Magnon Nesting in Driven Two-Dimensional Quantum Magnets

TL;DR

This work develops a non-equilibrium mechanism for dynamical instabilities in driven two-dimensional XXZ magnets, showing that a resonant parametric drive first generates magnon pairs and then, when their momentum distribution becomes nested, triggers a secondary instability that strongly enhances antiferromagnetic correlations at $\boldsymbol{q}=(\pi,\pi)$. The analysis combines a Holstein-Primakoff mapping, a random-phase approximation treatment of magnon interactions, and real-time truncated Wigner simulations to reveal how nesting-induced many-body correlations arise beyond free-particle physics. Importantly, the antiferromagnetic enhancement emerges even for ferromagnetic microscopic couplings, highlighting the genuinely non-equilibrium nature of the effect and its resemblance to nesting phenomena in fermionic systems while lacking an equilibrium bosonic counterpart. The results point to a broad platform—theory and experiments in solid-state magnets, quantum simulators, and ultracold atoms—for exploring non-equilibrium pattern formation and dynamical instabilities controlled by drive frequency and nesting geometry, with potential implications for manipulating order in quantum materials.

Abstract

We uncover a new class of dynamical quantum instability in driven magnets leading to emergent enhancement of antiferromagnetic correlations even for purely ferromagnetic microscopic couplings. A primary parametric amplification creates a frequency-tuned nested magnon distribution in momentum space, which seeds a secondary instability marked by the emergence of enhanced antiferromagnetic correlations, mirroring the instability of nested Fermi surfaces in electronic systems. In sharp contrast to the fermionic case, however, the magnon-driven instability is intrinsically non-equilibrium and fundamentally inaccessible in thermal physics. Its quantum mechanical origin sets it apart from classical instabilities such as Faraday and modulation instabilities, which underlie several instances of dynamical behavior observed in magnetic and cold-atom systems.

Figures (9)

• Figure 1: Secondary instability of nested magnons by resonant parametric driving. (a) Schematics of the setup considered in this work. An external parametric drive with frequency $\omega$ creates pair of magnons with opposite momenta. (b) Resonant drive triggers a primary instability manifested by the coherent generation of magnon pairs at resonant energies, corresponding to closed contours in momentum space (shown by dashes). (c) The primary instability can trigger a secondary instability, characterized by strong AFM correlations, if the driving frequency is adjusted such that the magnon distribution in the momentum space forms a nested shape, as depicted by the excitation profile in the middle.
• Figure 2: Magnon nesting for AFM coupling. (Left) Early-time magnon occupation in the momentum space due to parametric driving at the nesting frequency. (Center) Redistributed magnons at later times due to scattering processes, resembling a Fermi surface. (Right) Longitudinal correlation function ($C^{zz}_{\boldsymbol{k}}(t,t)$), showing AFM instability at $(\pi,\pi)$. The system consists of $100\times100$ spins, and the other parameters are $J/h=0.2$, $\Delta=-2$, $\xi/h=0.1$ and $S=5$.
• Figure 3: Magnon nesting for FM coupling. (Left) Early-time magnon occupation in the momentum space due to parametric driving at the nesting frequency. (Center) Magnon scattering modifies the distribution, which now resembles an inverted Fermi surface. (Right) Longitudinal correlation function ($C^{zz}_{\boldsymbol{k}}(t,t)$), showing AFM instability at $(\pi,\pi)$. Except for $\Delta=2$, the other parameters are the same as in Fig. \ref{['fig:xx_zz_AFM']}.
• Figure 4: (Top row) The time evolution of $C^{zz}_{\boldsymbol{q}}(t,t)$ for various driving frequencies (measured relative to the nesting frequency) is shown for momenta along a closed path through the Brillouin zone (depicted in the inset). Close to the nesting frequency, a secondary instability is triggered. (Bottom row) Magnon population at $\xi t=9.0$ (marked by dashes in the top row) for driving frequencies given in the top row, demonstrating the formation of instability close to nesting. The color-scales in the bottom panel are different, but have the same order of magnitude with $1.5 \lesssim n_\mathrm{max} \lesssim 3$ across different figures. The other parameters are the same as in Fig. \ref{['fig:xx_zz_AFM']}.
• Figure 5: (Left panel) Profile of $C^{zz}$ close to ${\boldsymbol{q}}=(\pi,\pi)$ for two different pulses with the same mean-frequency $(\omega_\mathrm{nest}-\omega_0)/2J=0.1$ and different widths. Pulses that are broader in the time domain create stronger instabilities. (Right panel) Snapshots of magnon distribution at three different times which are marked by dashes in the left panel. Nesting is strongest near the onset of secondary instability. Other parameters are the same as in Fig. \ref{['fig:xx_zz_AFM']}.