Dissipative Nonlinear Phononics: Nonequilibrium Quasiperiodic Order in Light-Driven Spin-Phonon System

Abstract

Nonlinear phononics has emerged as a powerful paradigm for the nonthermal control of quantum materials by engineering a conservative potential energy landscape. Here, we show that dissipation can serve as an additional control knob for nonequilibrium states in nonlinear phononics. We reveal a nontrivial role of dissipation by investigating a spin-phonon coupled system driven by circularly polarized light. By tuning the spin relaxation time $τ_s$, the steady state undergoes a transition from a trivial limit cycle to a temporally ordered state, which spontaneously breaks the discrete time-translation symmetry imposed by the drive. In this state, both the spin and phonon angular momentum exhibit persistent oscillations at an emergent frequency $Ω_s$, which is generally incommensurate with the driving frequency. This state is stabilized by a dissipation-induced phase lag between spin and phonon angular momentum that generates a feedback loop sustaining the oscillation. The dissipation-controlled transition can be described within a Landau-type framework using a pseudo-potential, where the order parameter has a $U(1)$ phase symmetry, and its amplitude is proportional to the oscillation amplitude of the phonon angular momentum.

Figures (9)

• Figure 1: Illustration of the spin-phonon coupled dynamics driven by a circularly polarized light. The steady state shows a longer period than the driving field, breaking the discrete time-translation symmetry. Green arrows indicate local spin.
• Figure 1: Stability analysis: real part of the Floquet exponents, $\text{Re}[\ln \mu]$, as a function of $\tau_s$, indicating stability when all values are negative. The parameters used are: $\chi_p = 4.0/\hbar$, $g=\chi_p(10/1.16^2)\hbar\omega$, $\Omega = 1.16\omega$, $F = 0.08\omega\sqrt{\hbar \omega}$ and $\omega\tau_p = 10$.
• Figure 2: (a) Trajectory of the limit cycle state at $\omega \tau_s = 32$. (b) Trajectory of the temporally ordered state with $\omega \tau_s = 4.339$. (c) Oscillating phonon angular momentum $L_z$ and spin $S$. (d) Fourier transform of the angular momentum. $\Omega_s$ denotes the main oscillation frequency. Other parameters: $\Omega = 1.16\omega$, $F = 0.08\omega\sqrt{\hbar \omega}$, $\chi_p = 4.0 / \hbar$, $g = \chi_p \left( \frac{10}{1.16^2} \right)\hbar\omega$, $\omega \tau_p = 10$.
• Figure 2: Fourier spectra of the phonon coordinates. Left panel, $Q_x(t)$, and right panel, $Q_y(t)$. The parameters used are $\Omega = 1.16\omega$, $F = 0.08\omega\sqrt{\hbar \omega}$, $\chi_p = 4.0/\hbar$, $g = \chi_p(10/1.16^2)\hbar\omega$, $\omega\tau_p = 10$ and $\omega\tau_s=19$.
• Figure 3: (a) Three-dimensional trajectory of $(Q_x,Q_y,S)$ that winds around a torus with parameters the same as those in Fig. \ref{['Trajectory_Fourier']}(b). (b) Amplitude of $\mathcal{F}(L_z)$ at $\Omega_s$ (see the inset) as a function of $\tau_s$. Black dots show numerical results, and the red line shows analytical results. Here $\chi_p = 4/\hbar$, $g=\chi_p(10/1.16^2)\hbar\omega$, $\Omega = 1.16\omega$, $F = 0.08\omega\sqrt{\hbar \omega}$, and $\omega\tau_p = 10$.