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Nonlinear Magnetic Orbital Hall Effect Induced by Spin-Orbit Coupling

Hui Wang, Huiying Liu, Yanfeng Ge, Xukun Feng, Jiaojiao Zhu, Jin Cao, Cong Xiao, Shengyuan A. Yang, Lay Kee Ang

Abstract

Electrical readout of 180$^\circ$ switching in strictly compensated collinear antiferromagnets remains a major challenge in antiferromagnetic spintronics. Electrical writing of perpendicularly magnetized ferromagnets by out-of-plane orbital torque remains an important challenge in orbitronics. In this work, we propose a second-order nonlinear magnetic orbital Hall effect in the source antiferromagnet as a simultaneous recipe for both difficulties. This orbitronics effect is induced by spin-orbit coupling and is odd in the Néel vector, thus is a unique effect that integrates both functionalities via electric control of the Néel vector in the source antiferromagnet. Our first-principles calculations in CuMnAs predict significant non-perturbative orbital effects from spin-orbit coupling, with a orbital Berry-curvature dipole mechanism. These findings unveil new possibilities opened by topological antiferromagnetic orbitronics.

Nonlinear Magnetic Orbital Hall Effect Induced by Spin-Orbit Coupling

Abstract

Electrical readout of 180 switching in strictly compensated collinear antiferromagnets remains a major challenge in antiferromagnetic spintronics. Electrical writing of perpendicularly magnetized ferromagnets by out-of-plane orbital torque remains an important challenge in orbitronics. In this work, we propose a second-order nonlinear magnetic orbital Hall effect in the source antiferromagnet as a simultaneous recipe for both difficulties. This orbitronics effect is induced by spin-orbit coupling and is odd in the Néel vector, thus is a unique effect that integrates both functionalities via electric control of the Néel vector in the source antiferromagnet. Our first-principles calculations in CuMnAs predict significant non-perturbative orbital effects from spin-orbit coupling, with a orbital Berry-curvature dipole mechanism. These findings unveil new possibilities opened by topological antiferromagnetic orbitronics.

Paper Structure

This paper contains 3 equations, 3 figures, 1 table.

Figures (3)

  • Figure 1: (a) Lattice structure of AFM orthorhombic CuMnAs with Néel vector $\bm n\parallel[001]$. (b) Brillouin zone of CuMnAs. The red dotted curve illustrates the nodal line in the $k_y=0$ plane around X point obtained without SOC. (c) Calculated band structure of CuMnAs [001] including SOC. (d) CPOC from nonlinear magnetic orbital and spin Hall conductivity $\chi_{zyy}^z$ as a function of chemical potential at $T=50$ K. (e,f) Distribution of $k$-resolved (e) $D_{zyy}^z(\text{O})$ and (f) $D_{zyy}^z(\text{S})$ on the intrinsic Fermi surface in the $k_y=0$ plane around the X point. The two green dots on the X-U line indicate the pair of Dirac points, which are related by $C_{2x}$.
  • Figure 2: Angular-dependent perpendicular CPOC from nonlinear MOHE in CuMnAs. (a) CuMnAs [001] and (b) CuMnAs [010] with $z$-axis as the out-of-plane direction. The $(001)$ plane is the contact interface to a target perpendicular ferromagnet. (c) Orientation of the Néel vector in the $yz$ plane, defined by the angle $\varphi$ measured from the [010] direction. (d) Angular dependence of the nonlinear orbital Hall conductivity $\chi_{zyy}^z$. The dashed line is a guide for eyes.
  • Figure 3: Schematic of the orbit-torque device for (100) contact plane between CuMnAs and a perpendicular ferromagnet. (a) CuMnAs [001] and (b) CuMnAs [010] with $x$ axis as the out-of-plane direction. (c) Angular dependence of the nonlinear orbital Hall conductivity $\chi_{xyy}^x$. Here, $\varphi$ is defined in Fig. \ref{['fig_device']}(c), and the dashed line is a guide for eyes.