Phase transitions induced by resonant light: a phenomenological approach

TL;DR

This work introduces a Landau-theory–based phenomenological framework for light-induced phase transitions mediated by resonant excitons, coupling a order parameter to two excitonic reservoirs with Langevin noise and temperature feedback. A cubic term γφ^3, with γ proportional to the exciton-population imbalance, tilts the free-energy landscape and enables threshold-like, non-thermal switching under resonant optical pumping. The model is validated by reproducing all-optical magnetization switching in CrI3, including helicity selectivity, detuning sensitivity, and a sharp fluence threshold, and is readily extended to other systems with competing excitonic channels such as 2D perovskites. Overall, the framework offers a general, experimentally testable platform to analyze and predict resonant, exciton-mediated LIPTs across diverse materials.

Abstract

We present a phenomenological framework to describe a subclass of light-induced phase transitions (LIPTs) in condensed matter systems, specifically those mediated by the resonant generation of excitons. Our approach extends the classical Landau theory by introducing dynamic coupling between the system's order parameter and complex excitonic fields, along with Langevin-type forces that drive the system toward states of minimal free energy. The model is applied in the context of all-optical resonant magnetization switching in two-dimensional magnetic materials, particularly reproducing the experimental findings for reverse magnetization by all-optical means for a monolayer CrI$_3$. Our phenomenological model can be applied to other systems characterized by an order parameter and excitonic fields created through resonant light, offering versatility and potential to guide future experimental and theoretical studies in LIPT phenomena.

Figures (5)

• Figure 1: Conceptual illustration of the resonant-exciton mechanism that underlies our Landau-type model for light-induced phase switching. The red dot shows schematically in which phase the system resides. Left panel: Free energy $F(\varphi)$ of the system as a function of the order parameter $\varphi$, characterizing the phase transition in the absence of external optical excitation. Two stable phases correspond to the two minima of the double-well potential with both ground (g) and excited (e) states. They are characterized by different energies of optical excitonic transitions $\hbar\omega_1\neq\hbar\omega_2$. When the system resides in phase 1 (left well), the corresponding excitonic population is zero. Right panel: The system's free energy profile is reshaped under an external optical pump resonant with the excitonic transition in phase 2, $E_{ph}=\hbar\omega_2$. The enhancing probability to create excitons in phase 2, but not in phase 1, drives the system into a new phase by lowering the corresponding free energy minimum, which is conditioned by the cubic coupling $\gamma\!\propto\!|\psi_1|^{2}-|\psi_2|^{2}$ that tilts the landscape. The additional Langevin noise allows the switching without raising the lattice above its critical temperature.
• Figure 2: Time-domain response of the coupled order-parameter / exciton / temperature model deep inside the ordered regime, $T_r<T_0$. Deep blue dashed curves correspond to a pump tuned exactly to the $\omega_1$ exciton of Phase 1; Yellow solid curves are obtained for the different frequency, resonant with the $\omega_2$ exciton of Phase 2. (a) Dependence of the order parameter $\varphi(t)$ on time. The resonant drive that is tuned to a frequency corresponding to a different phase from that in which the system is at the initial moment in time, first, reduces the metastable barrier and, aided by noise, flips $\varphi$ from the initial minimum to the opposite well. (b,c) Corresponding populations of the two excitonic reservoirs $|\psi_{1,2}|^{2}$. Only the exciton that is in resonance with the pump accumulates strongly, illustrating the phase-selective nature of optical absorption built into Eq. \ref{['eq:psi_dynamics_sel_S']}. (d) Temporal envelope of the square pump pulse ($t_0/\tau_\varphi\!=\!50$, fixed width) applied at the two different photon energies. (e) Transient lattice temperature. In both cases heating remains modest ($T/T_0<0.86$), confirming that reversal is non-thermal and driven by the cubic exciton term rather than by crossing $T_0$. (f) Landau free-energy density $F(\varphi)$ at $t=0$ (grey, identical for both runs) and at $t=90\tau_\varphi$ after the pulse has acted. In the yellow trace the cubic contribution has tilted the landscape, making the right-hand minimum the global energy minimum and leaving the system in Phase 2; in the deep blue trace the situation is opposite. Together the six panels demonstrate deterministic, excitonic-state-selective phase switching governed by resonant exciton pumping in the low-temperature limit.
• Figure 3: Example of single-pulse, fluence-dependent switching. Two identical Gaussian pulses, both resonant with the $\omega_{2}$ exciton, are applied but with different peak amplitudes producing fluences $F_{1}$ (solid blue) and $F_{2}\!<\!F_{1}$ (dashed violet). (a) Order-parameter trajectory $\varphi(t)$. The stronger pulse $F_{1}$ transiently suppresses the energy barrier and, helped by Langevin kicks, drives $\varphi$ across the saddle into the opposite minimum, achieving deterministic phase reversal. The weaker pulse $F_{2}$ lowers the barrier by a smaller amount; thermal noise then fails to complete the crossing and the system relaxes back to its initial state. (b,c) Populations of the two excitonic modes. Because both pumps are tuned to $\omega_{2}$, the $\psi_{2}$ density (c) demonstrates more intense growth whereas $\psi_{1}$ (b) remains low, evidencing the phase-selective absorption enforced by $S_{j}(\varphi)$. (d) Temporal profiles of the two Gaussian pumps with identical carrier frequency, but different amplitudes. (e) Transient lattice temperature. Even for $F_{1}$ the rise is modest ($T_{\max}/T_{0}\!\approx\!0.85$), confirming that switching is non-thermal and governed by the exciton-induced cubic term. (f) Landau free-energy density $F(\varphi)$ at $t=0$ (grey, identical for both runs) and at the pulse peak $t=t_{0}$. For $F_{1}$ (blue) the cubic contribution tilts the landscape enough to eliminate the left minimum, leaving the right-hand well as the global minimum; for $F_{2}$ (violet) the tilt is insufficient and the system ultimately returns to its original phase. These panels together illustrate the fluence threshold for single-shot, resonant all-optical switching between phases captured by the model.
• Figure 4: Multi-exciton pathway that underlies helicity-frequency-selective magnetization reversal in CrI$_3$. Initially (left panel) the flake resides in the $M\!\uparrow$ ferromagnetic state. Green (red) horizontal lines represent the corresponding spin-down (spin-up) excitons; superscripts $+/-$ label optical helicity $\sigma_{+},\sigma_{-}$ of each ladder. Two ladders are relevant: a lower--energy manifold ($\omega_{k}$) that couples to $\sigma_{+}$, and a higher--energy manifold ($\omega_{l}$) that couples to $\sigma_{-}$ only when the magnetization is $\uparrow$. A circularly polarised pump (center panel) is tuned into resonance with one of the ladders but carries the opposite helicity to the resident magnetic phase. The first photons are therefore absorbed only virtually, yet they seed an exciton population in the forbidden ladder of the current phase (excitons with spin-up at $\omega_{l},\sigma_{+}$ or with spin-down at $\omega_{l},\sigma_{-}$). Via the cubic term in Eq. \ref{['eqn:cri3_gamma']} this unbalanced population lowers the free--energy minimum of the opposite magnetic state and reduces the barrier between wells. When the barrier is sufficiently softened a stochastic fluctuation forces the order parameter across it. After the spin flips to $M\!\downarrow$ (right panel) the same photon energy now addresses an allowed ladder; real absorption then rapidly amplifies the exciton reservoir and locks the system into the new minimum. The mechanism is therefore (i) helicity-selective, (ii) threshold-like in fluence, and (iii) non-thermal, being driven by resonant exciton imbalance rather than lattice heating.
• Figure 5: Phase diagram for single-pulse all-optical switching in CrI$_3$ obtained from the multi-exciton Landau model. Colour encodes the final magnetic state as a function of pump-photon energy (horizontal axis) and fluence (vertical axis): red -- the magnetization relaxes back to its initial $M\!\uparrow$ orientation; blue -- the system flips deterministically to $M\!\downarrow$. Left panel: left-hand circular excitation ($\sigma_{-}$); right panel: right-hand circular excitation ($\sigma_{+}$). Only two narrow switching pockets appear, centred at the energy ranges where the pump is resonant with the helicity-opposite exciton ladders sketched in Fig. \ref{['fig:cri3_scheme']}. Inside each pocket reversal occurs only when the pulse fluence exceeds a specific threshold; below this value the cubic exciton term does not fully quench the metastable barrier. Black crosses are explicit simulation points. The topology -- two disjoint, helicity-dependent windows bounded by a sharp fluence threshold -- reproduces the experimental map reported in Ref. Zhang2022.