Chiral Altermagnets: Spin-Split Chiral Systems

• Chiral altermagnets are systems with compensated magnetic order that produce momentum-dependent spin splitting via exchange-driven interactions.
• They exhibit distinct chirality through lattice structure, noncollinear magnetic orders, and coupled quasiparticle responses, leading to chiral magnons, phonons, and topological effects.
• Their design principles leverage symmetry, multipolar form factors, and controlled exchange interactions to enable novel spin transport and device functionalities.

Chiral altermagnets are altermagnetic systems in which chirality enters through the lattice, the magnetic order, or the coupled quasiparticle sector. In the crystallographic setting, they combine a chiral crystal structure—without inversion or mirror planes—with compensated magnetic order that still yields momentum-dependent spin splitting and zero net magnetization. In a broader current usage, the term also covers chiral noncollinear or proper-screw magnetic orders whose symmetry allows altermagnetic-like spin splitting, chirality-selective magnon and phonon responses, and transport phenomena not reducible to conventional ferromagnetism or centrosymmetric antiferromagnetism. Across these realizations, the common feature is exchange-driven, symmetry-controlled chirality splitting without macroscopic ferromagnetic moment, linking electronic bands, magnons, phonons, and topological transport (Tenzin et al., 1 Aug 2025, Hu et al., 2024, Okamoto et al., 29 Nov 2025).

1. Symmetry definitions and taxonomies

The defining altermagnetic motif is a compensated magnetic structure with zero net magnetization but with momentum-dependent spin splitting. Several recent formulations emphasize different symmetry languages. One phenomenological construction defines altermagnets as long-range magnetically ordered crystals that break parity $P$ and time-reversal $T$ individually while preserving the combined $PT$ operation; this allows nonrelativistic, exchange-driven spin splitting in momentum space despite $M=0$. A more materials-oriented definition, used for prototypical compounds such as CrSb, MnTe, and the chiral dichalcogenides TM$_3$X$_6$, emphasizes that opposite magnetic sublattices are not related by pure translation or inversion, but by nontrivial crystal operations such as rotations or mirrors, so spin degeneracy is lifted in selected regions of the Brillouin zone (Okamoto et al., 29 Nov 2025, Consiglio et al., 6 Jul 2026, Tenzin et al., 1 Aug 2025).

Within this general class, chirality enters in at least three distinct ways. First, structurally chiral altermagnets such as TM$_3$X$_6$ lack both inversion and mirror symmetries in the lattice itself. Second, magnetic chirality may arise from proper-screw order, where the sign of $\chi=(S_i\times S_j)_z$ distinguishes left- and right-handed helices. Third, noncollinear chiral altermagnets can support odd multipolar order parameters not available in achiral settings, including effective dipolar components that generate hedgehog-like spin textures in momentum space. This literature therefore treats “chiral altermagnet” not as a single crystallographic species, but as a symmetry class in which chirality and staggered exchange act simultaneously on low-energy degrees of freedom (Okamoto et al., 29 Nov 2025, Hu et al., 2024).

A recurrent misconception is that zero net magnetization should imply either restored spin degeneracy or the absence of handed collective modes. The recent altermagnetic results contradict both expectations. In MnTe, CrSb, RuO$_2$, and TM$T$0X$T$1, vanishing net moment coexists with momentum-selective spin splitting, chiral magnon branches, and chirality-sensitive transport. Conversely, chirality in this context is not synonymous with strong spin-orbit coupling. Several key effects, including the minimal altermagnetic spin splitting and the magnon splitting in MnTe, are explicitly exchange-driven and nonrelativistic (Liu et al., 2024, Okamoto et al., 29 Nov 2025).

2. Microscopic Hamiltonians and momentum-space form factors

A minimal phenomenological description of exchange-driven altermagnetism is

$T$2

with $T$3. In this form, the spin splitting $T$4 is nonrelativistic and does not require spin-orbit coupling. The same framework generalizes group-theoretically by treating the exchange field $T$5 as an axial vector odd under $T$6 and $T$7 separately but even under $T$8, so the allowed couplings are $T$9-even bilinears of $PT$0 consistent with the magnetic point group (Okamoto et al., 29 Nov 2025).

For chiral metallic dichalcogenides TM$PT$1X$PT$2, a low-energy description is written as

$PT$3

where $PT$4 is the spin-independent band Hamiltonian, $PT$5 is atomic SOC, and $PT$6 is the staggered exchange field in sublattice space. In this class, SOC in the nonmagnetic chiral phase produces persistent spin textures, whereas low-temperature antiferromagnetic order overlays an altermagnetic sign-changing spin splitting whose detailed form depends sensitively on the Néel-vector orientation. For $PT$7, the leading nonrelativistic splitting in NiTa$PT$8S$PT$9 transforms like a $M=0$0-wave multipole, $M=0$1 (Tenzin et al., 1 Aug 2025).

The same multipolar logic appears in other chiral altermagnetic platforms. In K[Co(HCOO)$M=0$2], each spin channel is described near in-plane wavevector $M=0$3 by

$M=0$4

with $M=0$5. The $M=0$6-wave structure fixes the sign alternation of the spin splitting, while mirror-related left- and right-handed enantiomers reverse the sign of $M=0$7 and therefore the spin ordering of hinge states and anomalous responses (Xie et al., 18 Aug 2025).

In hexagonal altermagnets such as CrSb and MnTe, the momentum-space splitting likewise follows high-order angular form factors. CrSb and MnTe exhibit a six-lobed “$M=0$8-wave” pattern of $M=0$9 in the Brillouin zone, whereas the phonon angular momentum later discussed below can display an $_3$0-wave texture. The distinction is important: the symmetry of electronic spin splitting, magnon chirality splitting, and phonon angular momentum need not be identical, even when they are symmetry-linked within the same crystal (Consiglio et al., 6 Jul 2026, Kravchuk et al., 7 Apr 2025).

3. Chiral magnons and other collective spin excitations

The magnetic excitation spectrum is the sector in which chiral altermagnetism is most directly resolved. In $_3$1-MnTe, the minimal linear-spin-wave Hamiltonian yields two magnon branches

$_3$2

with chirality splitting

$_3$3

Here the splitting originates from the difference of tenth- and eleventh-nearest-neighbor symmetric exchanges, not from Dzyaloshinskii–Moriya terms. Inelastic neutron scattering on $_3$4-MnTe directly resolved a double peak off the nodal planes, with a splitting up to $_3$5 meV and a six-lobed $_3$6-wave contour in constant-energy slices (Liu et al., 2024).

Polarized inelastic neutron scattering subsequently established the handedness of these excitations and their switchability. In MnTe, the neutron chiral term $_3$7 changes sign between the two magnon modes, and field cooling in $_3$8 mT reverses the sign of $_3$9 for both branches. The reported chirality ratios were $_6$0 and $_6$1 on HYSPEC, and $_6$2 and $_6$3 on IN20, depending on whether the values were extracted from polarized inelastic or polarized diffraction measurements (Liu et al., 13 May 2026).

Circular-dichroism RIXS provided a complementary, mode-selective probe. In MnTe, the chiral altermagnon signal $_6$4 peaks at the magnon energy and follows the expected $_6$5-wave momentum dependence: it is near zero close to the nodal direction, maximal away from the node, and vanishes at the high-symmetry $_6$6 point where the two chiral branches become degenerate (Jost et al., 29 Jan 2025).

Theoretical work has refined this picture for both easy-axial and easy-planar $_6$7-wave systems. In easy-axial CrSb, the magnon splitting retains the nonrelativistic $_6$8-wave form and each branch carries a momentum-independent magnetic moment $_6$9. In easy-planar MnTe, by contrast, the branch magnetic moment becomes momentum-dependent, and the directly observable splitting parameter

$_3$0

restores a $_3$1-wave characterization even when the raw energy splitting alone does not (Kravchuk et al., 7 Apr 2025).

Chiral altermagnetic magnons also admit forms of controllability absent in conventional antiferromagnets. Dipole-dipole interactions can strongly hybridize opposite-chirality exchange magnons in a square-lattice altermagnet, producing avoided crossings with $_3$2–0.2 and anticrossing gaps $_3$3–20 GHz in the exchange-magnon regime. The coupling is highly anisotropic and maximal in the Damon–Eshbach geometry (Jin et al., 24 May 2025). In domain walls, bound chiral modes become gapless and move into the microwave band; for Cr$_3$4Te$_3$5O, low-$_3$6 bound states occur at a few GHz with splittings of several $_3$7s of MHz, and their dispersion depends strongly on the wall angle $_3$8 relative to the crystal axes (Zeng et al., 4 Jan 2026). A distinct control route exploits Rashba SOC in a two-sublattice $_3$9-wave model: the sign of $_6$0 can be reversed at fixed $_6$1, defining altermagnetism-dominated and SOC-dominated chirality regions separated by $_6$2 (Li et al., 26 Aug 2025).

Optical probes have been proposed to access not only magnon dispersions but also magnon quantum geometry. In a canting field, $_6$3-wave altermagnets develop nontrivial Berry curvature and quantum metric textures; bicircular Raman scattering then isolates the second-order light–magnon coupling and produces a two-magnon peak whose amplitude oscillates as $_6$4, providing an optical discriminator between altermagnets and ordinary antiferromagnets even when the magnon topology is trivial (Yuan et al., 4 Aug 2025).

4. Chiral phonons and spin-lattice amplification

The phonon sector has recently become central to the concept of chiral altermagnetism. Chiral phonons at wavevector $_6$5 carry orbital angular momentum $_6$6, and their magnetic moment obeys

$_6$7

In a proper-screw magnetic state, the spin texture

$_6$8

generates a pseudoscalar helicity $_6$9, which breaks mirror symmetries and acts as a chiral order parameter. In this setting, a Dzyaloshinskii–Moriya-like spin–phonon term leads effectively to

$\chi=(S_i\times S_j)_z$0

so the same helicity that generates exchange spin splitting also enhances chiral-phonon coupling (Okamoto et al., 29 Nov 2025).

This mechanism was demonstrated in the crystallographically polar and chiral compound (Mn,Ni)$\chi=(S_i\times S_j)_z$1TeO$\chi=(S_i\times S_j)_z$2, which supports a paramagnetic state, a helical spin state with magnetic chirality, and a collinear spin state without magnetic chirality. O $\chi=(S_i\times S_j)_z$3-edge RIXS resolved two high-energy phonon peaks with opposite circular polarizations. When the helix sets in, the circular dichroism in their intensities grows strongly: the ratio $\chi=(S_i\times S_j)_z$4 for left- versus right-circularly polarized photons increases by $\chi=(S_i\times S_j)_z$5 compared with both the paramagnetic and collinear phases. The same study reports an altermagnetic band splitting $\chi=(S_i\times S_j)_z$6 meV, approximately an order of magnitude larger than the relativistic SOC splitting, consistent with the observed $\chi=(S_i\times S_j)_z$7 enhancement of chiral-phonon coupling. Magnetometry and neutron diffraction confirm proper-screw order with $\chi=(S_i\times S_j)_z$8 $\chi=(S_i\times S_j)_z$9 and zero net moment (Okamoto et al., 29 Nov 2025).

A complementary first-principles perspective comes from CrSb and MnTe. These prototypical altermagnets host locally chiral phonon modes with finite phonon angular momentum and a six-lobed $_2$0-wave texture around $_2$1 or $_2$2. The lattice chirality is carried almost entirely by the pnictogen or chalcogen sublattice, while the momentum-dependent spin splitting originates from the transition-metal sublattice. In pristine P6$_2$3/mmc crystals, inversion and $_2$4 enforce cancellation between symmetry-related sublayers, so the total valley phonon angular momentum vanishes despite local circular motion. Isoelectronic symmetry lowering by chemical substitution—As for Sb in CrSb, or Se for Te in MnTe—removes that cancellation, producing finite valley chirality with $_2$5 while preserving altermagnetic band splitting (Consiglio et al., 6 Jul 2026).

The electron–phonon coupling in this setting is explicitly momentum dependent,

$_2$6

and frozen-phonon calculations show band repulsion and hybridization gaps $_2$7 with $_2$8–2 eV/\AA. A notable implication is that chiral lattice motion and altermagnetic spin splitting can arise on different atomic sublattices of the same crystal, yet still couple selectively in momentum space (Consiglio et al., 6 Jul 2026).

5. Spin transport, topological responses, and switching

Chiral altermagnets have become a platform for charge-to-spin conversion and for topological transport channels whose control variable is chirality rather than magnetization. In metallic chiral crystals TM$_2$9X$T$00, the nonmagnetic phase exhibits persistent spin textures covering the full Fermi surface; around $T$01 and $T$02, symmetry forces the SOC field to lie strictly along $T$03, suppressing Dyakonov–Perel dephasing and favoring long spin lifetimes. In NiTa$T$04S$T$05, the calculated Rashba–Edelstein susceptibility satisfies $T$06 near the Fermi level. Upon entering the altermagnetic phase, the response tensor becomes a sensitive probe of the Néel-vector orientation, with additional $T$07-odd components appearing when the Néel vector lies in the plane (Tenzin et al., 1 Aug 2025).

In noncollinear chiral altermagnets, chirality enables spin textures and transport responses even without relying on SOC. For Mn$T$08IrSi, Landau analysis allows both inversion-odd dipolar and inversion-even quadrupolar multipoles. The resulting effective spin texture combines a hedgehog component $T$09 with a quadrupole component, and first-principles calculations yield spin Hall conductivity of order $T$10 and Edelstein susceptibility of order $T$11. Both effects persist with and without SOC, identifying them as exchange-driven signatures of chiral noncollinear altermagnetism rather than Rashba-type responses (Hu et al., 2024).

A more device-oriented realization is the RuO$T$12/ferromagnet/Pt trilayer, where field-free perpendicular switching is driven by chiral dual spin currents. There the chirality vector

$T$13

is invariant under time reversal and determines switching polarity. The intrinsic $T$14-wave spin splitting of RuO$T$15 produces an $T$16-polarized spin component, and the noncollinear spin currents from RuO$T$17 and Pt generate a helical texture in the ferromagnet, equivalent to an effective in-plane exchange field. Anomalous Hall loops show a horizontal shift $T$18 mT at $T$19, unchanged when the current polarity is reversed; pulse-current switching reaches a switching ratio of $T$20 at $T$21 A/m$T$22 (Sun et al., 30 Dec 2025).

Chiral magnon dynamics can themselves drive Hall transport. Density-matrix perturbation theory gives

$T$23

and for a circular magnon mode in the $T$24-plane one obtains

$T$25

This “magnon-driven anomalous Hall effect” is symmetry-distinct from the equilibrium anomalous Hall effect and can remain finite in an altermagnet such as CrSb even when the static Hall response is forbidden (Liu et al., 20 Mar 2026).

Topological transport provides a further extension. A two-sublattice altermagnetic model with valley topology supports a helical spin-valley-momentum-locked phase with composite spin-valley Chern number $T$26, robust against nonmagnetic and long-range magnetic disorder, and a gate-induced chiral phase with $T$27, robust against all disorder types. First-principles calculations identify monolayer V$T$28STeO and VO-family compounds as candidate materials for this electrically switchable helical–chiral conversion (Chen et al., 6 Mar 2026). In a distinct three-dimensional route, K[Co(HCOO)$T$29] realizes a chiral second-order topological insulator with altermagnetic $T$30-wave spin splitting, alternating spin-up and spin-down hinge modes on hexagonal nanotubes, and sign-reversible anomalous Hall and magneto-optical responses between left- and right-handed enantiomers; the reported Kerr rotation reaches $T$31 and Faraday rotation $T$32 deg/cm (Xie et al., 18 Aug 2025). On the magnonic side, bilayer V$T$33WS$T$34 exhibits a magnonic quantum spin Hall effect with spin Chern number $T$35, helical edge states, and a momentum-resolved thermal Hall conductivity $T$36 with a $T$37-wave pattern (Yuan et al., 29 Jan 2026).

6. Materials platforms, design principles, and open problems

The diversity of material realizations already spans chiral metals, hexagonal antiferromagnets, rutiles, metal–organic frameworks, and bilayers. The following examples capture the present range.

System	Symmetry or order emphasized	Reported chiral-altermagnetic phenomenon
MnTe	$T$38-wave altermagnet; easy-planar in several analyses	chiral magnon splitting, switchable magnon chirality, locally chiral phonons (Liu et al., 2024)
CrSb	prototypical altermagnet with six-lobed spin splitting	locally chiral $T$39-wave phonons; momentum-dependent electron–phonon coupling (Consiglio et al., 6 Jul 2026)
NiTa$T$40S$T$41, NiNb$T$42S$T$43	chiral space group P6$T$4422	persistent spin textures and charge-to-spin conversion in chiral altermagnets (Tenzin et al., 1 Aug 2025)
RuO$T$45 trilayers	$T$46-wave altermagnet in a heterostructure	field-free switching by chiral dual spin currents (Sun et al., 30 Dec 2025)
K[Co(HCOO)$T$47]	chiral MOF, $T$48-wave splitting, SOTI	spin-polarized hinge modes and sign-reversible AHE/MOKE (Xie et al., 18 Aug 2025)

Several design rules recur across these studies. For spin-lattice functionality, the explicit recipe is to break $T$49 and $T$50 with a staggered axial-vector order parameter, preserve the symmetry channel that permits $T$51 coupling, and co-design phonon branches with nonzero $T$52 so that $T$53 can couple to the chiral order parameter (Okamoto et al., 29 Nov 2025). For large magnon chirality splitting in insulating altermagnets, rutile CuF$T$54 suggests a complementary exchange-engineering rule: use non-symmorphic-plus-time-reversal symmetry between sublattices, favor linear super-superexchange paths such as Cu–F$T$55F–Cu with strong $T$56-overlap, align Cu $T$57 and F $T$58 levels to minimize $T$59, and suppress competing long-range paths. In that case the difference $T$60 reaches $T$61 meV and produces a predicted maximum chiral magnon splitting of $T$62 meV (Ho et al., 22 Apr 2026).

The main open questions remain sharply defined in the literature. One concerns terminology and scope: some works reserve altermagnetism for compensated orders tied to specific $T$63-related symmetry constructions, while others extend the language to chiral noncollinear and proper-screw orders that generate analogous spin splitting or chirality-selective couplings. Another concerns experimental reach: bulk chiral splitting often lies in the THz regime, motivating the use of domain-wall modes, microwave switching schemes, and phase-sensitive optical probes. Further unresolved directions include direct branch-resolved measurements of magnon polarization, the effect of interfacial Rashba fields in heterostructures, the optimization of domain imbalance and domain-wall orientation control, and the search for additional chiral space groups where altermagnetism coexists with noncollinear order, superconductivity, or second-order topology (Zeng et al., 4 Jan 2026, Tenzin et al., 1 Aug 2025, Liu et al., 13 May 2026).

Taken together, the recent literature establishes chiral altermagnets as a symmetry-based framework rather than a single materials subclass. Their hallmark is that chirality and staggered exchange jointly reorganize quasiparticle spectra: electronic bands acquire sign-changing multipolar splitting, magnons become chirality-resolved and switchable, phonons inherit or amplify handedness through exchange coupling, and transport coefficients become programmable by structural handedness, valley selectivity, or coherent spin precession. This suggests that future classification of altermagnetic matter will likely proceed not only by magnetic point group, but also by how lattice chirality, magnetic chirality, and quasiparticle chirality are intertwined.