Quasi-Altermagnetism in Complex Magnetic Systems

• Quasi-altermagnetism is a phenomenon describing magnetic systems with nearly zero net magnetization and non-relativistic, momentum-dependent spin splitting under approximate symmetry conditions.
• It arises in systems with generalized, non-crystalline, or defect-induced symmetry breaking, which leads to significant spin-split electronic bands while maintaining compensated magnetism.
• The concept integrates various microscopic routes—including orbital ordering and lattice distortions—and underpins unique transport signatures and anomalous Hall effects.

Quasi-altermagnetism denotes a family of closely related magnetic situations in which the defining phenomenology of altermagnetism—zero or nearly zero net magnetization together with non-relativistic, momentum-dependent spin splitting—survives outside the strict setting of ideal crystalline altermagnets. Current usage is not uniform. In different works, the term refers to approximate altermagnets in correlated oxychalcogenides, quasicrystalline altermagnets protected by non-crystallographic symmetries, amorphous or non-crystalline orbital altermagnets, defect-perturbed MnTe with nearly compensated magnetization, and sliding bilayers with type-IV non-relativistic spin splitting at the Brillouin-zone center (Kaushal et al., 2024, Chen et al., 24 Jul 2025, d'Ornellas et al., 11 Apr 2025, Devaraj et al., 27 Aug 2025, Dhori et al., 18 Jun 2026). This suggests that quasi-altermagnetism is best understood as an umbrella term for altermagnetic phenomenology realized under approximate, generalized, or unconventional symmetry conditions.

1. Terminological scope

The literature uses “quasi-altermagnetism” in several distinct but overlapping senses. In correlated modified Lieb-lattice models for quasi-2D oxychalcogenides, it denotes cases where ideal altermagnetic symmetry is present only approximately because lattice distortions, spin–orbit coupling, disorder, and multi-orbital effects break the exact symmetry but leave a large, momentum-dependent spin splitting with approximately zero net magnetization (Kaushal et al., 2024). In quasicrystals, it denotes altermagnetic phases realized in aperiodic lattices with non-crystallographic rotational symmetries such as $C_8T$ and $C_{12}T$, giving $g$-wave and $i$-wave spin splitting (Chen et al., 24 Jul 2025). In amorphous systems, it denotes altermagnetic phenomenology without global crystal symmetry, stabilized instead by local spin–orbital order and a preserved local $C_4\mathcal{T}$ symmetry (d'Ornellas et al., 11 Apr 2025).

A further usage arises in defect and doping studies of MnTe. There, substitutional doping breaks the ideal altermagnetic symmetries, but the system still displays generic spin-split antiferromagnetic bands in momentum space together with nearly compensated magnetization; those states are explicitly called quasi-altermagnets (Devaraj et al., 27 Aug 2025). In sliding square-lattice bilayers, quasi-altermagnetism is introduced as a distinct subclass of compensated magnets with reversible type-IV non-relativistic spin splitting, where spin degeneracy at $\Gamma$ is lifted even without spin–orbit coupling and no valid opposite-spin sublattice connector remains in the spin-Laue group (Dhori et al., 18 Jun 2026). A different but related “quasi-” usage appears in spin–orbit-coupled altermagnets, where a uniaxial spin space-group quasi-symmetry suppresses the ferromagnetic spin moment while allowing a sizable anomalous Hall effect (Roig et al., 2024).

Usage	Defining feature	Representative paper
Approximate correlated altermagnet	Large momentum-dependent spin splitting with approximately zero net magnetization under realistic perturbations	(Kaushal et al., 2024)
Quasicrystalline altermagnet	$C_8T$ or $C_{12}T$ protected $g$-wave or $i$-wave splitting	(Chen et al., 24 Jul 2025)
Amorphous or non-crystalline altermagnet	Local orbital rotation replaces global crystal rotation	(d'Ornellas et al., 11 Apr 2025)
Defect-broken quasi-altermagnet	No symmetry connects up/down sublattices, but strong spin-split antiferromagnetic bands remain	(Devaraj et al., 27 Aug 2025)
Sliding coupled quasi-altermagnet	Type-IV NRSS with spin splitting at $C_{12}T$0 and switchable valley/spin polarity	(Dhori et al., 18 Jun 2026)
Quasi-symmetry-constrained altermagnet	Large AHE with strongly suppressed ferromagnetic spin moment	(Roig et al., 2024)

2. Symmetry principles

The shared structural core is the coexistence of compensated magnetization and spin-split spectra in the non-relativistic limit. In the modified Lieb-lattice Hubbard model, altermagnetism is identified by zero total magnetization,

$C_{12}T$1

finite staggered magnetization,

$C_{12}T$2

and spin-split electron bands with

$C_{12}T$3

almost everywhere in the Brillouin zone, but degenerate along $C_{12}T$4, yielding a characteristic $C_{12}T$5-like spin splitting (Kaushal et al., 2024). The symmetry condition is that opposite-spin sublattices are related by rotation or mirror but not by inversion or translation.

Quasicrystalline altermagnetism generalizes this logic from crystallographic $C_{12}T$6, $C_{12}T$7, and $C_{12}T$8 to non-crystallographic $C_{12}T$9 and $g$0. In the octagonal case,

$g$1

and the spin-resolved spectral functions satisfy

$g$2

which forces eight nodal directions; the dodecagonal case gives the analogous twelvefold structure (Chen et al., 24 Jul 2025). The classification of magnetism and altermagnetism in 2D quasicrystals sharpens this point: magnetic phases corresponding to 1D non-identity irreducible representations are generally altermagnetic, with the exception of those possessing parity-time symmetry (Shao et al., 21 Aug 2025).

In amorphous systems, global rotational symmetry of lattice positions is absent, but directional orbitals on each site still support a local combined symmetry $g$3. The ordered phase breaks both $g$4 and $g$5 but preserves $g$6, so the relevant “rotation” is orbital and local rather than crystallographic and global (d'Ornellas et al., 11 Apr 2025). In sliding square-lattice bilayers, quasi-altermagnetic states are characterized by an empty $g$7 sector in the spin-Laue group and by the absence of a valid opposite-spin sublattice connector; the consequence is type-IV NRSS, with spin splitting at $g$8 even without SOC (Dhori et al., 18 Jun 2026).

A distinct symmetry-based refinement concerns spin–orbit coupling. In realistic altermagnets, the anomalous Hall effect and the ferromagnetic spin moment share the same symmetry, yet their amplitudes can differ strongly. The SOC-enabled uniaxial spin space-group provides a quasi-symmetry that can forbid the SOC-linear coupling between $g$9 and $i$0, thereby suppressing the ferromagnetic spin moment even when a sizable AHE remains allowed (Roig et al., 2024).

3. Microscopic routes to quasi-altermagnetic behavior

One route is correlation-driven altermagnetism in realistic multi-sublattice Hubbard models. On the modified Lieb lattice, repulsive interactions stabilize spin-$i$1 altermagnetic Mott insulating ground states at fillings $i$2 and $i$3, and doping produces altermagnetic metals with $i$4-wave spin splitting and quasi-one-dimensional Fermi surfaces (Kaushal et al., 2024). This provides a direct microscopic template for quasi-altermagnetism in oxychalcogenides, where realistic perturbations convert ideal altermagnets into approximate ones.

A second route is spontaneous formation from orbital ordering. In a two-orbital square-lattice model with $i$5 and $i$6 orbitals, staggered antiferromagnetism and staggered orbital order coexist to produce a robust altermagnetic phase; the paper explicitly notes that a “quasi-altermagnetic” regime can be understood near phase boundaries, in fluctuation-dominated regions, or when spin splitting is present but not fully symmetry-protected (Leeb et al., 2023). A related itinerant route exploits the interplay between a Hubbard local repulsion and the presence of van Hove singularities. In that setting, altermagnetism is stable for a broad range of interactions and dopings, while weakened or strongly renormalized boundary regimes naturally suggest quasi-altermagnetic behavior (Giuli et al., 2024).

A third route is based on coincident Van Hove singularities enforced by non-symmorphic symmetry. In quasi-2D $i$7-Cl and related 2D space groups, coincident Van Hove singularities allow a new hopping interaction $i$8, which can drive weak-coupling instabilities including altermagnetism, nematicity, inter-band $i$9-wave superconductivity, and orbital altermagnetic order (Yu et al., 2024). This is a microscopic weak-coupling route to quasi-2D quasi-altermagnetism.

A fourth route replaces conventional crystal symmetry altogether. Quasicrystals support $C_4\mathcal{T}$0-wave and $C_4\mathcal{T}$1-wave altermagnetism through a real-space $C_4\mathcal{T}$2–$C_4\mathcal{T}$3-like spin–orbital model and self-consistent mean-field theory (Chen et al., 24 Jul 2025). Amorphous lattices support orbital altermagnetism via directional hopping matrices $C_4\mathcal{T}$4 and a Kugel–Khomskii-like interaction, leading to local spin–orbital order with altermagnetic spectral and transport signatures despite the absence of global crystal symmetry (d'Ornellas et al., 11 Apr 2025).

Further generalizations extend the concept beyond Landau order. In an exactly solvable $C_4\mathcal{T}$5 spin-orbital liquid, three distinct fractionalized altermagnets $C_4\mathcal{T}$6, $C_4\mathcal{T}$7, and $C_4\mathcal{T}$8 appear, and altermagnetic spin splitting is encoded in a momentum-dependent particle-hole asymmetry of fermionic parton bands (Neehus et al., 16 Apr 2025). In the Ising-Kondo lattice model with alternating next-nearest-neighbor hopping, numerically exact lattice Monte Carlo simulations reveal robust $C_4\mathcal{T}$9-wave AM-like phases in a correlated heavy-fermion setting; the model explicitly separates essential ingredients from idealizations, thereby clarifying how approximate or emergent quasi-altermagnetic behavior can arise in $\Gamma$0-electron systems (Zhao et al., 10 Jan 2026). A further unconventional mechanism is interstitial-electron altermagnetism in electrides, where Stoner instability acts on quasi-nucleus-free interstitial electrons rather than on atomic moments (Cheng et al., 27 Mar 2026).

4. Electronic structure, excitations, and transport

The electronic hallmark is spin splitting without uncompensated magnetization. In the modified Lieb-lattice Mott regime, spin-up and spin-down electron bands split almost everywhere in $\Gamma$1, except along $\Gamma$2, and the doped altermagnetic metal has cigar-shaped spin-up and spin-down hole pockets with quasi-one-dimensional character (Kaushal et al., 2024). The same work shows that the altermagnetic symmetry extends to collective excitations: sublattice-resolved dynamical spin structure factors exhibit an “altermagnetic splitting” of magnon bands, with spectra on the two sublattices related by a 90° rotation (Kaushal et al., 2024).

In quasicrystals, the absence of Bloch momentum is replaced by Fourier-projected spectral functions,

$\Gamma$3

and the spin difference $\Gamma$4 exhibits eightfold or twelvefold nodal patterns. The same symmetry appears in spin conductance measured in a double-tip STM geometry, where $\Gamma$5 changes sign under $\Gamma$6 or $\Gamma$7 and vanishes along symmetry-dictated directions (Chen et al., 24 Jul 2025).

Interaction-induced orbital altermagnetism yields a direct transport observable: the spin-splitter conductivity. In the AFM+OO coexistence phase, the longitudinal spin conductivity $\Gamma$8 is nonzero only when both antiferromagnetism and orbital order coexist, and the maximal spin splitter angle reaches $\Gamma$9 for a certain choice of parameters (Leeb et al., 2023). In amorphous orbital altermagnets, the total spectral function remains nearly isotropic while $C_8T$0 shows a $C_8T$1-symmetric $C_8T$2-wave-like pattern, and the total conductance is nearly isotropic while the spin-resolved conductance is strongly anisotropic (d'Ornellas et al., 11 Apr 2025).

Hall responses provide another diagnostic. In quasi-symmetry-constrained altermagnets, a sizable anomalous Hall effect can coexist with negligible ferromagnetic spin moment because the uniaxial spin space-group suppresses the SOC-linear $C_8T$3-$C_8T$4 coupling (Roig et al., 2024). Doped MnTe extends this point: pristine MnTe does not show anomalous Hall conductivity with out-of-plane magnetization, whereas suitable doping yields finite and varied AHC in both ideal altermagnets and quasi-altermagnets (Devaraj et al., 27 Aug 2025). In sliding coupled quasi-altermagnetic bilayers, AC$C_8T$5 and AC$C_8T$6 carry opposite Berry-curvature distributions and opposite-sign anomalous Hall conductivity, and interlayer sliding reverses the sign of the Hall response together with the spin-valley polarization (Dhori et al., 18 Jun 2026).

5. Representative platforms

A first materials class is quasi-2D oxychalcogenides with the “anti-CuO$C_8T$7” lattice structure. The modified Lieb lattice was proposed as the minimal 2D representation of materials such as La$C_8T$8O$C_8T$9Mn$C_{12}T$0Se$C_{12}T$1, KV$C_{12}T$2Se$C_{12}T$3O, and Rb$C_{12}T$4V$C_{12}T$5Te$C_{12}T$6O, and the theory connects its predictions to ARPES and neutron scattering signatures already discussed for these compounds (Kaushal et al., 2024). A second class consists of layered transition-metal oxides. In quasi-2D Ca$C_{12}T$7RuO$C_{12}T$8, the paper finds orbital-selective altermagnetism: $C_{12}T$9 orbitals are connected only by a roto-translation, whereas the quasi-two-dimensionality of the $g$0 bands allows an approximate mirror plane that strongly suppresses altermagnetism in that sector (Cuono et al., 2023). In YVO$g$1, altermagnetism is present in A-type, C-type, and G-type magnetic orders, with the Brillouin-zone symmetries and the strength of the non-relativistic spin splitting depending on the magnetic order and on the Coulomb repulsion $g$2 (Cuono et al., 2023).

A third class is quasicrystals and non-crystalline media. Octagonal and dodecagonal quasicrystals support $g$3-wave and $g$4-wave altermagnetism (Chen et al., 24 Jul 2025), while amorphous directional-orbital networks realize orbital altermagnetism without global crystal symmetry (d'Ornellas et al., 11 Apr 2025). A fourth class is defect- or stacking-engineered systems. Substitutionally doped MnTe exhibits ideal altermagnets and quasi-altermagnets across a large configuration space of spin space groups (Devaraj et al., 27 Aug 2025). Sliding Lieb-lattice bilayers based on Mn$g$5WS$g$6 and the Janus derivative Mn$g$7WS$g$8Se$g$9 realize altermagnetic and quasi-altermagnetic phases controlled by interlayer translation (Dhori et al., 18 Jun 2026). A fifth class is unconventional correlated or itinerant platforms, including $i$0-Cl near coincident Van Hove singularities (Yu et al., 2024), $i$1-electron systems described by the Ising-Kondo lattice model (Zhao et al., 10 Jan 2026), and 2D electrides such as monolayers Zr$i$2N and Ti$i$3N, where the magnetic carriers are interstitial electrons (Cheng et al., 27 Mar 2026).

6. Conceptual status and open questions

The term is not yet standardized. Several papers explicitly state that they do not themselves introduce “quasi-altermagnetism” but nonetheless clarify what such a regime might mean: interaction-induced altermagnetism from orbital ordering defines it as weakened, fluctuating, or partially symmetry-protected altermagnetic behavior near phase boundaries (Leeb et al., 2023); the amorphous-lattice work states that it essentially constructs what one might call a quasi-altermagnet (d'Ornellas et al., 11 Apr 2025); the interstitial-electron work notes that it does not explicitly use the phrase but naturally fits under a broader notion of quasi-altermagnetism (Cheng et al., 27 Mar 2026). By contrast, the sliding-bilayer study elevates quasi-altermagnetism to a distinct subclass with a precise spin-Laue classification and type-IV NRSS (Dhori et al., 18 Jun 2026), while the MnTe doping study uses it for defect-broken states with strong spin-split antiferromagnetic bands and nearly compensated magnetization (Devaraj et al., 27 Aug 2025).

Several open problems recur across these strands. In quasicrystals, the robustness of $i$4-protected nodal patterns to disorder, phason strain, and finite temperature remains open, as does the identification of realistic materials with the required orbital doublets and interaction scales (Chen et al., 24 Jul 2025). In amorphous systems, the microscopic origin of the Kugel–Khomskii-like interaction, finite-temperature stability in low dimensions, and the effect of disorder in local environments remain unresolved (d'Ornellas et al., 11 Apr 2025). In correlated lattice models, the interplay with superconductivity, multi-orbital extensions, and realistic perturbations beyond Hartree–Fock or small-cluster exact diagonalization remain active directions (Kaushal et al., 2024). In fractionalized altermagnets, confinement transitions, the role of spin–orbit coupling, and the experimental visibility of parton particle-hole asymmetry through gauge-invariant observables remain central issues (Neehus et al., 16 Apr 2025).

Taken together, these developments indicate that quasi-altermagnetism is not a single narrowly defined phase but a widening conceptual domain. It encompasses approximate, generalized, disorder-enabled, non-crystalline, fractionalized, and sliding-controlled realizations of compensated magnets with altermagnetic-like spin splitting. What unifies these cases is not one unique symmetry label, but the persistence of altermagnetic phenomenology—spin-split spectra, spin-polarized transport, and often vanishing or nearly vanishing net magnetization—after the ideal crystalline paradigm has been relaxed.