Boltzmann theory of the inverse Edelstein effect in a two-dimensional Rashba gas

TL;DR

This work tackles spin–charge interconversion at oxide–Rashba interfaces by formulating a semiclassical Boltzmann framework for the inverse Edelstein effect in a Rashba 2DEG adjacent to a ferromagnet. It yields closed-form analytical expressions for the IEE-induced charge current $I_c$ and the associated spin current $I_S$ in both high-density ($\mu\ge0$) and low-density ($\mu<0$) regimes, explicitly showing how $h_y$, $\alpha$, $\mu$, and device length $L_x$ control the conversion efficiency. The results reveal distinct HDR and LDR scalings (linear vs. quadratic in $\alpha$ near the band-crossing) and demonstrate that the spin current is not conserved due to spin–orbit coupling, with a spin-torque contribution emerging in the spin continuity equation. The analytical framework provides a transparent benchmark for experiments on oxide interfaces (e.g., LaAlO$_3$/SrTiO$_3$) and highlights the limitations of the Boltzmann approach near band edges, pointing to future extensions to time-dependent or density-matrix formalisms for nonlinear and coherent effects.

Abstract

We investigate the inverse Edelstein effect in a non-homogeneous system consisting of a ferromagnetic layer coupled to a Rashba two-dimensional electron gas. Within a semiclassical Boltzmann framework, we derive analytical expressions for the charge and spin currents and analyze their dependence on key parameters such as the chemical potential and the Rashba coupling strength. We show how interfacial exchange and spin-orbit interactions jointly control the efficiency of spin-to-charge conversion, leading to distinct regimes characterized by qualitatively different transport responses. A central outcome of our work is the availability of closed-form analytical results, which provide direct physical insight and enable a transparent and quantitative benchmarking with experiments on complex oxide interfaces, such as LaAlO$_3$/SrTiO$_3$.

Figures (7)

• Figure 1: Schematic of the setup used to study the inverse Edelstein effect (IEE). A ferromagnetic metal is placed in proximity to a two-dimensional electron gas (2DEG) with strong spin–orbit coupling. The magnetization of the ferromagnet undergoes precession around the $\hat{y}$ axis as a result of ferromagnetic resonance (FMR), induced by an external microwave driving field. The precessing magnetization injects spin angular momentum into the interfacial region of the 2DEG, generating a nonequilibrium spin accumulation polarized along $\hat{y}$. This spin accumulation arises from the balance between spin injection due to the magnetization dynamics and spin diffusion within the 2DEG. Through the inverse Edelstein effect, the interfacial spin accumulation is converted into a charge current flowing along the $\hat{x}$ direction in the 2DEG channel.
• Figure 2: Schematic representation of Fermi surfaces in HDR (a) at the equilibrium and (b) with an applied magnetic field $\mathbf{M}= M_y \hat{y}$. If an external magnetization is applied, the Fermi surfaces are shifted by a $\delta k$ in opposite directions. (c) Energy dispersion of the Rashba 2DEG and Fermi momenta at fixed energy for high-density regime (HDR) and low-density regime (LDR). Blue and red dots indicate the branches of the energy dispersion, respectively $+$ and $-$.
• Figure 3: Electric current as a function of the chemical potential $\mu$ for different values of the Rashba parameter $\alpha$, where $I_0= 5.63$ A. The dashed line at $\mu=0$ represents the crossover between LDR and HRD.
• Figure 4:
• Figure 5: Spin current as a function of the chemical potential for different values of $x$, for a fixed value of Rashba parameter $\alpha= 54$ meVÅ, considering the electronic correlation between the spin and the group velocity.