Cavity-induced coherent magnetization and polaritons in altermagnets

Abstract

Altermagnets feature antiparallel spin sublattices with $d$-, $g$-, or $i$-wave spin order, yielding nonrelativistic spin splitting without net magnetization. We show that embedding a two-dimensional $d$-wave altermagnet in a driven optical cavity induces a finite, tunable magnetization. Coherent photon driving couples selectively to electronic sublattices, and the resulting altermagnets' symmetry-broken spin texture yields a pronounced steady-state spin imbalance -- coherent magnetization -- absent in conventional antiferromagnets for the same lattice configuration. A mean-field Lindblad analysis reveals the dominance of quadratic over linear couplings. In the strong-coupling regime, distinct polariton signatures emerge in the steady state of induced magnetization. This work demonstrates cavity control of altermagnets for spintronic applications.

Figures (4)

• Figure 1: Schematic illustration of a laser-driven cavity setup hosting (left) a conventional $s$-wave antiferromagnet and (right) a $d_{x^2-y^2}$-wave altermagnet. The coherent laser drive excites cavity photons, which couple to spin textures via light-matter interaction. In the antiferromagnetic case, the spin populations remain nearly balanced under periodic driving, yielding minimal nonequilibrium polarization. In contrast, the anisotropic altermagnetic order due to staggered sublattices leads to a pronounced photoinduced imbalance between spin populations, as shown by the time evolution of the spin-resolved occupation difference $n_{\uparrow}(t)-n_{\downarrow}(t)$ (bottom panels).
• Figure 2: Time evolution of the spin imbalance $n_{\uparrow}(t)-n_{\downarrow}(t)$ for (a) varying $g_{\rm linear}$ with $g_{\rm quadratic}=0$ and (b) varying $g_{\rm quadratic}$ with $g_{\rm linear}=0$. All couplings reach a NESS, with stronger couplings accelerating the onset and enhancing the steady-state magnetization, reflecting cavity-induced sublattice symmetry breaking. Insets display coherent long-time oscillations, characteristic of the NESS, for several coupling strengths, obtained after subtracting their respective NESS values to align all traces around zero for comparison. Parameters: $\omega_{\rm photon}/J=0.5$, $\omega_{\rm laser}=\omega_{\rm photon}$, $\mathcal{E}_{\rm laser}/J=0.1$, $\gamma_{\rm electron}=\gamma_{\rm photon}=\kappa=0.02J$.
• Figure 3: Time-averaged cavity-induced magnetization in the NESS, $\overline{n}_{\uparrow}-\overline{n}_{\downarrow}$, as a function of (a) $g_{\rm linear}/J$ at $g_{\rm quadratic}=0$ and (b) $g_{\rm quadratic}/J$ at $g_{\rm linear}=0$, for various $\omega_{\rm photon}/J$ at $\omega_{\rm laser}=\omega_{\rm photon}$. At weak coupling, the response is perturbative, while above a critical coupling, it becomes strongly nonlinear due to polariton formation; see small gray circles and (c,d). Nonlinear enhancement is more pronounced for linear coupling at lower photon frequencies. (c,d) Magnetization versus $\omega_{\rm laser}/J$ at $\omega_{\rm photon}/J=1$, for different (c) linear and (d) quadratic couplings. Baseline magnetization $\overline{n}_0$ at $\omega_{\rm laser}/J=0.9$ is subtracted. A resonant peak near $\omega_{\rm laser}\simeq\omega_{\rm photon}$ appears for all $g_{\rm linear}$, except for $0.4<g_{\rm linear}/J<0.55$, where symmetric double peaks appear, signaling polariton formation, consistent with the position of small gray dot in (a). Parameters: $\mathcal{E}_{\rm laser}/J=0.1$ and $\gamma_{\rm electron}=\gamma_{\rm photon}=\kappa=0.02J$.
• Figure 4: (a) Cavity-induced coherent magnetization versus linear electron-photon coupling $g_{\rm linear}/J$ for several laser amplitudes $\mathcal{E}_{\rm laser}/J$. Larger drive amplitudes extend the nonlinear regime, shifting the onset of polariton formation to lower $g_{\rm linear}/J$. Steady-state spin imbalance $\overline{n}_{\uparrow} - \overline{n}_{\downarrow}$ as a function of coupling strength for (b) purely linear ($g_{\rm quadratic}/J = 0$) and (c) purely quadratic ($g_{\rm linear}/J = 0$) couplings, shown for different equal dissipation rates $\gamma_{\rm electron} = \gamma_{\rm photon} = \kappa$. In the linear case (b), the imbalance transitions from quadratic scaling at weak coupling to a steeper, nonlinear increase beyond a damping-dependent threshold. In the quadratic case (c), the response remains nearly quadratic but exhibits curvature changes at higher coupling. Parameters in (a): $\gamma_{\rm electron} = \gamma_{\rm photon} = \kappa = 0.02 J$ and $g_{\rm quadratic}/J = 0$; in (b): $\mathcal{E}_{\rm laser}/J = 0.1$. Fixed parameters: $\omega_{\rm photon}/J = 0.5$, $\omega_{\rm laser} = \omega_{\rm photon}$.