PT-Symmetric AFMs: Quantum Spintronics

• PT-symmetric antiferromagnets are magnetic materials where broken parity and time reversal create spin-degenerate band structures via combined PT symmetry.
• They exhibit dissipationless spin currents and nonreciprocal transport enabled by spin-orbit coupling and symmetry-imposed selection rules.
• Quantum geometry in these systems drives magneto-optical effects, nonlinear Hall responses, and tunable phonon propagation, all beneficial for spintronic applications.

A PT-symmetric antiferromagnet (PT-AFM) is a magnetic material in which both space inversion (parity, P) and time reversal (T) are individually broken by the magnetic order, yet their product—parity-time symmetry (PT)—remains an exact symmetry of the system. This symmetry class enforces distinctive constraints on the electronic, magnetic, and lattice properties, leading to emergent responses such as dissipationless transport, nonreciprocal phenomena, quantum-geometry-driven effects, and symmetry-selective diffraction patterns. PT-AFMs play a central role in modern spintronics and quantum material research due to their robust high-temperature phases, strongly anisotropic response tensors, and compatibility with device architectures free from net magnetization or stray fields.

1. Symmetry Constraints, Classification, and Band Structure

PT symmetry acts as a combined antiunitary operation, preserving the Bloch Hamiltonian at each momentum $\mathbf{k}$. In a PT-symmetric AFM, every Bloch state $|\psi_{n\mathbf{k}},\sigma\rangle$ comes with a degenerate partner of opposite spin at the same $\mathbf{k}$, guaranteeing $E_{n\mathbf{k}\uparrow}=E_{n\mathbf{k}\downarrow}$. This twofold degeneracy, analogous to Kramers degeneracy in systems with both T and P, is enforced for all $\mathbf{k}$. The direct consequence is a spin-degenerate band structure and the vanishing of all band-geometric quantities odd under PT, including the Berry curvature at every $\mathbf{k}$ (Zhu et al., 5 Oct 2025, Bhowmick et al., 25 Sep 2025).

Magnetic point group (MPG) analysis partitions AFMs into symmetry classes. PT-AFMs occur in MPGs containing the anti-inversion $1'$, such as $2'/m$, $m'mm$, and $4/m'm'm'$. These classes prohibit net ferromagnetism or piezomagnetism but allow linear magnetoelectric effects (Lovesey et al., 26 Jul 2024). Within this symmetry regime, 29 PT-symmetric MPGs are further subdivided by additional elements (fractional translations, rotational symmetries), controlling which physical response tensors are allowed and which vanish identically (Zhu et al., 5 Oct 2025, Wu et al., 24 May 2025).

2. Spin-Orbit Coupling and Longitudinal Spin Currents

Although PT symmetry enforces spin-degenerate bands, spin current responses that are even under T and PT can survive if enabled by spin-orbit coupling (SOC) and proper MPG orientation. The linear response (Kubo) formula for the longitudinal spin conductivity

$$\sigma^{s,k}_{ii} = -\frac{e}{\hbar} \sum_{n\neq m} \int\frac{d\mathbf{k}}{(2\pi)^3} \frac{f_{n\mathbf{k}}-f_{m\mathbf{k}}}{(E_{m\mathbf{k}}-E_{n\mathbf{k}})^2} \;\Im\left\langle n\mathbf{k}|J^s_i|m\mathbf{k}\right\rangle \left\langle m\mathbf{k}|v_i|n\mathbf{k}\right\rangle$$

shows that SOC mixes the PT doublets, allowing a finite, T-even longitudinal spin conductivity even within spin-degenerate PT-AFMs (Zhu et al., 5 Oct 2025). First-principles density-functional theory (DFT) calculations confirm that materials such as L1$_0$–MnPt and Mn$_2$Au display sizable longitudinal spin conductivities ($\sigma^{s,z}_{xx}=\,-\,\sigma^{s,z}_{yy}=276$ and $113\,\hbar/2e\,\Omega^{-1}\mathrm{cm}^{-1}$ respectively), comparable to PT-broken systems.

The generation and detection of such spin currents is highly anisotropic with respect to the Néel vector, giving an additional mechanism for phase and device control in spintronic architectures, with characteristic detection protocols (e.g., TMR measurements, AFM/FM bilayer spin-torque resonance, spin Seebeck detection) (Zhu et al., 5 Oct 2025).

3. Nonreciprocal and Nonlinear Transport Phenomena

PT symmetry enables odd-parity corrections to otherwise centrosymmetric band dispersions, resulting in asymmetric $E(\mathbf{k})$ and allowing for nonreciprocal electric and thermal responses. These include:

• Nonreciprocal conductivity: Third-order tensors $\chi_{ijk}$ permit currents quadratic in field, $J_i = \chi_{ijk}E_jE_k$, with components selected by MPG symmetry (Wu et al., 24 May 2025, Watanabe et al., 23 Mar 2024).
• Photocurrent generation: PT-AFMs host the gyration current ($\sigma^\text{gyro}_{a;xy}$), a P-odd, T-odd second-order photocurrent unique to the class, allowing detection of antiferromagnetic order without net magnetization (Watanabe et al., 23 Mar 2024).
• Anomalous skew-scattering nonlinear Hall (ASN) effect: In clean PT-AFM metals, a nonlinear Hall response arises purely from cooperative skew scattering and Berry curvature, vanishing for individual contributions but surviving as a PT-even effect. ASN also uniquely generates circular-polarization–sensitive (chiral) photocurrents in the THz regime (Ma et al., 2022).

The presence of asymmetric band dispersions, observed in AI-predicted AFM1 (odd-parity) materials, is a direct result of the PT-induced symmetry constraints on the Hamiltonian, as confirmed by DFT and symmetry-based classification (Wu et al., 24 May 2025).

4. Quantum Geometry: Metric-Induced Magneto-Optical and Noise Effects

In PT-symmetric AFMs, all Berry curvature–driven effects are symmetry-forbidden, but the real part of the quantum geometric tensor—the quantum metric $g_{ab}(\mathbf{k})$—remains finite and governs phenomena previously thought to be forbidden, such as:

• Magneto-optical effects (MOEs): Quantum-metric–induced finite off-diagonal optical conductivities $\sigma_{xy}^g(\omega)$ give rise to observable Kerr and Faraday rotations, with demonstrated magnitudes in CoAgPO$_4$ and strained bilayer CrI$_3$ of up to tens of milliradians (Li et al., 6 Mar 2025).
• Nonlinear quantum-metric thermal noise: Intrinsic, relaxation-time–independent noise scaling as $E^2$ directly probes the quantum metric, with peak signatures at Fermi surface energy and vanishing of Berry curvature–related contributions, as shown in CuMnAs (Bhowmick et al., 25 Sep 2025).

These effects are accessible in device and spectroscopic setups by tuning the symmetry via strain or field, providing both a basic physical probe and a path toward exploiting quantum geometry in functional materials.

5. Nonreciprocal Phonons and Spin-Lattice Effects

PT-AFMs enable macroscopic nonreciprocal acoustic phonon propagation without external fields or net magnetization. Flexo-viscosity ($\tau^H$) and flexo-torque ($\tau^M$) terms in the elastic theory, derived from the molecular Berry curvature of electronic ground states under lattice deformation with SOC, yield intrinsic differences in sound velocity for oppositely directed propagation (Ren et al., 12 Jul 2024). These effects manifest as $k$-odd corrections in the phonon dispersion that are controlled by the Néel vector and can be enhanced or electrically tuned via Rashba spin-orbit fields, suggesting electrically switchable phononic functionalities.

6. Experimental Signatures, Candidate Materials, and Emergent Multipoles

PT-symmetric AFMs manifest in a broad array of crystal classes and are realized in established compounds, e.g., Cr$_2$O$_3$, CuMnAs, Mn$_2$Au, and the low-dimensional compound Cu$_2$(MoO$_4$)(SeO$_3$) (Lovesey et al., 26 Jul 2024). Key experimental fingerprints include:

• Selection rules in scattering experiments: Linear magnetoelectric effect, twofold azimuthal oscillations, and null circular dichroism in x-ray and neutron diffraction, dictated by the real-valued scattering tensors uniquely enforced by PT symmetry.
• Multipole order: Strong contributions from magnetic quadrupoles (T$^2_Q$), Dirac multipoles (anapoles G$^1_Q$), and purely magnetic forbidden Bragg peaks, indicating high-rank order and suppression of trivial interference (Lovesey et al., 26 Jul 2024).
• Hidden Zeeman-type spin splitting (HZSS): PT symmetry supports layer- and sublattice-resolved spin polarization, spatially segregated yet degenerate, which can be unmasked by an out-of-plane field, as illustrated in layered MnSe (Sheoran et al., 2023).

AI-driven screening of materials databases, incorporating symmetry filters and DFT workflows, has identified dozens of verified and candidate PT-AFM1 compounds with robust ground-state energy preference, broadening the available materials palette for quantum and spintronic devices (Wu et al., 24 May 2025).

7. Theoretical Implications and Spintronic Applications

The physical responses enabled by PT symmetry—dissipationless and anisotropic spin currents, quantum-metric–driven optics and noise, electrically switchable transport, and topological effects—provide an expanded functional platform for spintronics and optoelectronics. Key advantages include the absence of net magnetization or stray fields, efficient current-induced Néel vector switching, high-frequency dynamics, and the ability to probe or control order via symmetry-selective transport or spectroscopy (Zhu et al., 5 Oct 2025, Watanabe et al., 23 Mar 2024).

A plausible implication is that nearly any PT-symmetric AFM with broken enough spatial symmetries and strong SOC can serve as an efficient and tunable spin-current source, antiferromagnetic memory element, or platform for quantum-geometry–based optoelectronic control. The symmetry-imposed selection rules further allow for clear separation of intrinsic and extrinsic effects, making PT-AFMs particularly attractive for fundamental paper as well as device integration.