Magnetizing weak links by time-dependent spin-orbit interactions: momentum conserving and non-conserving processes

TL;DR

The paper shows that a time-periodic Rashba spin-orbit interaction, induced by a rotating electric field applied to a weak link between non-magnetic leads, can generate a nondissipative magnetization along the junction axis. Using a single-dot two-terminal model and Keldysh Green's functions in the wide-band limit, the authors derive explicit expressions for the magnetization on the dot and in the leads, revealing a fundamental link between momentum-conserving and momentum-non-conserving processes. A central result is that the dot magnetization contains a time-independent component along $\hat{\mathbf{x}}$ in symmetric or biased setups, and the sum of lead magnetizations yields a nondissipative contribution as well. The magnetization is tunable by the ellipticity of the rotating field, by the bias voltage, and by gate-induced asymmetry, offering a pathway to electrically control spin in non-magnetic devices and to implement spin-based quantum operations.

Abstract

Rashba spin-orbit interactions generated by time-dependent electric fields acting on weak links (that couple together non-magnetic macroscopic leads) can magnetize the junction. The Rashba spin-orbit interaction that affects the spins of electrons tunneling through the weak links changes their momentum concomitantly. We establish the connection between the magnetization flux induced by processes that conserve the momentum and the magnetization created by tunneling events that do not. Control of the induced magnetization can be achieved by tuning the polarization of the AC electric field responsible for the spin-orbit Rashba interaction (e.g., from being circular to linear), by changing the applied bias voltage, and by varying the degree of a gate voltage-induced asymmetry of the device.

Figures (3)

• Figure 1: (color online) Schematic plot of the device: a single-level (of energy $\varepsilon^{}_{d}$) quantum dot is attached by two weak links (of lengths $d^{}_{L, R}$) to two electron reservoirs, denoted $L$ and $R$, with chemical potentials $\mu^{}_{L,R}$, respectively. The rotating electric fields, produced by the potentials $v^{}_{y,z}(t)$, induce spin-dependent tunneling through the links.
• Figure 2: The magnetization vector induced on the dot. The slanted line (blue) vector that coincides with the $\hat{\bf x}$ direction is for $d_{L}=d_{R}$, and is time-independent. The dashed line (magenta) vector lying on the $x-z$ plane is for $d^{}_{R}=1.5 d^{}_{L}$ and $\Omega t=\pi/2$, and the dot-dashed (red) vector in the $x-y$ is for $d^{}_{R}=0.5 d^{}_{L}$ and $\Omega t=\pi$. The circles (black and Green) show the entire rotation for $t=\{0, 2\pi/\Omega\}$.
• Figure 3: (color online) The vectors of the magnetizations formed on the leads, for $d^{}_{L}=d^{}_{R}$.The left lead magnetization has components along $\hat{\bf x}$ (yellow solid line) and along $\hat{\bf z}$ at $\Omega t=\pi/2$, portrayed by the dashed (green) arrow. The dot-dashed (red) arrow shows the magnetization vector in the right lead at $\Omega t=\pi$. The cyan vertical dashed line along $\hat{\bf x}$ shows the $\hat{\bf x}$ component of the right lead magnetization vector. The circle in magenta shows the entire rotation for $t=\{0, 2\pi/\Omega \}$.