Out-of-Plane Nonlinear Orbital Hall Torque

Abstract

Despite recent advances in orbitronics, generating out-of-plane orbital torques essential for field-free deterministic switching of perpendicular magnetization remains a key challenge. Here, we propose a strategy to produce such unconventional torques across broad classes of materials, by leveraging the nonlinear orbital Hall effect. We demonstrate that this nonlinear orbital response is dramatically amplified by topological band degeneracies, where it overwhelmingly dominates the spin response even in systems with strong spin-orbit coupling. These features are confirmed via a quantitative investigation of representative topological metals RhSi, YPtBi, and PbTaSe$_2$, by combining our theory with first-principles calculations. The resulting orbital torques substantially surpass those from linear mechanisms reported thus far. These findings propel the research of orbital transport into the nonlinear regime, broaden the scope of orbital source materials, and establish a new pathway towards high-performance orbitronic devices.

Figures (3)

• Figure 1: Nonlinear CP orbital current response in Weyl model. (a) Calculated intrinsic NOHE conductivity $\chi_{zxx}^z$ (red curve) versus chemical potential $\mu$. The blue dashed curve is for the corresponding nonlinear spin current response. (b) $k$-resolved contribution to $\chi_{zxx}^z$ for $\mu$ slightly above the Weyl point. The unit of color map is $\mathrm{nm^{3}/V}$. Here, we take $m=1.2 m_e$, $\nu=1.0\ \text{eV}\cdot \text{\AA}$, and $T = 20$ K.
• Figure 2: (a) Lattice structure and (b) Brillouin zone of $\mathrm{RhSi}$. (c) Calculated band structure with SOC. Left panel shows the enlarged view of the dashed box around $\Gamma$. (d) Calculated NOHE conductivity $\chi_{zxx}^z$(O) (red curve) versus chemical potential at room temperature. The blue dashed curve is for the corresponding nonlinear spin current response $\chi_{zxx}^z$(S). (e) $k$-resolved contributions to NOHE $\chi_{zxx}^z$ around the $\Gamma$ point on the intrinsic Fermi level in $\Gamma$-M-R plane. The unit of color map is $\mathrm{\AA^{3}/V}$.
• Figure 3: Switchable CP NOHE in YPtBi. (a) Lattice structure of $\mathrm{YPtBi}$. (b) Band structure with SOC included. (c) Calculated NOHE conductivities $\chi_{zxx}^z$ and $\chi_{zyy}^z$ (red curves) versus chemical potential at room temperature. The blue curves show the results for the corresponding nonlinear spin current responses. (d,e) Schematic figure for a bilayer device structure. The CP orbital current generated from NOHE in the bottom layer (and the resulting torque on the top magnetic layer) can be switched by controlling the driving current direction (in $x$ or $y$ direction).