Giant Out-of-Plane Magnetic Orbital Torque of Altermagnets from Spin-Group Symmetry Breaking

Abstract

To search for nontrivial spintronic characters of altermagnets has been a focus in spintronics, with numerous attentions paid to spin-group symmetry dictated non-relativistic effects, such as the spin-splitting torque (SST). Here, we go beyond this paradigm by unveiling the magnetic orbital torque (MOT) that is enabled only by spin-group symmetry breaking of real altermagnets with spin-orbit coupling. This effect enables generating unconventional out-of-plane orbital current with collinear orbital polarization from all 10 spin Laue groups of centrosymmetric altermagnets, which is critical for field-free manipulation of perpendicular magnetization that is a key for next-generation information technology. We reveal perturbative and non-perturbative effects of spin-group symmetry breaking, and unveil that MOT is a much more generic effect of real altermagnets than SST. Our first-principles calculations predict giant out-of-plane MOTs at room temperature in the absence of and competing with SST in experimentally identified altermagnets CrSb and FeSb2, respectively. These findings uncover new fundamental physics in altermagnetic spintronics, and open up broad vistas of altermagnets in magnetic memory.

Figures (3)

• Figure 1: SOC dependence of magnetic orbital and spin transport in a 2D ATM model (\ref{['model']}). a Nonrelativistic band structure. Spin-up and -down bands are denoted by red and blue color. b Band structure with SOC strength $\lambda_{\parallel}=\lambda_z=0.1t_1$. $t_1$ is the nearest inter-sublattice hopping. c Dependence of $\sigma^L$ and $\sigma^S$ on the strength $\lambda_z$ of spin-conserving SOC, when the spin-flip SOC $\lambda_{\parallel}$ is turned off. $\tau$ is the relaxation time. d Same as c, but with the roles of spin-flip and spin-conserving SOC interchanged. In c and d, the chemical potential is $\mu=-0.1$ eV. e Same as c, with $\mu=0.2$ eV. f Same as d, with $\mu=0.2$ eV. The unit of $\sigma /\tau$ is $\hbar~e^{-1}~\Omega^{-1}~\text{cm}^{-1}~\text{fs}^{-1}$.
• Figure 2: CPOC and CPSC induced by SOC in CrSb. a-b The crystal structure and Brillouin zone ( a) as well as nonrelativistic band structure ( b) of CrSb. c Calculated $\sigma_{xy}^{L_x}/\tau$ and $\sigma_{xy}^{S_x}/\tau$ versus chemical potential. d$\sigma_{xy}^{L_x}$ and $\sigma_{xy}^{S_x}$ at different temperatures. e-f Spin-conserving and spin-flip contributions to magnetic orbital ( e) and spin ( f) Hall conductivities.
• Figure 3: SOC induced CPOC competing with non-relativistic CPSC in FeSb$_2$. a Crystal structure and Brillouin zone of FeSb$_2$. b The non-relativistic band structure of FeSb$_2$. c Calculated $\sigma_{yx}^{L_y}/\tau$ and $\sigma_{yx}^{S_y}/\tau$ versus chemical potential. d Magnetic orbital and spin Hall conductivities at different temperatures, with orbital and spin polarizations both parallel and transverse to ${\bf N}$. e Spin-conserving and spin-flip contributions to $\sigma^{L_y}_{yx}$. f-g Spin-conserving ( f) and spin-flip ( g) contributions to $k$-resolved $\sigma^{L_y}_{yx}$ on the $k_y=0$ plane.