Trembling motion of electrons driven by Larmor spin precession

TL;DR

The paper investigates electrically read spin dynamics in spin-orbit coupled semiconductors by optically initializing a spin ensemble in strained InGaAs under an in-plane magnetic field and detecting a GHz-scale AC current. The current follows $I_{spin}(t) = I_0 e^{-t/T_2^*} cos(\omega_L t + \phi)$, linking spin precession to charge motion and revealing both PDTM and SGE components, with the amplitude linearly increasing with $|B|$ and SOI strength. The amplitudes combine as $I_0(B_x) = \sqrt{I_{SGE}^2 + (K_{PDTM} B_x)^2}$, and the linear dependence on the SO coupling constant $\beta_{yx}$ supports a spin-orbit-driven trembling mechanism. The work presents a Zitterbewegung-like quantum interpretation of the effect, demonstrates a fast, spin-sensitive electric readout, and suggests extensions to topological and 2D materials with strong SOI.

Abstract

We show that the initialization of an ensemble of electrons in the same spin state in strained n-InGaAs subject to a perpendicular magnetic field triggers an AC electric current at GHz frequencies. The AC current emerges in the absence of any driving force and survives until the coherent precession of the electron spins is lost. The current amplitude increases linearly with both the spin-orbit coupling strength and the external magnetic field. The generation mechanism of the observed oscillatory charge motion can be fruitfully described in terms of the periodic trembling motion of spin-polarized electrons, which is a solid-state analog to the Zitterbewegung of free Dirac electrons. Our results demonstrate that the hidden consequence of relativistic quantum mechanics is realized and can be studied in a rather simple solid-state system at moderate temperatures. Furthermore, the large amplitude of the AC current at high magnetic fields enables ultra-fast spin sensitive electric read-out in solids.

Figures (3)

• Figure 1: (a) Sample geometry and pulsed optical spin excitation. The electron spin ensemble is excited along the $z$ direction by circularly polarized ps laser pulses with a pulse repetition time of 12.5 ns. The high-frequency current in InGaAs is detected by a phase-triggered sampling oscilloscope through coplanar waveguides (CPW). Four different crystal directions can be contacted. (b) Illustration of the spin precession driven trembling electron motion (PDTM). Electron spin precession yields a periodic displacement of the electrons along the $x$-direction which results in an AC current oscillating at the Larmor frequency. (c) Time-resolved current traces along the $[110]$ crystal direction recorded after pulsed optical excitation for $\sigma^+$ and $\sigma^-$ polarizations at $B_x = 1$ T and $T = 50$ K and averaged over about $10^5$ measurements. The inset shows a close-up of both current traces. (d) Time-dependent AC current $I_{\rm spin} = [I(\sigma^+)-I(\sigma^-)]/2$ as determined from both traces in panel (c). TRFR of electron spin precession under identical experimental conditions. (f) Illustration of AC current generated by the spin-galvanic effect (SGE), where the largest currents are generated for electron spins pointing along the $\pm$ y-directions. (g) and (h) show respective AC current and TRFR traces measured along the $[1\overline{1}0]$.
• Figure 2: $B$-field dependence of spin precession driven electric current. (a), Time-resolved current along the $[1 1 0]$ direction in InGaAs at various $B$ fields. Larmor precession frequency and magnitude of AC current increase with increasing $B$ field strength while the sign of the AC current reverses when reversing the $B$ field direction. (b) Amplitude $I_0$ of AC current vs $B_x$. The linear increase of $I_0$ with $B_x$ indicates a strong PDTM with a weak SGE visible at small $B_x$. The red solid line is a fit to Eq. \ref{['Separation1']}. (c) $I_0$ vs $B_x$ for a sample measured along the $[1\overline{1}0]$ direction. The weak increases of $I_0$ with increasing $|B_x|$ indicate the dominance of SGE over PDTM.
• Figure 3: Dependence of coupling strength $K_{\rm PDTM}$ of the periodic trembling motion on the spin-orbit coupling constant $\beta_{yx}$. The data points are obtained from a number of InGaAs devices where the AC current is probed along different crystal directions. The overall linear behavior is suggesting that SO coupling is decisive to the generation of the PDTM component of the AC current.