Magnon Circular Photogalvanic Effect

• Magnon CPGE is a nonlinear quantum phenomenon where circularly polarized light transfers angular momentum to generate a directed dc magnon spin current in magnetically ordered insulators.
• The effect is described by second-order response theory and quantum geometric principles, enabling tunable control via light polarization, incidence angle, and microscopic symmetry breaking.
• Experimental detection relies on converting magnon currents into measurable voltages using the inverse spin Hall effect, offering a contact-free method for ultrafast spin current control.

The magnon circular photogalvanic effect (CPGE) is a nonlinear quantum phenomenon in which circularly polarized electromagnetic radiation generates a directed dc magnon spin current in magnetically ordered insulators. Rooted in the conservation of angular momentum between photons and magnons, the CPGE is a bosonic counterpart to the electronic photogalvanic effect but drives the transport of spin (rather than charge) through coherent optical processes. Crucially, the phenomenon depends on both the microscopic symmetry of the magnetic lattice—typically requiring broken inversion or time-reversal—and the specific polarization and incidence geometry of the illumination. Magnon CPGE offers a contact-free, ultrafast, and highly tunable mechanism for generating and controlling magnonic spin currents in both antiferromagnetic and ferromagnetic insulators. It is underpinned by rigorous theoretical frameworks including nonlinear response theory, quantum geometry of magnon bands, and explicit microscopic Hamiltonians. Experimental detection relies predominantly on the conversion of optically generated magnon currents into detectable voltages via the inverse spin Hall effect in proximate nonmagnetic metals.

1. Microscopic Mechanisms and Model Hamiltonians

The magnon CPGE is fundamentally a second-order light–matter interaction, where the angular momentum from circularly polarized photons is transferred to magnonic excitations. The minimal microscopic model consists of a magnetically ordered system described by an effective spin Hamiltonian, such as

$$H_0 = \sum_{\langle ij \rangle} J_{ij} S_i \cdot S_j + J_z \sum_{\langle ij \rangle} S_i^z S_j^z - g\mu_B B_0 \sum_i S_i^z$$

for a uniaxial antiferromagnet on a honeycomb lattice (Boström et al., 2021, Proskurin et al., 2018). After Holstein–Primakoff and Bogoliubov transformations, the Hamiltonian yields magnon modes with energies $\epsilon_{\alpha/\beta, k}$. The presence of either a time-dependent electric field (via Aharonov–Casher effect) (Wang et al., 2023) or a magnetic field (via Zeeman coupling) enables light–magnon coupling. In the dipole approximation, light–magnon interactions can generate single- or multi-magnon processes, with the CPGE typically associated with two-magnon Raman-type transitions in antiferromagnets (Boström et al., 2021) or one-magnon processes in certain symmetry-broken contexts (Gu et al., 22 Aug 2025).

For ferromagnets or systems described by a general bosonic BdG Hamiltonian,

$$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$

the magnons can also be driven via the Aharonov–Casher phase, leading to additional quantum-geometric and topological contributions (Wang et al., 2023).

2. Nonlinear Response Theory and Analytical Formulation

Magnon CPGE is quantitatively described by second-order Kubo response theory: $$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$ where the nonlinear "photoconductivity" tensor $\sigma^{(2)}_{z\nu\lambda}$ encompasses competing contributions from injection, shift, and geometric (Berry curvature) processes (Gu et al., 22 Aug 2025).

Key features include:

• The injection-type term, reflecting resonant magnon absorption, is sharply peaked at the eigenfrequencies $\omega = \omega_{l,0}$ and proportional to the magnon group velocity $v_l^z(\bm k)$ and occupation factors $n_B(\omega)$ (Gu et al., 22 Aug 2025, Ishizuka et al., 2021).
• The circular photogalvanic current is given by

$$J^z_{\text{circ}} = \pm|B_0|^2\, \Im\, \sigma^{(2)}_{zxy}(0; \omega, -\omega) \propto H$$

where the sign depends on light helicity and the direction of an applied static magnetic field (Gu et al., 22 Aug 2025).

• For two-magnon CPGE, the current has the general structure

$$\langle J \rangle \propto \frac{G}{\hbar\omega_{\mathrm{in}} \Gamma} \sum_k (n_\alpha + n_\beta + 1) (v_\alpha + v_\beta) |t_{q_{\mathrm{in}},k}|^2 \delta(\hbar\omega_{\mathrm{in}} - \epsilon_\alpha(k) - \epsilon_\beta(-k))$$

where $\epsilon_{\alpha/\beta, k}$0 depends on laser intensity, and $\epsilon_{\alpha/\beta, k}$1 is a matrix element encoding optical selection rules (Boström et al., 2021). In collinear antiferromagnets, third- and fifth-rank susceptibilities govern the symmetry-allowed CPGE channels (Boström et al., 2021, Proskurin et al., 2018).

3. Symmetry Constraints and Selection Rules

The magnitude and nature of the magnon CPGE are determined by the magnetic point-group symmetry, inversion breaking, and details of the magnon band structure:

• In collinear antiferromagnets with $\epsilon_{\alpha/\beta, k}$2 and combined time-reversal and inversion ($\epsilon_{\alpha/\beta, k}$3) symmetry, only a subset of the fifth-order nonlinear susceptibility tensor survives. Conservation of angular momentum restricts efficient magnon pair generation to circular polarization with net $\epsilon_{\alpha/\beta, k}$4 (Boström et al., 2021).
• For bilayer antiferromagnets (e.g., CrI$\epsilon_{\alpha/\beta, k}$5, CrBr$\epsilon_{\alpha/\beta, k}$6), the two-magnon term dominates the CPGE, and does not require Dzyaloshinskii–Moriya interaction (DMI) or k-asymmetry in the dispersion (Ishizuka et al., 2021). In contrast, ferromagnets or systems with DMI can realize both one-magnon and geometric shift contributions (Wang et al., 2023, Proskurin et al., 2018).
• The effect vanishes in the case of normal (θ = 0) or grazing (θ → π/2) incidence, or under linear polarization, and is maximized for specific oblique angles due to rotational symmetry breaking (Boström et al., 2021). The current reverses upon switching the light helicity.

Symmetry Table (extracted from (Boström et al., 2021, Ishizuka et al., 2021)):

Symmetry	Process Allowed	CPGE Channel
Inversion + TI	Two-magnon only	Fifth-order tensor
Broken inversion	One/two-magnon	Second/fifth-order
DMI present	One-magnon geometric	Berry curvature

4. Quantum Geometry and Topological Aspects

The CPGE in magnonic systems is strongly linked to quantum geometric properties of magnon bands:

• Berry curvature, quantum metric, and the full quantum geometric tensor $\epsilon_{\alpha/\beta, k}$7 appear explicitly in microscopic expressions for the photogalvanic conductivity (Wang et al., 2023).
• The circularly polarized (CP) response selectively probes the antisymmetric (Berry curvature) part of $\epsilon_{\alpha/\beta, k}$8:

$\epsilon_{\alpha/\beta, k}$9

where $$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$0 is the band-resolved Berry curvature and $$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$1 is the velocity difference between bands (Wang et al., 2023).

• Tuning the lattice geometry (e.g., breathing kagome lattice) or strain can drive topological transitions in magnon bands, producing pronounced CPGE signatures and enabling optical detection of magnon Chern topology (Wang et al., 2023).

5. Material Realizations and Parameter Regimes

Several classes of magnets have been proposed or analyzed for observing magnon CPGE:

• Collinear honeycomb antiferromagnets: Monolayer MnPS$$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$2 with parameters $$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$3, $$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$4, $$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$5, $$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$6, $$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$7 (Boström et al., 2021).
• Bilayer Cr trihalides: CrI$$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$8 and CrBr$$H_0 = \frac{1}{2} \sum_{k} \Psi_k^{\dagger} \mathbb{H}_0(k) \Psi_k$$9, with interlayer antiferromagnetic coupling and tunable resonance frequencies spanning 10 GHz–1 THz (Ishizuka et al., 2021).
• Magnetoelectric Cr$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$0O$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$1: Exhibits CPGE under circularly polarized microwaves in the presence of static $$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$2 (Gu et al., 22 Aug 2025).
• Breathing kagome ferromagnets: Pyrochlore/rare-earth compounds supporting topologically nontrivial magnon bands (Wang et al., 2023).

Typical parameters for induced current densities and voltages:

Material	J (meV)	CPGE Current	Detection Signal	Reference
MnPS$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$3	1.54	$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$4 up to $$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$5 (est.)	$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$6mV (Pt detector)	(Boström et al., 2021)
CrI$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$7	2.01	$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$8	$$\langle J^z \rangle = \int d\omega \sum_{\nu,\lambda} \sigma^{(2)}_{z\nu\lambda}(0; \omega, -\omega) B_\nu(\omega) B_\lambda(-\omega)$$9 detectable	(Ishizuka et al., 2021)
Cr$\sigma^{(2)}_{z\nu\lambda}$0O$\sigma^{(2)}_{z\nu\lambda}$1	$\sigma^{(2)}_{z\nu\lambda}$2	$\sigma^{(2)}_{z\nu\lambda}$3 (for $\sigma^{(2)}_{z\nu\lambda}$4 mT)	ISHE voltage flips with $\sigma^{(2)}_{z\nu\lambda}$5	(Gu et al., 22 Aug 2025)

6. Experimental Detection and Control

Detection of optically generated magnon currents uses several established techniques:

• The magnon current diffuses to metal contacts (often Pt) at sample edges, where it is converted into a transverse charge current via the inverse spin Hall effect (ISHE) (Boström et al., 2021, Ishizuka et al., 2021).
• The ISHE voltage depends on the spin-Hall angle, resistivity, spin-diffusion length, and geometry of the heavy-metal layer, with typical signals in the microvolt-to-millivolt range (Boström et al., 2021).
• Key experimental fingerprints:
  • Hallmark sign-reversal of $\sigma^{(2)}_{z\nu\lambda}$6 with light helicity or static field direction (Gu et al., 22 Aug 2025).
  • Resonant enhancement at magnon frequencies; vanishing effect for linear polarization.
  • Robustness to spurious signals from spin pumping or spin Seebeck effect due to unique symmetry and field/power dependencies (Gu et al., 22 Aug 2025).
• Control variables include angle of incidence, polarization, laser intensity, and (in some cases) uniaxial strain to manipulate magnon band topology (Wang et al., 2023).

7. Applications and Prospects

Magnon CPGE opens strategies for ultrafast, all-optical, and contact-free spin current generation in insulating magnets with potential applications in spintronics:

• All-optical spin-current diodes and terahertz detectors based on inversion-broken magnets (Ishizuka et al., 2021).
• Tunable optical control of magnon flow, suitable for on-chip magnonics, due to the ability to selectively excite spin current channels via light helicity and incidence (Boström et al., 2021).
• Probing and controlling topological phase transitions in magnon bands via optical conductivity measurements, leveraging the correspondence between Berry curvature and the CPGE response (Wang et al., 2023).
• Device geometries exploiting the CPGE as a means of rapid magnon injection for spin-logic or memory elements, or in hybrid optospintronic circuits.

Experimental feasibility is bolstered by the accessibility of GHz–THz sources, the maturity of spin-current detection via ISHE, and the large theoretical signal strengths predicted for suitable materials. The magnon CPGE thus provides a platform for exploring the interplay of quantum geometry, symmetry, and nonequilibrium spin transport in complex magnets (Boström et al., 2021, Ishizuka et al., 2021, Wang et al., 2023, Proskurin et al., 2018, Gu et al., 22 Aug 2025).