Inversion-Asymmetric AFMs

• Inversion-asymmetric AFMs are antiferromagnetic systems lacking pure inversion symmetry, leading to unique spin responses such as NSOT and odd-parity spin splitting.
• They can be globally noncentrosymmetric, structurally centrosymmetric with broken magnetic inversion, or locally asymmetric within PT-symmetric configurations, each enabling distinct transport phenomena.
• Research employs theoretical models and semiclassical analysis to uncover contributions from mechanisms like Rashba-like effects, Berry-curvature-driven responses, and asymmetric impurity scattering.

Searching arXiv for recent and directly relevant papers on inversion-asymmetric antiferromagnets and closely related AFM symmetry/transport mechanisms. Inversion-asymmetric antiferromagnets (AFMs) are antiferromagnetic states in which inversion symmetry is absent in the relevant magnetic or local crystal environment, so that the ordered phase lacks a symmetry operation that would restore the antiferromagnetic pattern under spatial inversion. Across current literature, this notion appears in several closely related forms: globally noncentrosymmetric crystals with AFM order; structurally centrosymmetric crystals whose magnetic order breaks inversion in the magnetic space group; and $\mathcal{PT}$-symmetric collinear AFMs with locally inversion-asymmetric magnetic sublattices. In each case, the absence of pure inversion symmetry enables responses forbidden in inversion-symmetric settings, including Néel spin-orbit torque (NSOT), odd-parity spin splitting, nonreciprocal spin transport, Berry-curvature-driven Hall effects, and symmetry-required surface magnetization or hinge-state structures (Sarkar et al., 20 Apr 2026).

1. Symmetry definitions and forms of inversion asymmetry

In collinear bipartite AFMs, the local moments satisfy

$\mathbf{M}_A=-\mathbf{M}_B,$

so the total magnetization vanishes. Many AFMs of current interest preserve combined space-time inversion symmetry $\mathcal{PT}$, which maps the two magnetic sublattices into each other and guarantees Kramers-like double degeneracy of Bloch states at each $\mathbf{k}$ (Sarkar et al., 20 Apr 2026). In such systems, inversion asymmetry often does not mean the absence of $\mathcal{PT}$, but rather the absence of pure $\mathcal{P}$ as a symmetry of the magnetic state or of the local environment.

A central distinction is between global and local inversion asymmetry. In tetragonal CuMnAs, the global crystal can be inversion symmetric, but the magnetic structure breaks pure $\mathcal{P}$ while preserving $\mathcal{PT}$; each Mn sublattice feels a Rashba-like local inversion asymmetry with opposite sign on $A$ and $B$ (Sarkar et al., 20 Apr 2026). The same logic appears in the honeycomb AFM model with zero spin splitting, which is globally inversion symmetric in the structural sense but locally inversion-asymmetric in the magnetic sense because the two sublattices experience opposite exchange fields $\mathbf{M}_A=-\mathbf{M}_B,$0 (Zhang et al., 20 Jun 2026). This locally inversion-asymmetric, globally $\mathbf{M}_A=-\mathbf{M}_B,$1-symmetric setting permits spin–pseudospin coupling without lifting spin degeneracy.

A second form of inversion asymmetry is order-driven and magnetic rather than structural. In cubic Mn$\mathbf{M}_A=-\mathbf{M}_B,$2Ge, the parent crystal is centrosymmetric with space group $\mathbf{M}_A=-\mathbf{M}_B,$3, but the non-collinear, non-coplanar magnetic order breaks inversion in the magnetic space group and breaks $\mathbf{M}_A=-\mathbf{M}_B,$4, enabling Berry-curvature-driven anomalous Hall response despite negligible net magnetization (Hu et al., 10 Feb 2026). A related formalization appears in centrosymmetric nonsymmorphic crystals with multiplicity-2 Wyckoff positions, where mixed-parity irreducible representations at ordering vector $\mathbf{M}_A=-\mathbf{M}_B,$5 permit inversion-asymmetric antiferromagnetic order as an itinerant instability; the resulting coplanar AFM is the inversion-asymmetric phase in that framework (Lee et al., 23 Feb 2025).

This literature therefore uses “inversion-asymmetric AFM” in three precise senses: a globally noncentrosymmetric AFM; a magnetically inversion-broken AFM in a structurally centrosymmetric crystal; or a $\mathbf{M}_A=-\mathbf{M}_B,$6-symmetric AFM with sublattice-resolved local inversion asymmetry. These forms are symmetry-distinct, but all support response channels absent in inversion-symmetric antiferromagnets.

2. Collinear inversion-asymmetric AFMs and Néel spin-orbit torque

In collinear $\mathbf{M}_A=-\mathbf{M}_B,$7-symmetric AFMs, a current-induced spin polarization is written as

$\mathbf{M}_A=-\mathbf{M}_B,$8

Only $\mathbf{M}_A=-\mathbf{M}_B,$9-odd spin susceptibilities generate a staggered spin polarization,

$\mathcal{PT}$0

appropriate for NSOT, because a $\mathcal{PT}$1-odd susceptibility satisfies $\mathcal{PT}$2 whereas a $\mathcal{PT}$3-even susceptibility gives a uniform response (Sarkar et al., 20 Apr 2026). In the conventional picture for CuMnAs and Mn$\mathcal{PT}$4Au, the relevant channel is the Drude-like Edelstein response produced by local inversion asymmetry on the magnetic sublattices.

The current-induced spin polarization is decomposed semiclassically as

$\mathcal{PT}$5

with $\mathcal{PT}$6 and $\mathcal{PT}$7. The standard channels are the Drude term $\mathcal{PT}$8, the intrinsic anomalous term $\mathcal{PT}$9, the side-jump term $\mathbf{k}$0, and the conventional skew term $\mathbf{k}$1. Among these, only the Drude susceptibility is $\mathbf{k}$2-odd; the intrinsic anomalous, side-jump, and conventional skew channels are $\mathbf{k}$3-even and therefore do not directly contribute to NSOT in collinear $\mathbf{k}$4-symmetric AFMs (Sarkar et al., 20 Apr 2026).

A new mechanism extends this picture. In tetragonal CuMnAs, asymmetric impurity scattering combined with the anomalous spin polarizability (ASP)

$\mathbf{k}$5

produces an additional $\mathbf{k}$6-odd spin susceptibility $\mathbf{k}$7. The corresponding contribution,

$\mathbf{k}$8

is extrinsic but band-geometry-driven: the antisymmetric third-order scattering rate is Berry-curvature-dependent, while the disorder-induced spin correction is proportional to ASP. Their product is $\mathbf{k}$9-odd and therefore yields a staggered spin polarization (Sarkar et al., 20 Apr 2026).

The CuMnAs minimal model, [ \mathcal{H}= -2t\cos\frac{k_x}{2}\cos\frac{k_y}{2}\,\tau_x\sigma_0 -t'(\cos k_x+\cos k_y)\tau_0\sigma_0 +\lambda\,\tau_z(\sigma_y\sin k_x-\sigma_x\sin k_y)