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

Abstract

Abstract One of the cornerstone effects in spintronics is spin pumping by dynamical magnetization that is steadily precessing (around, for example, the z-axis) with frequency ω 0 due to absorption of low-power microwaves of frequency ω 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 ( I S x ( t ) , I S y ( t ) , I S z ) ∝ ω 0 is time-independent while I S x ( t ) and I S y ( t ) oscillate harmonically in time with a single frequency ω 0 whereas pumped charge current is zero I ≡ 0 in the same adiabatic ∝ ω 0 limit. Here we employ more general approaches than the ‘standard model’, namely the time-dependent nonequilibrium Green’s function (NEGF) and the Floquet NEGF, to predict unforeseen features of spin pumping: namely precessing localized magnetic moments within a 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 α ( t ) and charge I(t) currents. All four of these functions harmonically oscillate in time at both even and odd integer multiples N ω 0 of the driving frequency ω 0. The cutoff order of such high harmonics increases with SOC strength, reaching N m a x ≃ 11 in the one-dimensional FM or AFM models chosen for demonstration. A higher cutoff N m a x ≃ 25 can be achieved in realistic two-dimensional (2D) FM models defined on a honeycomb lattice, and we provide a prescription of how to realize them using 2D magnets and their heterostructures.