Floquet Odd-Parity Collinear Magnets

• Floquet odd-parity collinear magnets are periodically driven antiferromagnets where off-resonant circularly polarized light induces a spin splitting that is odd under momentum inversion.
• Their mechanism hinges on a Floquet-engineered commutator term generating p-wave or f-wave like splitting, which can drive topological phase transitions such as Chern insulators or Weyl semimetals.
• First-principles studies and DFT analyses in materials like MnPSe3 and MnPS3 confirm experimental signatures including ARPES detectable spin-split bands and chiral edge modes in magneto-transport measurements.

Searching arXiv for papers on Floquet odd-parity collinear magnets and closely related odd-parity altermagnetism/magnons. Floquet odd-parity collinear magnets are periodically driven compensated collinear magnets, typically originating from conventional antiferromagnets, in which light-induced nonequilibrium terms lift spin degeneracy so that the spin splitting becomes odd under momentum inversion. In the notation used for collinear antiferromagnets, the defining relation is $\Delta(s,\mathbf{k})=-\Delta(s,-\mathbf{k})$, in contrast to the even-parity spin splitting of conventional altermagnets. Recent work shows that off-resonant polarized light, especially circularly polarized light (CPL), can convert spin-degenerate collinear antiferromagnets into $p$-wave or $f$-wave odd-parity magnets, and in dimerized lattices can dynamically generate odd-parity $p$-wave altermagnets that further realize Chern-insulating or Weyl-semimetal phases under appropriate drive conditions (Zhu et al., 4 Aug 2025, Liu et al., 25 Aug 2025).

1. Definition and symmetry framework

The starting point is a conventional collinear antiferromagnet with two sublattices related by inversion and with zero net magnetization. In the symmetry language used for Floquet odd-parity collinear magnets, the undriven system typically possesses both $[C_{2}\Vert P]$ and $[C_{2}T\Vert E]$. The first enforces $$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$, while the second enforces $$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$; together they imply spin degeneracy. An altermagnet is then a compensated collinear magnet whose bands are spin-split in momentum space, whereas an odd-parity collinear magnet is defined by a spin splitting odd under $\mathbf{k}\rightarrow-\mathbf{k}$ (Zhu et al., 4 Aug 2025).

A broader symmetry classification of irradiated 2D collinear antiferromagnets identifies four relevant protecting spin-space-group operations in equilibrium: $[C_{2}\Vert \mathcal{P}]$, $p$0, $p$1, and $p$2. Under in-plane driving with $p$3, the last two remain exact and therefore do not permit spin splitting, whereas odd-parity spin splitting under irradiation appears when the protecting symmetry is $p$4 or $p$5 and is broken by the light-matter coupling (Huang et al., 28 Jul 2025).

A persistent misconception in this area is that odd-parity spin splitting is restricted to non-collinear magnetic configurations. Recent Floquet analyses explicitly show that periodic driving provides a route to odd-parity magnetism in conventional collinear antiferromagnets, including systems without intrinsic spin-orbit coupling in the microscopic mechanism emphasized for dimerized lattices (Huang et al., 28 Jul 2025).

2. Floquet construction and microscopic mechanism

The standard construction uses a time-periodic vector potential $p$6 and Peierls or minimal coupling, written in the cited works as $p$7 or $p$8. Because the Hamiltonian is periodic in time, Floquet theory introduces Fourier components

$p$9

and in the off-resonant high-frequency regime the leading van Vleck effective Hamiltonian is

$f$0

In the generic formulation for irradiated collinear antiferromagnets, the commutator term is the source of the odd-parity splitting; in model form it appears as a spin-dependent contribution $f$1 with $f$2 odd in momentum (Zhu et al., 4 Aug 2025).

The microscopic origin is model dependent but structurally similar across the electronic realizations. In a dimerized lattice, CPL mixes the $f$3 and $f$4 kinetic terms at $f$5, and their commutator produces an additional $f$6 term odd in momentum, dynamically emulating spin-orbit-like $f$7-wave splitting without intrinsic SOC. In the nearest-neighbor honeycomb model, the same Floquet commutator yields an imaginary next-nearest-neighbor hopping analogous to the Haldane pattern, but acting in a spin-split collinear antiferromagnetic background (Liu et al., 25 Aug 2025).

The same logic extends to bosonic spin excitations. For magnons, a circularly polarized electric field produces an Aharonov-Casher phase on magnon hopping, and the first-order Floquet-Magnus term generates a three-spin scalar-chirality interaction. After projection onto the collinear Néel background, that term reduces to an effective next-nearest-neighbor Dzyaloshinskii-Moriya interaction, which is the odd-parity mass responsible for $f$8- or $f$9-wave magnon splitting (Zhang et al., 29 May 2026).

3. Wave-form classification: $p$0-wave and $p$1-wave sectors

Two symmetry-distinct odd-parity patterns dominate the electronic literature. In lattices without a protecting threefold rotational symmetry, the induced splitting is $p$2-wave, represented in the minimal rhombic model by

$p$3

with coefficients scaling as $p$4. In honeycomb systems with $p$5 symmetry, the induced splitting is $p$6-wave; in the minimal model it takes the explicit form

$p$7

which yields the characteristic six-petal pattern in the spin-resolved Fermi surface (Zhu et al., 4 Aug 2025).

A more general symmetry analysis shows that the wave form can be controlled by the polarization state of the drive. In hexagonal collinear antiferromagnets, CPL preserves the higher rotational symmetry and produces an $p$8-wave basis, while elliptically polarized light (EPL) or bicircular light (BCL) lowers the effective point-group symmetry so that the commutator term transforms as a $p$9-wave basis $[C_{2}\Vert P]$0. Reversing the helicity $[C_{2}\Vert P]$1 flips the sign of the induced splitting, and reducing the crystal symmetry from $[C_{2}\Vert P]$2 to $[C_{2}\Vert P]$3 or $[C_{2}\Vert P]$4, for example by uniaxial strain, also enforces a $[C_{2}\Vert P]$5-wave component (Huang et al., 28 Jul 2025).

The candidate materials identified for 2D collinear antiferromagnets fall into three categories:

Category	Driven odd-parity response	Representative materials
I	Monolayer hexagonal Néel AFMs; CPL $[C_{2}\Vert P]$6-wave, EPL/BCL $[C_{2}\Vert P]$7-wave	MnPS$[C_{2}\Vert P]$8, MnPSe$[C_{2}\Vert P]$9, Fe$[C_{2}T\Vert E]$0O$[C_{2}T\Vert E]$1, MnS, MnSe, MnTe, MnBi$[C_{2}T\Vert E]$2Te$[C_{2}T\Vert E]$3
II	AFM bilayers of two identical FM monolayers; CPL $[C_{2}T\Vert E]$4-wave	RuO$[C_{2}T\Vert E]$5, VSe$[C_{2}T\Vert E]$6, NbSe$[C_{2}T\Vert E]$7, TaS$[C_{2}T\Vert E]$8, FeCl$[C_{2}T\Vert E]$9, FeBr$$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$0, MnO$$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$1
III	AFM bilayers of ferri- or uncompensated ferrimagnets; CPL $$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$2-wave	NiRuCl$$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$3

This classification is restricted by the requirement that the two sublattices are not connected by $$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$4 or $$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$5, but do admit either $$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$6 or $$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$7 in equilibrium (Huang et al., 28 Jul 2025).

4. Dimerized lattices and Floquet odd-parity altermagnets

A particularly explicit realization is the PT-symmetric collinear antiferromagnet on a 2D dimerized square lattice. Its static Bloch Hamiltonian is

$$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$8

with $$\varepsilon(s,\mathbf{k})=\varepsilon(-s,-\mathbf{k})$$9, $$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$0, inter-dimer hopping $$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$1, and staggered exchange $$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$2. This model has spinful PT symmetry $$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$3 with $$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$4, hence Kramers degeneracy in the undriven state (Liu et al., 25 Aug 2025).

Under normally incident CPL,

$$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$5

the leading Floquet correction produces the effective Hamiltonian

$$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$6

with

$$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$7

The induced term

$$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$8

satisfies $$\varepsilon(s,\mathbf{k})=\varepsilon(s,-\mathbf{k})$$9 and therefore has odd inversion parity, identified in the paper as a $\mathbf{k}\rightarrow-\mathbf{k}$0-wave form (Liu et al., 25 Aug 2025).

Because the underlying dimerized lattice supports a Dirac band structure, the driven state is not merely spin-split but topological under suitable parameters. The same analysis extends to stacked dimerized layers, where arbitrary-incidence CPL generates two odd-parity terms, $\mathbf{k}\rightarrow-\mathbf{k}$1 and $\mathbf{k}\rightarrow-\mathbf{k}$2 in the $\mathbf{k}\rightarrow-\mathbf{k}$3 channel, enabling Weyl semimetals in three dimensions (Liu et al., 25 Aug 2025).

5. Floquet-induced topology

The topological content of Floquet odd-parity collinear magnets is one of their defining features. In the honeycomb $\mathbf{k}\rightarrow-\mathbf{k}$4-wave model, the Floquet term acts as a valley- and spin-dependent Dirac mass. Expanding around $\mathbf{k}\rightarrow-\mathbf{k}$5 and $\mathbf{k}\rightarrow-\mathbf{k}$6, the masses are $\mathbf{k}\rightarrow-\mathbf{k}$7 and $\mathbf{k}\rightarrow-\mathbf{k}$8, and when $\mathbf{k}\rightarrow-\mathbf{k}$9 exceeds $[C_{2}\Vert \mathcal{P}]$0 the total Chern number jumps from $[C_{2}\Vert \mathcal{P}]$1 to $[C_{2}\Vert \mathcal{P}]$2 for right-handed CPL. Numerical ribbon calculations confirm the corresponding chiral edge states and quantized Hall conductivity $[C_{2}\Vert \mathcal{P}]$3 (Zhu et al., 4 Aug 2025).

In the dimerized $[C_{2}\Vert \mathcal{P}]$4-wave altermagnet, the transition is controlled by the Floquet scale relative to the staggered exchange. The CPL-induced $[C_{2}\Vert \mathcal{P}]$5 shift breaks spinful PT, and when $[C_{2}\Vert \mathcal{P}]$6 the gap closes and reopens. Near the two Dirac points $[C_{2}\Vert \mathcal{P}]$7 with $[C_{2}\Vert \mathcal{P}]$8, two cones flip as the effective mass changes sign, producing a total Chern number $[C_{2}\Vert \mathcal{P}]$9 in the 2D phase diagram (Liu et al., 25 Aug 2025).

The 3D extension yields a Weyl semimetal rather than a fully gapped Chern insulator. Weyl nodes appear in the $p$00 plane when

$p$01

which gives at least four Weyl points, with inversion-related nodes carrying opposite chirality (Liu et al., 25 Aug 2025).

Later work broadened the topological landscape. In a 2D collinear antiferromagnetic multilayer with layer-dependent coupling to CPL, Floquet engineering induces $p$02-wave odd-parity altermagnetism and a nonequilibrium quantum anomalous Hall effect with tunable Chern numbers up to $p$03, attributed to layer- and valley-dependent band inversions (Tian et al., 12 Mar 2026). In the Cr$p$04CH$p$05 monolayer, equilibrium higher-order topology characterized by the symmetry indicator $p$06 survives under CPL while the system develops an odd-parity $p$07-wave altermagnetic state; the corner states persist up to approximately $p$08, beyond which the gap closes and an altermagnetic semimetal emerges (Zou et al., 18 May 2026).

6. First-principles realizations and experimental signatures

First-principles calculations provide direct material support for the Floquet picture. In monolayer MnPSe$p$09, a DFT plus Wannier plus Floquet treatment with right-handed CPL at $p$10 and $p$11 gives spin splitting of the two top valence bands by up to $p$12, an $p$13-wave sixfold Fermi-surface pattern, and anomalous Hall conductivity reaching approximately $p$14 when the Fermi energy is tuned just below the gap (Zhu et al., 4 Aug 2025).

A wider first-principles survey using Wannier-based tight-binding models examined MnPS$p$15, FeCl$p$16 bilayer, and NiRuCl$p$17 under $p$18 and light intensity $p$19. All are spin-degenerate without light or SOC, but under right-handed CPL exhibit clear odd-parity spin splitting: MnPS$p$20 shows splitting up to approximately $p$21 at $p$22 with six $p$23-wave lobes, FeCl$p$24 bilayer shows approximately $p$25 and converts from $p$26-wave to twofold $p$27-wave under EPL or BCL, and fully compensated ferrimagnetic NiRuCl$p$28 shows approximately $p$29 near $p$30 (Huang et al., 28 Jul 2025).

The dimerized-lattice construction specifies complementary drive conditions: the frequency must be off-resonant with $p$31 bandwidth, numerically chosen as $p$32; the amplitude should be of order unity, $p$33–$p$34, so that $p$35 and $p$36; and the polarization should be strictly circular to break time-reversal symmetry while preserving $p$37, which enforces $p$38 (Liu et al., 25 Aug 2025).

Proposed probes are correspondingly specific. Angle-resolved photoemission should observe spin-split bands satisfying $p$39 in the odd-parity phases. In 2D Chern-insulating regimes, transport should show Hall conductance $p$40 controlled by CPL handedness. In 3D Weyl phases, negative magnetoresistance and Fermi arcs are expected, with Fermi arcs on surfaces normal to $p$41 or $p$42 but spin-split on $p$43-normal surfaces. Additional proposals include time- and spin-resolved ARPES, photo-induced anomalous Hall measurements, magnetic circular dichroism, and second-harmonic generation of spin currents (Liu et al., 25 Aug 2025, Zhu et al., 4 Aug 2025).

7. Extensions: magnons, excitons, and mixed-parity regimes

The electronic Floquet odd-parity collinear magnet has rapidly become the template for a broader odd-parity program. In magnonics, a complete spin-point-group classification has been formulated for odd-parity magnon splitting in 2D collinear antiferromagnets. There the leading odd-parity splitting types are again $p$44- and $p$45-wave, and circularly polarized light or loop currents provide the effective time-reversal-breaking mechanism. In bilayer systems, dynamical modulation can drive a topological magnon phase transition accompanied by chiral edge modes and an abrupt jump in the magnon thermal Hall conductivity (Zhang et al., 29 May 2026).

In the Haldane-Hubbard setting, topological excitons in the paramagnetic phase condense at $p$46 and drive the system into a collinear Néel state identified as an odd-wave magnet. In the ordered phase the low-energy collective modes become odd-parity magnons with characteristic $p$47-wave splitting, and the magnon topology changes when the electronic bandgap closes. That work explicitly notes potential realizations in Floquet-driven materials and cold atomic gases (Eto et al., 4 Jun 2026).

Other developments loosen the dichotomy between even- and odd-parity responses. In a two-sublattice two-orbital hexagonal model, circularly polarized light induces pure odd-parity altermagnetism at zero staggered potential $p$48, but for finite $p$49 yields mixed-parity spin splitting; in that construction, the odd-parity limit is a $p$50-wave Floquet altermagnet near $p$51 (Zhuang et al., 6 May 2026). A distinct route uses phase-locked two-color linearly polarized light to induce a static $p$52 order symmetry-equivalent to a translationally invariant $p$53-odd loop-current order, which in a collinear altermagnet produces a controllable mixed-parity spin texture rather than a purely odd-parity one (Yu, 4 May 2026).

Taken together, these results indicate that Floquet odd-parity collinear magnets are best understood not as a single model system but as a symmetry-governed nonequilibrium class. Their essential ingredients are a compensated collinear magnetic background, a light field that removes the symmetry enforcing $p$54 while retaining the relation between opposite spins at opposite momenta, and a commutator-generated odd-in-momentum Floquet term. This suggests a unifying viewpoint in which electronic altermagnets, odd-parity magnons, higher-order topological antiferromagnets, and loop-current-assisted mixed-parity states are different realizations of the same driven symmetry principle.