A Purely Magnetic Route to High-Harmonic Spin Pumping

TL;DR

The paper addresses generating high-harmonic spin pumping without relying on spin-orbit coupling, via nonlinear magnetic dynamics. A second static magnetic order transverse to the precession axis reshapes the adiabatic spectrum to give $ε_± = -2γ cos k ± sqrt(J_0^2 + J_1^2 + 2 J_0 J_1 sin θ cos ω t)$, introducing explicit time dependence that enables HHG. Using a minimal 1D model and non-equilibrium transport simulations with $tkwant$, the authors show that finite $J_1$ yields higher harmonics in spin currents while the charge current remains symmetry-forbidden. The results establish a purely magnetic route to ultrafast spin pumping, applicable to a broad class of magnetic systems, and point toward terahertz spin-current generation without SOC.

Abstract

Spin pumping provides a fundamental route for dynamical spin transport, yet in its conventional form it produces only linear spin responses at the driving frequency. Recent studies have shown that spin-orbit coupling (SOC) can lift these restrictions and enable highly nonlinear spin and charge currents. Here we propose a distinct mechanism for high-harmonic spin pumping that does not rely on spin-orbit interactions. We show that nonlinearities in the adiabatic energy spectrum--rather than SOC itself--constitute the essential ingredient for high-harmonic generation in pumped spin currents. Such nonlinearities can arise in purely magnetic systems when a secondary magnetic order parameter is introduced perpendicular to the cone axis of a precessing magnetic moment. As a result, spin pumping and its higher harmonics emerge even in the complete absence of SOC. Our findings establish a new route to ultrafast spin pumping based solely on magnetic structure and dynamics.

Figures (3)

• Figure 1: Charge and spin currents for standard spin pumping ($J_1=0$). Panel (a) shows the Fourier spectra of the spin ($\rm{I_{\omega}^{\sigma_x, \sigma_y, \sigma_z}}$) and charge ($\rm{I_{\omega}^{\sigma_0}}$) currents, while panel (b) displays the corresponding time-domain signals. The calculation is performed at Fermi energy $E_F=-1.8\gamma$ with driving frequency $\omega=0.01\,\gamma/\hbar$ and precession cone angle $\theta=22.5^{\circ}$.
• Figure 2: Charge and spin currents in the presence of a static transverse magnetic order. Panels (a) and (c) show the Fourier spectra and time-domain signals, respectively, for a precession cone angle $\theta=\pi/8$. Panels (b) and (d) display the same quantities for the in-plane precession configuration $\theta=\pi/2$. The exchange couplings are $J_0=1$ and $J_1=2$, in units of $\gamma$. The Fermi energy and driving frequency are the same as in Fig. \ref{['fig1']}.
• Figure 3: Calculated dc components of the pumped spin current polarized along the $y$ [(a)] and $z$ [(b)] directions are shown as functions of the driving frequency $\omega$ for precession cone angles ranging from $\theta=\pi/8$ to $\pi/2$. The pumped currents are evaluated for $J_0 = J_1 = 2\gamma$. The dashed brown and black lines correspond to linear fits of the underlying data.