}}$) of charge current. The horizontal axis indicates the parallel component of $\mathit{q}$ with respect to the charge current. These modes are affected by the charge current only in the exchange-dominant regime. The inset magnifies the area indicated by the dotted box, clearly showing the shift of the spectrum around the $\mathit{q}=0$ point. (c) Schematic of the easy-plane (EP) AMF. (d) The spin wave dispersions of the EP-AFM in the absence (${\omega }_{\mathit{q},1}^{\mathrm{EP}}$ and ${\omega }_{\mathit{q},2}^{\mathrm{EP}}$) and presence (${\omega }_{\mathit{q}{\mathit{u}}_J,1}^{\mathrm{EP}},{\omega }_{\mathit{q}{\mathit{u}}_J,2}^{\mathrm{EP}}$, and ${\omega }_{\mathit{q}{\mathit{u}}_t,1}^{\mathrm{EP}}$) of charge current. In the mixing-dominant regime, only the ${\omega }_{\mathit{q},1}^{\mathrm{EP}}$ mode couples to the charge current. In (a) and (c), the arrows ${\mathit{m}}_1^{\mathrm{e}}$ and ${\mathit{m}}_2^{\mathrm{e}}$ indicate the equilibrium configurations of ${\mathit{m}}_1$ and ${\mathit{m}}_2$.

Figure 2

(a) and (b) Schematics of the AFMs with bipartite and layered sublattice structures, respectively. The dotted boxes indicate the $j\mathrm{th}$ unit cells, where the sublattice 1 (2) contributes the magnetization ${\mathit{m}}_{j_1}$ (${\mathit{m}}_{j_2}$). $t$ and $t^{\prime }$ represent the nearest-neighbor hopping parameters between intra- and intersublattice sites, respectively. (c) Schematic of the coarse-grained model in Eq. (3), where both of the sublattice magnetizations ${\mathit{m}}_1$ and ${\mathit{m}}_2$ are continuous and defined at every point in space. The atomistic lattice structures and the electron hopping natures are reflected in the kinetic energy tensor of the electron.