Nonlinear spin and orbital Rashba-Edelstein effects induced by a femtosecond laser pulse: Simulations for Au(001)

TL;DR

The paper addresses ultrafast nonlinear Rashba-Edelstein effects on Au(001) triggered by a femtosecond laser pulse with carrier energy $\hbar \omega = 3.0$ eV and envelope width $\tau = 10$ fs. It develops a real-space Slater-Koster tight-binding model including atomic SOC and RSOC and propagates the density matrix via the von Neumann equation to compute time-resolved SAM, OAM, and their currents. The authors find RSOC-enabled SEE and OEE with distinct temporal profiles; SAM and OAM currents include both longitudinal and transversal channels and exhibit beating patterns and even/odd harmonic content distinguishing RSOC-driven from intrinsic dynamics, with post-pulse activity persisting in the absence of damping. The results offer insights for ultrafast spintronics and orbitronics and identify directions for extending the model to more realistic substrates and dissipative environments.

Abstract

Rashba-type spin-orbit coupling gives rise to distinctive surface and interface phenomena, such as spin-momentum locking and spin splitting. In nonequilibrium settings, one of the key manifestations is the (Rashba-)Edelstein effect, where an electric current generates a net spin or orbital polarization perpendicular to the current direction. While the steady-state behavior of these effects is well studied, their dynamics on ultrafast timescales remain largely unexplored. In this work, we present a theoretical investigation of the ultrafast spin and orbital Edelstein effects on an Au(001) surface, triggered by excitation with a femtosecond laser pulse. These effects are intrinsic and inherently nonlinear. Using a real-space tight-binding model combined with time evolution governed by the von Neumann equation, we simulate the electron dynamics in response to the pulse. Our results reveal pronounced differences between the spin and orbital responses, offering detailed insights into their distinct temporal profiles and magnitudes. We further explore the associated charge, spin, and orbital currents, including the emergence of laser-induced spin and orbital Hall effects. Finally, we quantify the angular momentum transfer mediated by the light-matter interaction. These findings shed light on the intricate ultrafast dynamics driven by spin-orbit coupling and offer guidance for the design of next-generation spintronic and orbitronic devices.

Figures (6)

• Figure 1: Sketch of the ultrafast spin and orbital Edelstein effect in a two-dimensional system. (a) A linearly polarized laser pulse with electric field $E$ along the $+x$-direction (violet) impinges perpendicular to the sample (gray; located in the $xy$ plane). $O_y$ (red) is the laser-induced in-plane angular momentum $O$ (either spin or orbital angular momentum) along the $+y$-direction. (b) Same as (a) but half a period later: $E$ and $O_y$ point along the $-x$- and the $-y$-direction, respectively.
• Figure 2: Ultrafast spin and orbital Edelstein effect in a Au(001) monolayer. Panel (a): electric field of the laser pulse (in arbitrary units). For parameters, see the text. Panels (b) and (c): photo-induced $y$-components $\braket{s_{y}}(t)$ and $\braket{l_{y}}(t)$ of spin and orbital angular momenta, respectively. Thicker lines in (b) and (c) represent the data convoluted with a Gaussian with standard deviation $\sigma = \unit[10]{fs}$ to visualize the main trends better. Vertical lines indicate the maxima of the laser's electric field.
• Figure 3: Photo-induced longitudinal currents in a Au(001) monolayer. Panel (a): probability current $\braket{j_{x}}(t)$ between next-nearest neighbor sites in $x$-direction. Panels (b) and (c): as panel (a) but for the $y$-polarized spin and orbital angular momentum currents $\braket{j_{x}^{s_y}}(t)$ and $\braket{j_{x}^{l_y}}(t)$, respectively. Like in Figure \ref{['fig:SAM-OAM']}, thicker lines represent the data convoluted with a Gaussian, and vertical lines indicate the maxima of the laser's electric field.
• Figure 4: Photo-induced transversal currents of spin and orbital moment in an Au(001) monolayer. Panels (a) and (b): $x$- and $z$-polarized currents of spin angular momentum $\braket{j_{y}^{s_x}}(t)$ and $\braket{j_{y}^{s_z}}(t)$, respectively. Panels (c) and (d), the respective $x$- and $z$-polarized orbital angular momentum currents $\braket{j_{y}^{l_x}}(t)$ and $\braket{j_{y}^{l_z}}(t)$ are shown, as indicated. Like in Figure \ref{['fig:SAM-OAM']}, thicker lines represent the data convoluted with a Gaussian, and vertical lines indicate the maxima of the laser's electric field.
• Figure 5: Laser-induced currents in a Au(001) sample without Rashba spin-orbit coupling. Panel (a): longitudinal probability current $\braket{j_{x}}(t)$ between next-nearest neighbor sites in $x$-direction. Panels (b) and (c): transversal $z$-polarized spin and orbital angular momentum currents in $y$-direction $\braket{j_{y}^{s_z}}(t)$ and $\braket{j_{y}^{l_z}}(t)$, respectively. Like in Figure \ref{['fig:SAM-OAM']}, thicker lines represent the data convoluted with a Gaussian, and vertical lines indicate maxima of the laser's electric field.