---
title: Inversion-Asymmetric AFMs
url: https://www.emergentmind.com/topics/inversion-asymmetric-antiferromagnets-afms
type: topic
---

# Inversion-Asymmetric AFMs

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 [2604.18097].

## 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 \(\mathbf{k}\) [2604.18097]. 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 \(B\) [2604.18097]. 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 \(\pm\Lambda\) [2606.21860]. This locally inversion-asymmetric, globally \(\mathcal{PT}\)-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\(_3\)Ge, the parent crystal is centrosymmetric with space group \(Pm\bar{3}m\), but the non-collinear, non-coplanar magnetic order breaks inversion in the magnetic space group and breaks \(\mathcal{PT}\), enabling Berry-curvature-driven anomalous Hall response despite negligible net magnetization [2602.09479]. A related formalization appears in centrosymmetric nonsymmorphic crystals with multiplicity-2 Wyckoff positions, where mixed-parity irreducible representations at ordering vector \(\mathbf{Q}\) permit inversion-asymmetric antiferromagnetic order as an itinerant instability; the resulting coplanar AFM is the inversion-asymmetric phase in that framework [2502.16417].

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 \(\mathcal{PT}\)-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 \(\mathcal{PT}\)-symmetric AFMs, a current-induced spin polarization is written as
\[
\delta S^\nu = \chi^{\nu;b} E_b.
\]
Only \(\mathcal{PT}\)-odd spin susceptibilities generate a staggered spin polarization,
\[
\delta\mathbf{S}_N=\delta\mathbf{S}_A-\delta\mathbf{S}_B,
\]
appropriate for NSOT, because a \(\mathcal{PT}\)-odd susceptibility satisfies \(\chi_A^{\nu;b}=-\chi_B^{\nu;b}\) whereas a \(\mathcal{PT}\)-even susceptibility gives a uniform response [2604.18097]. In the conventional picture for CuMnAs and Mn\(_2\)Au, 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
\[
\delta S^\nu=\sum_l s_l^\nu f_l,
\]
with \(s_l^\nu=s_l^{\nu,0}+s_l^{\nu,\mathrm{anm}}+s_l^{\nu,\mathrm{sct}}\) and \(f_l=f^0+f^{\mathrm{in}}+f^{\mathrm{sj}}+f^{\mathrm{sk3}}\). The standard channels are the Drude term \(s^{\nu,0}f^{\mathrm{in}}\), the intrinsic anomalous term \(s^{\nu,\mathrm{anm}}f^0\), the side-jump term \(s^{\nu,\mathrm{sct}}f^{\mathrm{in}}+s^{\nu,0}f^{\mathrm{sj}}\), and the conventional skew term \(s^{\nu,0}f^{\mathrm{sk3}}\). Among these, only the Drude susceptibility is \(\mathcal{PT}\)-odd; the intrinsic anomalous, side-jump, and conventional skew channels are \(\mathcal{PT}\)-even and therefore do not directly contribute to NSOT in collinear \(\mathcal{PT}\)-symmetric AFMs [2604.18097].

A new mechanism extends this picture. In tetragonal CuMnAs, asymmetric impurity scattering combined with the anomalous spin polarizability (ASP)
\[
\gamma_{n\mathbf{k}}^{\nu,b}=-2\hbar^2\,\mathrm{Im}\sum_{n'\neq n}\frac{s^\nu_{nn'}(\mathbf{k})\,v^b_{n'n}(\mathbf{k})}{(\varepsilon_{n\mathbf{k}}-\varepsilon_{n'\mathbf{k}})^2}
\]
produces an additional \(\mathcal{PT}\)-odd spin susceptibility \(\chi_{\rm AS}^{\nu;b}\). The corresponding contribution,
\[
\delta S^\nu_{\rm AS}=\sum_{n\mathbf{k}} s^{\nu,\mathrm{sct}}_{n\mathbf{k}}\,f^{\mathrm{sk3}}_{n\mathbf{k}},
\]
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 \(\mathcal{PT}\)-odd and therefore yields a staggered spin polarization [2604.18097].

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)

Source: https://www.emergentmind.com/topics/inversion-asymmetric-antiferromagnets-afms