---
title: Light-Induced Odd-Parity Magnetism
url: https://www.emergentmind.com/topics/light-induced-odd-parity-magnetism
type: topic
---

# Light-Induced Odd-Parity Magnetism

Light-induced odd-parity magnetism denotes a class of driven magnetic states in which periodic irradiation generates spin splitting that is odd under momentum inversion, typically \(\Delta E(\mathbf{k})=-\Delta E(-\mathbf{k})\) or \(E_s(\mathbf{k})=E_{-s}(-\mathbf{k})\), while the underlying system can remain a compensated antiferromagnet with zero net magnetization [2508.02542]. In the current literature, the phenomenon is realized mainly through Floquet engineering: circularly polarized, elliptically polarized, bicircular, or phase-locked two-color fields modify effective spin-space-group symmetries and produce \(p\)-wave or \(f\)-wave spin textures in collinear, coplanar, and spin-orbital magnets, and even in magnon bands; in several platforms the same mechanism also generates higher-order topology, Chern phases, Weyl phases, or orbital Hall responses [2507.20705][2605.19184][2605.31411].

## 1. Definition and conceptual scope

In the nonrelativistic compensated-magnet literature, “odd parity” usually refers to the momentum parity of the spin splitting rather than to an inversion-odd real-space magnetic order parameter. The clearest formulation is the driven Cr\(_2\)CH\(_2\) case, where odd parity is defined by \(\Delta E(\mathbf{k})=-\Delta E(-\mathbf{k})\); the paper is explicit that this means odd momentum parity of the spin splitting, not odd spatial parity of a real-space magnetic order parameter [2605.19184]. In this sense, odd-parity magnetism is the odd-\(\mathbf{k}\) counterpart of altermagnetic spin splitting: the magnet remains compensated, but its quasiparticle bands acquire a momentum-antisymmetric spin polarization.

A second usage appears in the multipole literature. There, odd-parity magnetism refers to inversion-odd magnetic order parameters such as the layer-staggered spin multipole \(\hat M_{\rm O}=\sum_j \hat S_{j1}-\hat S_{j2}\), or to odd-parity magnetic quadrupole order encoded in antisymmetric spin-orbital polarization in momentum space [2505.20907][2105.09444]. These usages are related but not identical: one centers on the symmetry of band spin splitting, the other on the symmetry of the underlying magnetic order parameter.

A third extension concerns bosonic excitations. In odd-parity magnonics, the odd object is the magnon-band splitting, \(\Delta(\mathbf{k})=-\Delta(-\mathbf{k})\), rather than an equilibrium inversion-odd magnetic ground state [2605.31411]. The common thread across these branches is that odd parity is diagnosed in momentum space, but the microscopic carrier can be an electronic Bloch band, a spin-orbital composite texture, or a magnon branch.

| Context | Defining object | Representative source |
|---|---|---|
| Floquet odd-parity electronic magnetism | \(\Delta E(\mathbf{k})=-\Delta E(-\mathbf{k})\) or \(E_s(\mathbf{k})=E_{-s}(-\mathbf{k})\) | [2605.19184], [2507.20705] |
| Odd-parity multipole magnetism | \(\hat M_{\rm O}=\sum_j \hat S_{j1}-\hat S_{j2}\) | [2505.20907] |
| Odd-parity magnetic quadrupole order | odd-parity MQ with spin-orbital-momentum locking | [2105.09444] |
| Odd-parity magnons | magnon splitting \(\Delta(\mathbf{k})=-\Delta(-\mathbf{k})\) | [2605.31411] |

## 2. Symmetry principles and Floquet routes

The dominant electronic mechanism is symmetry-selective Floquet lifting of spin degeneracy. In conventional collinear antiferromagnets, two spin-group symmetries commonly enforce spin degeneracy: \([C_2\|P]\), giving \(\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})\), and \([C_2T\|E]\), giving \(\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})\). Circularly polarized light breaks \([C_2T\|E]\) while preserving \([C_2\|P]\), so the spin degeneracy is lifted but the remaining relation still forces odd-parity spin splitting [2508.02542]. In dimerized antiferromagnets the same logic is reformulated through the survival of \([C_{2\perp}\|\mathcal P]\) after the light field destroys the spinful \(\mathcal{PT}\) symmetry that had enforced double degeneracy [2508.18360].

At the Hamiltonian level, these works use a Peierls-substituted time-periodic tight-binding model and the high-frequency Floquet expansion
\[
H_{\mathrm{eff}}=H_0+\sum_{n\ge1}\frac{[H_{-n},H_n]}{n\omega}+O(\omega^{-2}),
\]
or equivalent van Vleck/Magnus forms. The commutator term is the central source of odd-parity magnetism: it encodes virtual photon absorption and emission and generates symmetry-selective effective hoppings or mass terms that are odd in momentum. In honeycomb and dimerized models this correction can take the form of a Haldane-like imaginary next-nearest-neighbor hopping or an inversion-odd mass term, thereby tying odd-parity spin splitting directly to Floquet-induced topology [2508.02542][2508.18360].

A second optical route does not rely on circular polarization. In altermagnets driven by a phase-locked two-color linearly polarized field,
\[
{\bf A}(t)=(A_1\cos 2\omega t,\;A_2\cos(\omega t+\phi),\;0),
\]
the time-averaged cubic composite
\[
L_A=\overline{A_xA_y^2}
\]
transforms as \((P,T)=(-,-)\). Its coupling to the intrinsic altermagnetic order produces an induced odd-parity spin-splitting component; microscopically this appears as
\[
l_z=-\frac18 A_1A_2^2\,t_{z0}\cos k_x\sin k_y \propto k_y,
\]
so an even-parity \(k_xk_y\sigma_z\) altermagnetic splitting becomes a tunable mixed-parity \((k_xk_y+c\,k_y)\sigma_z\) texture [2605.03026]. Closely related spin-orbital models show that off-resonant CPL induces purely odd-parity altermagnetism at zero staggered potential and mixed-parity altermagnetism at finite staggered potential, with the parity class fixed by which mirror and inversion-related spin symmetries survive in the Floquet Hamiltonian [2605.05205].

## 3. Materials platforms and representative realizations

The most developed material-specific realization is the Cr\(_2\)CH\(_2\) monolayer. In equilibrium it is a stable A-type antiferromagnet, the AFM state is lower in energy than the FM state by about \(0.76\) eV, the phonon spectrum has no imaginary modes, and the bulk gap is about \(0.655\) eV. Topologically it is a \(\mathcal C_3\)-protected higher-order topological insulator with \(\chi^{(3)}=(-2,1)\) and fractional corner charge \(Q_c^{(3)}=4e/3\). Under circularly polarized light, at \(\hbar\omega=9\) eV and \(eA/\hbar=0.2\,\text{\AA}^{-1}\), the Floquet bands develop an \(f\)-wave odd-parity altermagnetic splitting governed by the effective symmetry \([C_2\|\overline{3}_{001}]\), while the corner states remain intact over a broad driving window [2605.19184].

A broader symmetry program targets conventional 2D collinear antiferromagnets. For systems preserving either \([ \mathcal C_2\|\mathcal P]\) or \([ \mathcal C_2\|\mathcal C_{2z}]\), but not the symmetry classes \([ \mathcal C_2\|\tau]\) or \([ \mathcal C_2\|\mathcal M_z]\), Floquet irradiation can universally induce odd-parity spin splitting. First-principles plus Floquet calculations verify this in MnPS\(_3\) monolayer, FeCl\(_2\) bilayer, and NiRuCl\(_6\) bilayer, using \(\hbar\omega=10\) eV and \(eA_0/\hbar=0.3\,\text{\AA}^{-1}\); under circularly polarized light the induced texture is \(f\)-wave, while elliptically polarized light, bicircular light, or uniaxial strain convert it to \(p\)-wave [2507.20705].

A closely related honeycomb realization is monolayer MnPSe\(_3\). Under right-handed circularly polarized light with \(\tilde A=0.2\,\text{\AA}^{-1}\) and \(\hbar\omega=5\) eV, first-principles Floquet calculations show \(f\)-wave odd-parity spin splitting, a maximal splitting of about \(40\) meV, and anomalous Hall conductivity reaching about \(6\,e^2/h\) when the Fermi level is tuned near \(-0.1\) eV. Because the threefold-related symmetry \([C_2\|\overline{3}_{001}]\) survives under the drive, the splitting is \(f\)-wave; uniaxial strain is proposed as a route to a \(p\)-wave odd-parity phase [2508.02542].

Light-induced odd-parity magnetism is not limited to these Floquet-engineered cases. Coplanar single-\(q\) helimagnets provide an equilibrium reference class in which odd-parity spin textures already exist, with \(\langle \hat{\mathbf n}\!\cdot\!\mathbf S(\mathbf K)\rangle=-\langle \hat{\mathbf n}\!\cdot\!\mathbf S(-\mathbf K)\rangle\). Generalized-Bloch-theorem calculations on MnI\(_2\), NiI\(_2\), and metallic MnTe\(_2\) show \(f\)-wave order for commensurate \(\mathbf Q=(1/3,1/3)\) spirals and \(p\)-wave order for more generic \(\mathbf Q\), providing a static baseline for future photoinduced control schemes [2604.08233].

## 4. Topological consequences and collective excitations

Odd-parity Floquet magnetism often appears together with nontrivial topology because the same light-generated commutator terms act both as spin-splitting fields and as topological masses. In Cr\(_2\)CH\(_2\), the driven odd-parity altermagnetic phase coexists with \(\mathcal C_3\)-protected higher-order topology. The system remains insulating for \(eA/\hbar\in[0,0.55]\,\text{\AA}^{-1}\) at \(\hbar\omega=9\) eV, corner-localized in-gap states remain sharply localized, and only at about \(eA/\hbar\approx0.55\,\text{\AA}^{-1}\) does the gap close and the system evolve into an altermagnetic semimetallic state; even at \(eA/\hbar=0.6\,\text{\AA}^{-1}\), the characteristic \(f\)-wave spin texture survives [2605.19184].

In honeycomb collinear antiferromagnets, the Floquet correction can be written as a Haldane-like next-nearest-neighbor hopping. The low-energy Dirac masses are
\[
H_K=t'(q_x\sigma_x+q_y\sigma_y)+(sm_z-\eta m')\sigma_z,\qquad
H_{K'}=t'(-q_x\sigma_x+q_y\sigma_y)+(sm_z+\eta m')\sigma_z,
\]
with \(m'=9J_1^2(\tilde A)/\omega\). When \(m'=m_z\), the gap closes; for \(m'>m_z\), the \(f\)-wave odd-parity magnet becomes an antiferromagnetic Chern insulator with \(\mathcal C=-2\) for right-handed CPL and \(\mathcal C=+2\) for left-handed CPL, confirmed by two chiral edge states traversing the gap [2508.02542].

Dimerized collinear antiferromagnets provide a second topological route. There the CPL-generated odd-parity \(p\)-wave mass
\[
-\eta F(A_0,\omega)\sin k_y\cos k_x\,\sigma_z
\]
competes with the staggered exchange mass. In 2D, when the Floquet mass exceeds the antiferromagnetic mass, the system enters a Chern-insulating phase with total Chern number \(C=2\eta\); in stacked 3D versions, the same mechanism produces Weyl semimetals with symmetry-related Weyl nodes and Berry-curvature monopoles [2508.18360].

Layered platforms can amplify these effects. In the bilayer VSi\(_2\)N\(_4\) proposal, CPL converts hidden spin-layer locking into \(f\)-wave odd-parity altermagnetism and drives a nonequilibrium QAHE with tunable Chern numbers up to \(C=\pm8\). The same band inversions strongly reshape the orbital Hall effect: the model equilibrium plateau is \(-3.94\,e/2\pi\), a sub-resonant driven state reaches \(-12.00\,e/2\pi\), and topological phases display values such as \(-8.05\,e/2\pi\) and \(-6.07\,e/2\pi\) [2603.11483].

The odd-parity idea also extends to bosonic spin excitations. In collinear antiferromagnets, circularly polarized light generates a scalar spin-chirality term that reduces to a next-nearest-neighbor Dzyaloshinskii–Moriya interaction in the ordered background. The resulting magnon splitting is governed by
\[
D(\mathbf{k})=2S^2\sum_{\mathbf d}J_{\alpha\beta}^{(1)}\sin(\mathbf{k}\!\cdot\!\mathbf d),
\]
so \(D(-\mathbf{k})=-D(\mathbf{k})\) and the magnon branches acquire odd-parity splitting. In bilayer A-type antiferromagnets, this can drive a topological magnon transition with \(C_{\text{total}}=2\), chiral edge modes, and an abrupt jump in magnon thermal Hall conductivity [2605.31411].

## 5. Methods, diagnostics, and measurable signatures

The standard computational workflow combines first-principles electronic structure, Wannierization, Peierls-substituted light coupling, and high-frequency Floquet theory. Cr\(_2\)CH\(_2\) is treated with VASP using PBE within GGA+\(U\), \(U=3\) eV on Cr \(3d\) orbitals, a 550 eV cutoff, \(13\times13\times1\) \(k\)-mesh, and \(20\) \AA\ vacuum; edge states are obtained with a Green-function approach and corner states from finite triangular flakes before the Floquet analysis is applied to the Wannier Hamiltonian [2605.19184]. Equilibrium helimagnets are analyzed differently: the generalized Bloch theorem reduces single-\(q\) spiral calculations to the primitive crystallographic cell and reconstructs supercell-resolved spin textures through reciprocal-space downfolding, which is particularly useful for long-period or nearly incommensurate odd-parity magnets [2604.08233].

The most direct diagnostic is momentum-resolved spectroscopy of the driven spin texture. Several studies explicitly point to spin-resolved ARPES or pump-probe tr-ARPES as the natural probe of opposite splittings at \(K\) and \(K'\), of odd-in-\(\mathbf{k}\) constant-energy maps, and of the \(p\)-wave or \(f\)-wave angular form of the Floquet bands [2605.19184]. Transport is a second major route. In MnPSe\(_3\), the driven anomalous Hall conductivity reaches about \(6\,e^2/h\) near \(-0.1\) eV; in VSi\(_2\)N\(_4\), the driven orbital Hall conductivity and QAHE plateaus provide a combined orbitronic-topological fingerprint of the odd-parity Floquet state [2508.02542][2603.11483].

Finite-geometry observables are especially important when odd-parity magnetism coexists with topology. Cr\(_2\)CH\(_2\) retains corner-localized states under driving, while honeycomb and dimerized Floquet odd-parity magnets exhibit chiral edge states in their Chern phases [2605.19184][2508.02542]. In spin-orbital magnets, the electrically driven spin-resolved orbital Edelstein effect,
\[
m_i^s=\alpha_{ij}^sE_j,\qquad
\alpha_{ij}^{S}=\alpha_{ij}^{\uparrow}-\alpha_{ij}^{\downarrow},
\]
is proposed as a complementary probe of the parent spin-orbital order underlying the odd- and mixed-parity Floquet states [2605.05205]. For magnons, neutron scattering, Brillouin light scattering, THz pump-probe spectroscopy, and thermal Hall measurements are the natural probes of odd-parity band nonreciprocity and its topological consequences [2605.31411].

## 6. Conceptual boundaries, controversies, and open directions

A central boundary condition is that light does not generically produce odd parity. In coplanar antiferromagnets whose reference symmetry is \([\bar C_{2z}\|\mathcal T]\), circularly polarized light breaks the odd-parity constraint and dynamically generates the missing even-parity counterpart, with \(\sigma_z(\mathbf{k})=\sigma_z(-\mathbf{k})\) and a \(d_{xy}\)-wave texture rather than an odd-parity phase [2601.03358]. A related distinction appears in the \((P,T)=(+,+)\) Ising spin-order framework: there, CPL induces even-parity ferromagnetic or altermagnetic splitting, while odd-parity spin splitting is produced instead by parity-breaking electric fields [2603.12330]. Light-induced odd-parity magnetism is therefore symmetry-selective, not a universal consequence of optical driving.

A second recurring issue is the distinction between a Floquet-reconstructed electronic symmetry class and a genuinely new microscopic magnetic order parameter. The Cr\(_2\)CH\(_2\) analysis is explicit on this point: the evidence concerns Floquet-induced lifting of band degeneracy and odd-parity spin splitting, not a time-dependent spin-dynamics or self-consistent nonequilibrium calculation proving a new real-space magnetic order. The safer interpretation is a reclassification of the antiferromagnetic electronic state into an odd-parity altermagnetic Floquet phase [2605.19184]. More broadly, several Floquet studies work in an off-resonant or high-frequency regime and do not provide detailed heating, dissipation, or pulse-duration analyses, even when topological transitions are mapped in detail [2508.18360][2603.11483].

The outstanding opportunity is the size of the candidate space. Spin-group analysis identifies 48 candidate materials for static odd-parity magnets spanning collinear, coplanar, and noncoplanar orders [2510.05512], while exchange-driven non-symmorphic antiferromagnet theory identifies 67 materials in the Magndata database for odd-parity spin splitting induced by antiferromagnetic exchange [2501.02057]. Together with the demonstrated Floquet routes in Cr\(_2\)CH\(_2\), MnPSe\(_3\), MnPS\(_3\), FeCl\(_2\), NiRuCl\(_6\), VSi\(_2\)N\(_4\), and odd-parity magnon platforms, this suggests that light-induced odd-parity magnetism is best viewed as a symmetry-engineering program: a way of converting compensated magnets into momentum-odd spin-split phases whose parity, angular harmonics, and topological content are controlled by the residual symmetries of the driven Hamiltonian.

Source: https://www.emergentmind.com/topics/light-induced-odd-parity-magnetism