High-Harmonic Spin and Charge Pumping in Altermagnets

TL;DR

The paper investigates magnetically driven high-harmonic generation in altermagnets, a class of materials with momentum-dependent spin splitting but zero net magnetization. It uses exact nonequilibrium quantum transport in simple 2D and realistic 3D tight-binding models to follow the adiabatic evolution of energy levels under a precessing magnetic order. A key finding is the emission of hundreds of harmonics in spin and charge channels with amplitudes near the fundamental, enabled only when the driving axis is noncollinear with the altermagnetic order; in-plane dynamics can yield up to the 300th harmonic. This nonrelativistic mechanism suggests bulk three-dimensional altermagnets as promising platforms for terahertz emitters and nonlinear spintronic devices, with broad robustness across parameter space.

Abstract

We report the emergence of highly nonlinear spin and charge pumping in an altermagnetic system driven by magnetic dynamics. The nonrelativistic spin-momentum coupling inherent to altermagnets generates a giant momentum dependent spin splitting, leading to strong spin-flip scattering in the presence of a precessing magnetic order driving the altermagnetic system out of equilibrium. Our simulations reveal the emission of hundreds of harmonics under realistic conditions, with amplitudes far exceeding those obtained in light-driven schemes. Notably, in contrast to ferromagnetic and conventional antiferromagnetic systems, where nonlinear emission typically requires additional spin-orbit coupling, altermagnets intrinsically support high-harmonic spin and charge pumping. These results identify altermagnetic systems as a promising platform for efficient THz emitters and highly nonlinear spintronic devices.

Figures (5)

• Figure 1: Left panel: Fourier spectra of the lowest-energy level for the simplified and the realistic models [Eqs. \ref{['simple_model']} and \ref{['realistic']}]. The altermagnetic order parameter is kept static, while the driving magnetic order precesses around the $z$ axis (corresponding to the third configuration shown in the right panel) with a cone angle $\theta=\pi/8$. The instantaneous energy levels are evaluated at $\mathbf{k}=(\pi/2,0)$ for Eq. \ref{['simple_model']} and at $\mathbf{k}=(\pi/2,\pi/2,\pi)$—corresponding to the midpoint of the A–Z path in the three dimensional Brillouin zone—for Eq. \ref{['realistic']}. The parameters of the realistic model in Eq. \ref{['realistic']} correspond to those of RuO$_2$ given in Ref. Roig2024. Right panel: Selection rules for the relevant magnetic configurations. HHG occurs only when the precession axis of the driven magnetic order is noncollinear with the ferromagnetic moment.
• Figure 2: Schematic of the magnetic configuration employed in the numerical simulations. A time-dependent magnetic order precesses around the $z$ axis (red cone) in the presence of an altermagnetic order parameter oriented along the $x$ axis (blue arrow). The magnetic scattering region (blue rectangle) is connected to a normal-metal lead (red rectangle), where the resulting time-dependent carrier currents are evaluated.
• Figure 3: Altermagnetic band structures for different magnetic configurations. The first column shows the band structure in the absence of magnetic dynamics. The second column displays the spin-polarized bands for a precession cone angle, $\theta=\pi/8$. The third column shows the bands for fully in-plane dynamics, $\theta=\pi/2$. In the upper row, the hopping parameter is set to $\gamma_0=0$, while in the lower row it is set to $\gamma_0=\gamma$. In all panels, the Hamiltonian is diagonalized at time $t=0$.
• Figure 4: Fourier spectrum of the charge current pumped from the altermagnet. The driving frequency is set to $\omega=0.01\,\gamma/h$. The Fermi energy is chosen as $\varepsilon_{\rm F}=0$ for $\gamma_0=\gamma$ and $\varepsilon_{\rm F}=-J$ for the gapped case ($\gamma_0=0$). The precession cone angle is $\theta=\pi/8$. The data are represented on a linear scale.
• Figure 5: Fourier spectrum of the charge current pumped out of the altermagnet for fully in-plane magnetic dynamics, corresponding to a precession cone angle $\theta=\pi/2$. All other parameters are identical to those used in Fig. \ref{['fig:fig2']}. The data are represented on a linear scale.