Pulsed Magnetophononics in Gapped Quantum Magnets

TL;DR

The paper studies ultrafast control of magnetism via magnetophononics in a gapped quantum magnet using a minimal spin-phonon model: an alternating $S=\tfrac{1}{2}$ chain with a driven zero-momentum optic phonon, treated with bond-operator theory and GKSL dynamics. It introduces a phonon-bitriplon approximation to capture hybridization, beating, and sum/difference-frequency excitations, and demonstrates how pulse width and amplitude produce transient band-engineering effects. The analysis reveals a robust low-frequency envelope beat as energy shuttles between lattice and spin sectors, and identifies measurable signatures in the phonon and triplon spectra that are enhanced near band-edge DOS peaks. The CuGeO$_3$ material is used to argue for experimental feasibility in real quantum magnets, highlighting how dimensionality and DOS structure shape observability of transient magnetophononic phenomena and guiding future ultrafast investigations. Overall, the work provides a predictive framework for transient, nonequilibrium magnetophononic dynamics and paves the way for spectroscopic control of spin-phonon hybrid states in quantum materials.

Abstract

One route to the control of quantum magnetism at ultrafast timescales is magnetophononics, the modulation of magnetic interactions by coherently driven lattice excitations. Theoretical studies of a gapped quantum magnet subject to continuous, single-frequency driving of one strongly coupled phonon mode find intriguing phenomena including mutually repelling phonon-bitriplon excitations and global renormalization of the spin excitation spectrum. Because experiments are performed with ultrashort pulses that contain a wide range of driving frequencies, we investigate phonon-bitriplon physics under pulsed laser driving. We use the equations of motion to compute the transient response of the driven and dissipative spin-phonon system, which we characterize using the phonon displacement, phonon number, and triplon occupations. In the Fourier transforms of each quantity we discover a low-frequency energetic oscillation between the lattice and spin sectors, which is an intrinsically nonequilibrium collective mode, and demonstrate its origin as a beating between mutually repelling composite excitations. We introduce a phonon-bitriplon approximation that captures all the physics of hybridization, collective mode formation, and difference-frequency excitation, and show that sum-frequency phenomena also leave clear signatures in the repsonse. We model the appearance of such magnetophononic phenomena in the strongly-coupled spin-chain compound CuGeO$_3$, whose overlapping phonon and spin excitation spectra are well characterized, to deduce the criteria for their possible observation in quantum magnetic materials.

Figures (29)

• Figure 1: Schematic representation of an alternating spin chain with interaction parameters $J$ and $J'$, spin damping $\gamma_{\rm s}$, and a magnetophononic coupling $g$ to the strong bond ($J$). Blue ellipses denote dimer singlets and the red ellipse a triplon excitation. The optic phonon is nondispersive with frequency $\omega_0$ and damping $\gamma$. The incident laser pulse, characterized by its peak electric field ($E_0$), width ($T_p$), and central frequency ($\omega_d$, which we set equal to $\omega_0$), causes direct driving only of the phonon.
• Figure 2: Bitriplon dispersion ($2\omega_{k}$, red) and density of states [$D(2\omega_{k})$, blue] for a spin chain with coupling ratio $\lambda = 0.5$, computed for $N =1000$ dimers using as the triplon broadening a spin damping $\gamma_s = 0.01 J$. Beige shading represents the energy window of the bitriplon band for the infinite system of ideal (undamped) triplons.
• Figure 3: (a) Time traces showing the electric fields of four light pulses with increasing widths, $T_{p} = 2 \pi n / \omega_{d}$ for $n = 1$, 3, 6, and 12. The drive frequency is $\omega_{d} = 1.45 J$ and the peak electric field is $E_{0} = 4\times 10^{-3} \omega_{d}$. We set $\hbar = 1$ and measure the time in units of $J^{-1}$. (b) Moduli of the Fourier transforms of these four pulses, illustrating the increase in spectral content with decreasing pulse width.
• Figure 4: Time evolution of the phonon displacement, $q(t)$, obtained with a standard driving pulse of width $T_p = 3 (2\pi / \omega_{0})$ and peak electric field $E_{0} = 4 \times 10^{-3} \omega_{0}$ incident on a spin chain coupled to a single phonon mode with frequency $\omega_0 = 1.45 J$ with four different coupling strengths, $g/J = 0.1$, 0.3, 0.5, and 0.7.
• Figure 5: Fourier transform, $\tilde{q} (\omega)$, of the four $q(t)$ signals in Fig. \ref{['fig:q_q0_w0_145']}, compared with the situation for a chain with $g = 0$.