Magnon–Exciton Drag in CrSBr and Beyond

• Magnon–exciton drag is defined as the efficient momentum transfer from magnons to excitons, resulting in ultrafast exciton drift and enhanced transport phenomena.
• Experimental studies in CrSBr reveal anomalous exciton dynamics such as superdiffusion, negative diffusion coefficients, and nearly isotropic expansion despite anisotropic mass.
• Theoretical models based on Boltzmann transport and exciton–magnon scattering quantify the momentum exchange, highlighting the role of strong coupling and magnetic phase transitions.

The magnon-exciton drag effect describes the efficient transfer of linear momentum from itinerant spin excitations (magnons) to optically active electron–hole pairs (excitons) in magnetically ordered materials, resulting in a collective exciton drift and enhanced transport phenomena. This mechanism operates via strong exciton–magnon coupling and dominates optical quasiparticle propagation near magnetic phase transitions in antiferromagnetic semiconductors, particularly in van der Waals compounds such as CrSBr. The effect is characterized by nearly isotropic and ultrafast exciton expansion, anomalously large diffusion coefficients, and features—such as superdiffusivity and sign-reversal drift velocities—that cannot be explained by conventional exciton transport mechanisms such as phonon drag or exciton–exciton interactions (Dirnberger et al., 9 Jul 2025, Iakovlev et al., 5 Dec 2025).

1. Theoretical Underpinnings of Magnon–Exciton Drag

Magnon–exciton drag emerges when a non-equilibrium population of magnons, typically established by ultrafast optical or thermal gradients, imparts momentum to excitons via scattering events. The theoretical framework is rooted in the exciton–magnon interaction Hamiltonian:

$$H_\text{int} = \sum_{k,q} g_{k,q} X_{k+q}^\dagger X_k m_q + \text{h.c.}$$

Here, $X_k^\dagger$ ($X_k$) creates (annihilates) an exciton of center-of-mass momentum $k$ and $m_q$ is the magnon annihilation operator at wavevector $q$. The coupling matrix element $g_{k,q}$ can often be treated as isotropic for small $k$, $q$ or with weak angular dependence.

A macroscopic magnon current $j_m = -\chi_m \nabla T_\text{spin}$ (with $\chi_m$ the magnon conductivity) gives rise to a drag force per exciton density $n_X$:

$F_\text{drag} = \alpha j_m$

where the drag coefficient $\alpha \simeq \hbar |g|^2 D_m \nu_m$ depends on the magnon density of states $D_m$ and group velocity $\nu_m$ near thermal energies. In steady state, the exciton cloud acquires a drift velocity $v_d = \mu_X \alpha j_m$ where the mobility $\mu_X = D_X/(k_B T)$ and $D_X$ is the bare exciton diffusion constant (Dirnberger et al., 9 Jul 2025).

Microscopically, the dominant processes comprise exciton–magnon scattering, two-magnon absorption, and emission. In bilayer CrSBr, these interactions arise from a magnon-induced local tilt of antiparallel Cr layer magnetizations, activating otherwise spin-forbidden interlayer tunneling and generating an effective four-particle coupling between excitons and magnons. The full Boltzmann treatment yields a relaxation time $\tau_{XM}$ for exciton–magnon momentum exchange, with the rate:

$$1/\tau_{XM} = 8\pi |V|^2 \mathcal{D}^M \mathcal{D}^X (k_B T/\hbar) \Phi(T)$$

with $\mathcal{D}$ the effective density of states and $\Phi(T) \simeq 6(k_B T/E_0^M)$ for $k_B T \gg E_0^M$, the magnon gap (Iakovlev et al., 5 Dec 2025).

2. Experimental Manifestations in CrSBr

Time-resolved photoluminescence (PL) imaging in few- and bilayer CrSBr provides direct evidence for magnon-exciton drag. Key observations include:

• At $T \approx T_N = 132\,\text{K}$, exciton clouds exhibit nearly isotropic in-plane expansion (despite the strongly anisotropic exciton mass tensor), with the effective diffusion coefficient reaching $D^* \sim 150\,\text{cm}^2/\text{s}$—over two orders of magnitude larger than expected from phonon-limited diffusion ($D_X \lesssim 1\,\text{cm}^2/\text{s}$). Corresponding root-mean-square velocities reach $v_\text{rms} \sim 1$–$3\,\text{km/s}$ within the first $20$ ps.
• At low temperatures ($T = 4\,\text{K}$), low fluence yields negative diffusion coefficients ($D^* < 0$, $D^* \approx -13\,\text{cm}^2/\text{s}$ along $b$), corresponding to inward drift velocities ($v_\text{in} \approx -3\,\text{km/s}$), while higher fluence reverts to positive $D^*$ and moderate expansion.
• In bilayer samples at $T = 4\,\text{K}$ (FM phase): PL profiles undergo superdiffusive broadening with $\Delta \sigma^2 \propto t^\alpha$, $\alpha = 1.3$–$2.1$ over $\sim15\,\text{ps}$, and radial velocities as high as $41\,\text{km/s}$; normal diffusion is restored upon heating to $\sim60\,\text{K}$.

Collectively, these findings cannot be ascribed to phonon drag, exciton–exciton interactions, or pure thermoelectric effects, given the magnitude, sign reversal, temperature dependence, and isotropy of the observed dynamics (Dirnberger et al., 9 Jul 2025).

3. Microscopic Mechanism and Boltzmann Transport Theory

Microscopic theory derived using Boltzmann transport formalism incorporates the explicit magnon spectrum—including exchange, single-ion anisotropy, and long-range dipolar effects—and quantifies the exciton–magnon scattering and associated momentum exchange. The effective Hamiltonian involves only two-magnon processes due to angular-momentum conservation in the AFM ground state:

$$H_\text{int} = -\frac{V}{\mathcal{S}} \sum_{k,q,p} \{\cdots\} x_{k+q}^\dagger x_k$$

The dipolar interaction, in particular, generates magnon branches with negative group velocity at low $k$, leading to the experimentally observed negative drag and contraction of the exciton cloud at low $T$ and low fluence.

Solving the coupled kinetic equations for exciton and magnon distributions under a magnon drift velocity $u$, the steady-state exciton velocity approaches the magnon velocity in the regime of strong drag (small $\tau_{XM}$):

$v = (1 + \tau_{XM}\Gamma)^{-1} u$

where $\Gamma$ denotes phonon and disorder scattering. The resulting drag-induced enhancement of exciton diffusion is nearly isotropic and can vastly exceed intrinsic anisotropic values, especially near $T_N$ (Iakovlev et al., 5 Dec 2025). Scattering times are sub-picosecond and decrease strongly with magnon population, rendering magnon scattering dominant among all exciton relaxation channels.

4. Distinctive Features and Distinction from Conventional Mechanisms

The magnon–exciton drag effect displays several unique signatures:

• Isotropic Enhancement: Despite a mass anisotropy $M^x / M^y \sim 20$, the effective diffusivity $D_{\mathrm{eff}}$ is nearly isotropic owing to the near isotropy of the magnon dispersion ($\nu_m$) in CrSBr.
• Non-monotonic $T$-dependence: $D_{\mathrm{eff}}$ peaks at $T_N$ concomitant with the divergence of magnetic susceptibility and maximum magnon population/conductivity, unlike behaviors expected from phonon drag or exciton–exciton processes.
• Sign Reversal and Superdiffusion: Negative drag at low $T$ arises from backward-wave (Damon–Eshbach–like) magnon modes with negative group velocity induced by dipole-dipole interactions. Superdiffusive broadening in bilayers is attributed to collective magnon–exciton scattering beyond equilibrium distributions.
• Inefficacy of Alternate Mechanisms: Quantitative estimates show that phonon- or disorder-limited diffusion, exciton–exciton annihilation, and phonon wind cannot account for the observed diffusion rates, temperature profiles, or reversals.

A table summarizing core microscopic processes involved is provided below for reference:

Process	Description	Role in Drag Effect
Exciton–magnon scattering	Two-magnon exchange processes transferring momentum	Dominant; sets $\tau_{XM}$
Two-magnon absorption	Exciton absorbs two magnons, changing state	Enhances diffusion, broadening
Two-magnon emission	Exciton emits two magnons	Contributes to isotropy, relaxation

5. Broader Implications and Materials Platform

The magnon–exciton drag effect represents a broadly applicable mechanism for control of optical transport in low-dimensional magnetic semiconductors. Key implications include:

• Universality: Any material with sufficiently strong exciton–magnon coupling and high magnon conductivity (e.g., NiPS$_3$, MnPS$_3$, CrI$_3$) is expected to display drag-induced exciton transport anomalies, especially near magnetic phase transitions with large magnons densities and susceptibilities.
• Heterostructures: In van der Waals heterostructures, proximity-induced magnon flux from a magnetic insulator (e.g., CrSBr) can "spill over" and drive excitons in adjacent nonmagnetic semiconductor layers (e.g., WSe$_2$, MoSe$_2$), enabling magnon-mediated control of exciton dynamics beyond purely magnetic systems.
• Opto-spintronic Applications: Potential applications include all-optical exciton steering by local temperature or spin current engineering, hybrid magnon–exciton logic devices, and tunable exciton interconnects leveraging long magnon coherence and low-loss spin transport channels (Dirnberger et al., 9 Jul 2025, Iakovlev et al., 5 Dec 2025).

6. Outlook and Open Directions

The rapid progress in the study of magnon–exciton drag opens several avenues for further research:

• Detailed mapping of magnon spectra and their anisotropy in diverse compounds to optimize drag efficiency and directionality.
• Control and engineering of negative-group-velocity magnon modes to realize programmable exciton contraction and expansion.
• Non-equilibrium and strong-pumping regimes, including superdiffusive transport and the breakdown of detailed balance, as platforms for exploring new optical phenomena.
• Integration into scalable devices for ultrafast, reconfigurable opto-spintronic circuits exploiting collective magnon–exciton phenomena.

These developments position magnon–exciton drag as a fundamental transport mechanism at the intersection of magnonics and excitonics, with both conceptual and technological implications for next-generation hybrid spin–photonics systems (Dirnberger et al., 9 Jul 2025, Iakovlev et al., 5 Dec 2025).