Domain Walls in Antiferromagnets

• Domain walls in antiferromagnets are extended solitonic textures that separate regions with different Néel order orientations, including Bloch, Néel, and chiral types.
• Their energetics arise from a balance between exchange, anisotropy, and magnetoelastic effects, enabling tunable, high-speed dynamics driven by spin-transfer and spin–orbit torques.
• Topological and quantum properties revealed by advanced imaging and magnonic techniques pave the way for innovative memory, logic, and spintronic applications.

Domain walls in antiferromagnets are extended, solitonic textures of the Néel order parameter that separate regions with different antiferromagnetic domain orientations. Their structure, energetics, dynamics, and emergent functionalities have become central subjects in modern condensed matter and spintronics research, distinguishing antiferromagnetic texture physics from their ferromagnetic counterparts. Rich phenomenology arises in systems ranging from classical collinear compounds to synthetic and quantum antiferromagnets—extending further to topological and altermagnetic systems—through mechanisms that couple spin, lattice, topology, and electronic degrees of freedom.

1. Classification and Structure of Antiferromagnetic Domain Walls

Domain walls in antiferromagnets are classified according to the symmetry of the order parameter rotation across the interface and the underlying lattice and anisotropy:

• Bloch and Néel Domain Walls: In collinear antiferromagnets such as Cr₂O₃, 180° domain walls can realize both Bloch- and Néel-type spin structures depending on the relative strength of in-plane magnetocrystalline anisotropy and residual surface “demagnetizing” effects. For Bloch walls (twist angle χ = ±π/2), the staggered magnetization rotates within the wall plane; for Néel walls (χ = 0, π), it rotates perpendicular to the wall (Wornle et al., 2020). Wall profile solutions are generically modeled as

$\theta(x) = \pm 2\arctan[\exp(x/\Delta)],$

with wall width $\Delta$ controlled by exchange and anisotropy ($\Delta = \sqrt{A/K}$), and distinct experimental widths observed for Néel ($\sim$42 nm) and Bloch ($\sim$65 nm) types in Cr₂O₃.

• Composite and Chiral Walls: In synthetic antiferromagnets and multicomponent systems, domain walls often host composite or chiral structures, including networks with topological defects (bi-merons, bi-skyrmions), as observed in Co/Ru/Co multilayers, where domain walls consist of junctions between Néel-type and transverse wall segments connected by coupled vortex-like excitations ((Kolesnikov et al., 2017); (Saxena et al., 22 Aug 2024)).
• Atomically Sharp Walls: In certain quantum antiferromagnets (e.g., CuMnAs), domain walls can be atomically sharp, with a 180° reorientation of the Néel vector occurring across adjacent atomic layers. This observation falls beyond the scope of traditional micromagnetic theory and reflects the impact of crystalline symmetry and spin-orbit effects stabilizing such abrupt boundaries (Krizek et al., 2020).

2. Energetics, Elasticity, and Magnetoelastic Coupling

The wall structure and stability derive from a competition of exchange, anisotropy, and, where relevant, magnetoelastic energies:

• Exchange and Anisotropy: The energy density in the continuum limit is modeled as

$$e = A (\partial_x\theta)^2 + A \sin^2\theta (\partial_x\phi)^2 + K \sin^2\theta,$$

where $A$ is the exchange stiffness and $K$ is the uniaxial anisotropy (Wornle et al., 2020). For more complex systems (e.g., frustrated or row-wise antiferromagnets), higher-order exchange and biquadratic couplings ($-B_1(\mathbf{S}_i \cdot \mathbf{S}_j)^2$) play pivotal roles in stabilizing nontrivial wall textures ((Spethmann et al., 2020); (Saxena et al., 22 Aug 2024)).

• Elastic and Magnetoelastic Effects: Magnetoelastic coupling influences both wall orientation and energetics. The total energy for a 90° wall, incorporating elastic, magnetoelastic, exchange, and anisotropy contributions, reads

$W = W^{(el)} + W^{(mel)} + W^{(exc)} + W^{(ani)},$

with $$W^{(mel)} = (\Lambda/2)[(\varepsilon_{11}-\varepsilon_{22})(n_1^2-n_2^2) + 4\varepsilon_{12} n_1 n_2]$$ and exchange/aniso as above (Vergallo et al., 2023). Minimization yields nonlinear coupled PDEs, and notably, incompatibility-driven volume effects favor wall orientations rotated by $45^\circ$ relative to crystalline axes, a result evident in domain wall orientation selection in strained lattices.

• Domain Wall Elasticity and Mechanics: Real domain walls in antiferromagnets act as elastic objects. When traversing engineered topographic features (e.g., mesas in Cr₂O₃), they experience geometric “refraction” analogous to Snell’s law, governed by their elastic tension $\gamma = 4\sqrt{\mathcal{A}K}$ (Hedrich et al., 2020). This elastic response mediates pinning, depinning, and manipulation, establishing the mechanical foundation for potential memory architectures.

3. Dynamics: Current- and Field-Driven Motion

Antiferromagnetic domain wall dynamics, in contrast to those in ferromagnets, are described by models respecting the bipartite structure and relativistic invariance of the order parameter equations (modified by damping and torques):

• Dead and Alive Stages; Multiple Walker Breakdowns: Unlike single-threshold Walker breakdown in ferromagnets, antiferromagnets exhibit multiple Walker regimes due to Lorentz contraction of the wall width as velocity increases—$\Delta(v) \sim \Delta_0\sqrt{1-v^2/v_g^2}$—where velocity approaches the magnon group velocity $v_g$. Dynamic transitions arise as the wall tilt angle $\phi_U$ reaches critical values, with solutions to

$$\sin(2\phi_U) = -\frac{M}{\alpha\gamma(J_{AF}+K_h)}\left[\frac{u(\beta-\alpha)}{\Delta} + \gamma B_{SO}\right],$$

and velocity $v = u\beta/\alpha + (\gamma B_{SO}\Delta)/\alpha$ (Lee et al., 2023).

• Spin-Orbit and Spin-Transfer Torques: Spin-polarized currents drive a rich set of wall behaviors, contingent upon current polarization:
  • Perpendicular spin polarization induces steady precession of the wall, yielding profiles $\tan(\Theta/2) = \exp[\pm(x-x_0)/\ell]$, $\ell = 1/\sqrt{1-\omega^2}$, with precession frequency $\omega \propto$ applied torque (Theodorou et al., 26 Sep 2025).
  • In-plane polarization leads to pure translation with velocity $v = (\pi/(2\alpha))\tilde{T}_2$ (where $\tilde{T}_2$ is the normalized torque amplitude). The dynamic wall profile becomes asymmetric at high velocity, deviating from parity, often with exponential and algebraic decay on opposing sides of the wall ((Theodorou et al., 26 Sep 2025); (Theodorou et al., 16 Mar 2025); (1904.02491)).
• Spin-Wave and Magnonic Control: Spin waves (magnons) may exert helicity-dependent forces on domain walls in the presence of Dzyaloshinskii-Moriya interaction (DMI), enabling control over wall velocity and direction. In biaxial AFMs, DMI lifts the degeneracy between spin-wave helicities, and the group velocity, force, and momentum transfer depend explicitly on spin-wave polarization (1705.01572).
• Ultra-high Speed and Inertia: Domain walls in synthetic and natural antiferromagnets exhibit inertia and can reach velocities approaching or exceeding tens of kilometers per second ((1904.02491); (Theodorou et al., 16 Mar 2025)). Unlike in ferromagnetic tracks, breakdown is avoided, but care must be taken with edge-induced nucleation and DMI-tuned stability.

4. Topological and Quantum Properties

Antiferromagnetic domain walls can host or induce states not present in the bulk:

• Electronic Topology and Protected States: In antiferromagnetic topological insulators (AFTIs), domain walls separate regions of opposite magnetization—created by time-reversal. The topological response is determined by the mirror Chern number, and the protection depends on whether the mirror symmetry is spinful or spinless (Naselli et al., 15 May 2025).
  • In spinful-mirror AFTIs, the wall itself is gapped unless it ends at a ferromagnetic surface, where chiral edge states emerge.
  • In spinless-mirror AFTIs, the wall acts as an embedded 2D semimetal hosting gapless Dirac-like states.
• Activation of Hall and Orbital Magnetization in Altermagnets: In pure altermagnets (antiferromagnets with translation-preserving alternating order), the bulk anomalous Hall effect (AHE) is forbidden by symmetry. However, domain walls locally lift the symmetry constraints, resulting in nonzero AHE and orbital magnetization, as shown via Kubo formula calculations in rutile lattices (Sorn et al., 21 May 2025). The effect is field-controllable due to field–domain wall chirality coupling (Lifshitz invariant-like), and is generically allowed in altermagnets with appropriate symmetry (generalizable via group-theoretical analysis).

5. Experimental Probes and Manipulation Techniques

Modern imaging and control techniques provide nanoscale access to domain walls:

• Imaging:
  • Nanoscale scanning diamond magnetometry (NV center scanning tips) enables direct measurement of the stray field profile and local chirality, as demonstrated in Cr₂O₃ (Wornle et al., 2020).
  • Cryogenic magnetic force microscopy (MFM) detects domain wall contrast in uniaxial AFMs due to local enhancement of magnetic susceptibility or net moment, with domain wall energy scaling as $E_{DW} \propto \sqrt{AK}$ (Sass et al., 2019).
  • Direct imaging of atomically sharp walls is achieved via differential phase contrast scanning transmission electron microscopy, revealing thickness down to a single lattice spacing (Krizek et al., 2020).
• Manipulation:
  • Local topographic features (mesas) engineered via lithography or focused ion beams reshape the domain wall energy landscape, enabling wall pinning, bending, and depinning (laser dragging), as observed in Cr₂O₃ (Hedrich et al., 2020).
  • Spin-polarized STM imaging and atom manipulation provide atomic-scale control and detection of domain wall motion, including demonstration of friction and mobility anisotropy in row-wise AFMs (Spethmann et al., 2020).
  • Strain fields, induced mechanically or via adsorption (e.g., via Ar bubbles), locally reconfigure domain wall networks and enable chiral junction engineering with emergent topological orbital moments (Saxena et al., 22 Aug 2024).
• Magnonic Radar: Scattered spin-waves (magnonic radar) probe both translational and angular velocities of domain walls in synthetic antiferromagnets through dual Doppler shifts (translational and angular), offering high-fidelity dynamic detection (Lan et al., 2 Sep 2025).

6. Implications for Spintronic Devices and Functionalities

Antiferromagnetic domain walls, given their unique dynamics, topological properties, and coupling to electronic and lattice degrees of freedom, are candidates for next-generation device applications:

• Memory and Logic: Fast and inertial domain wall motion enables THz logic and memory, and the absence of stray fields supports high-density integration ((Böhm et al., 2019); (Kolesnikov et al., 2017)).
• Topological Devices: Domain wall conductance channels—hosted either at domain wall intersections, surfaces, or interfaces with ferromagnets—afford robust, reconfigurable modes, essential for topological logic (Naselli et al., 15 May 2025).
• Magneto-Orbital and Hall Functionality: Engineering domain wall chirality in altermagnets via external fields activates spin–orbit and orbital responses, offering new classes of Hall sensors and actuators (Sorn et al., 21 May 2025).
• Nanoscale Rewritable Architectures: Elastic domain wall mechanics and strain-tunable chiral junctions point toward fully rewritable, dense memory arrays where information is encoded in domain wall position and type ((Hedrich et al., 2020); (Saxena et al., 22 Aug 2024)).

7. Open Directions and Experimental Signatures

Key research trajectories and experimental signatures include:

• Quantum stabilization of unexpected wall profiles (e.g., atomically sharp walls supported by DFT beyond spin-Hamiltonians; (Krizek et al., 2020)).
• Multiple Walker breakdowns in current-driven domain wall motion due to Lorentz contraction, measurable in synthetic antiferromagnetic tracks as velocity plateaus or abrupt transitions in velocity–current plots (Lee et al., 2023).
• Hall and orbital magnetization signals arising uniquely at domain walls in symmetry-forbidden materials, detectable using sensitive transport or X-ray circular dichroism techniques (Sorn et al., 21 May 2025).
• Real-time dynamic detection of domain wall velocities and precession via magnonic radar based on frequency-resolved spin-wave scattering (Lan et al., 2 Sep 2025).

In summary, domain walls in antiferromagnets uniquely combine rich internal structure, fast and tunable dynamics, and emergent topological and orbital functionalities, all governed by a subtle interplay of symmetry, exchange, spin–orbit, and magnetoelastic couplings. Their role as both information carriers and sources of novel phenomena establishes them as central objects of paper at the frontier of spintronics, quantum materials, and nanotechnology.