Efficient Electrical Spin Splitter Based on Nonrelativistic Collinear Antiferromagnetism

Spin-current generation by electrical means is among the core phenomena driving the field of spintronics. Using ab initio calculations we show that a room-temperature metallic collinear antiferromagnet ${\mathrm{RuO}}_2$ allows for highly efficient spin-current generation, arising from anisotropically spin-split bands with conserved up and down spins along the Néel vector axis. The zero net moment antiferromagnet acts as an electrical spin splitter with a 34° propagation angle between spin-up and spin-down currents. The corresponding spin conductivity is a factor of 3 larger than the record value from a survey of 20 000 nonmagnetic spin-Hall materials. We propose a versatile spin-splitter-torque concept circumventing limitations of spin-transfer and spin-orbit torques in present magnetic memory devices.

Figure 1

Schematics of the anisotropic band splitting due to collinear antiferromagnetism and of the spin-splitter effect. (a) For an electric field $\mathbf{E}$ applied along one of the $⟨110⟩$ axes, the spin-up and spin-down charge currents are parallel but of different magnitudes due to the band anisotropies. As a result, the longitudinal charge current is spin polarized. (b),(c) For $\mathbf{E}$ along one of the $⟨100⟩$ axes, the spin-up and spin-down charge currents combine in an unpolarized longitudinal charge current and in a pure transverse spin current. (d) In the absence of relativistic spin-orbit coupling, spin is conserved and the spin-up and spin-down charge currents are split by an angle that is determined by the bands’ anisotropy. In ${\mathrm{RuO}}_2$, the angle $\alpha \approx 34°$.

Figure 2

Electrical spin-splitter effect in ${\mathrm{RuO}}_2$ from ab initio calculations. (a) Spin-up and -down Fermi surfaces. (b) Crystal structure. (c) Anisotropic electronic densities. (d) Anisotropic magnetization densities calculated without spin-orbit coupling [9]. (e) $\mathcal{T}$-odd charge-spin conversion ratio calculated with and without (solid and dashed line) spin-orbit coupling and the Néel vector along the [001] direction. (f) Comparison of the corresponding longitudinal charge conductivity and transverse odd spin conductivity calculated with and without (solid and dashed lines) spin-orbit coupling.

Figure 3

Spin-splitter-torque concept. (a) $\mathcal{T}$-odd spin-splitter charge-spin conversion ratio as a function of the in-plane Néel vector angle highlighting that the polarization of the spin current follows the Néel vector. (b) $\mathcal{T}$-even spin-Hall charge-spin conversion ratio as a function of the scattering rate. (c),(d) Schematics of antiferromagnetic (red)–ferromagnetic (gray) bilayer with two different orientations of the ${\mathrm{RuO}}_2$ crystal. Configuration (c) gives a spin current in the antiferromagnet propagating in the out-of-plane direction, which can generate a spin-splitter torque on the magnetization of the ferromagnet. Configuration (d) gives an in-plane spin current and, therefore, generates no spin-splitter torque.