High-harmonic generation in spin and charge current pumping at ferromagnetic or antiferromagnetic resonance in the presence of spin-orbit coupling

TL;DR

This paper predicts that spin and charge currents generated by precessing magnetic moments in ferromagnetic or antiferromagnetic materials with spin-orbit coupling exhibit high-harmonic oscillations, extending beyond the standard model's predictions.

Contribution

The study employs NEGF and Floquet-NEGF methods to reveal high-harmonic generation in spin and charge pumping, which was not accounted for in traditional models.

Findings

Currents oscillate at multiple harmonics of the driving frequency.

High-harmonic cutoff increases with spin-orbit coupling strength.

Realistic 2D models can achieve up to 25 harmonics.

Abstract

One of the cornerstone effects in spintronics is spin pumping by dynamical magnetization that is steadily precessing (around, e.g., the $z$-axis) with frequency $\omega_0$, due to absorption of low-power microwaves of frequency $\omega_0$ under the resonance conditions and in the absence of any applied bias voltage. The two-decades-old "standard model" of this effect, based on the scattering theory of adiabatic quantum pumping, predicts that component $I^{S_z}$ of spin current vector $\big( I^{S_x}(t),I^{S_y}(t),I^{S_z} \big) \propto \omega_0$ is time-independent while $I^{S_x}(t)$ and $I^{S_y}(t)$ oscillate harmonically in time with a single frequency $\omega_0$; whereas pumped charge current is zero $I \equiv 0$ in the same adiabatic $\propto \omega_0$ limit. Here we employ more general than "standard model" approaches, time-dependent nonequilibrium Green's function (NEGF) and Floquet-NEGF, to predict unforeseen features of spin pumping -- precessing localized magnetic moments within ferromagnetic metal (FM) or antiferromagnetic metal (AFM), whose conduction electrons are exposed to spin-orbit coupling (SOC) of either intrinsic or proximity origin, will pump both spin $I^{S_\alpha}(t)$ and charge $I(t)$ currents. All four of these functions harmonically oscillate in time at both even an odd integer multiples $N\omega_0$ of the driving frequency $\omega_0$. The cutoff order of such high-harmonics increases with SOC strength, reaching $N_\mathrm{max} \simeq 11$ in the chosen-for-demonstration one-dimensional FM or AFM models. Higher cutoff $N_\mathrm{max} \simeq 25$ can be achieved in realistic two-dimensional (2D) FM models defined on the honeycomb lattice, where we provide prescription on how to realize them using 2D magnets and their heterostructures.