Altermagnetic Proximity Mechanisms

• Altermagnetic proximity is the phenomenon where momentum-dependent spin splitting is transferred from an altermagnet to an adjacent material, creating a unique reciprocal-space magnetic texture.
• It differs from ferromagnetic and conventional antiferromagnetic proximity by inducing a symmetry-structured, momentum-anisotropic splitting without generating net magnetization.
• Key applications include modulating superconducting properties, driving topological superconductivity, and enabling valleytronics through precise control of interfacial coupling.

Searching arXiv for papers on altermagnetic proximity and closely related heterostructures. Altermagnetic proximity is the interfacial transfer of the defining electronic hallmark of altermagnetism—momentum-dependent spin splitting with vanishing net magnetization—from an altermagnet into an adjacent material. In the literature, this transfer is not a single universal mechanism but a family of proximity phenomena: inverse proximity into conventional superconductors via a spin- and momentum-dependent self-energy, direct imprinting of momentum-alternating spin splitting into nonmagnetic van der Waals layers, geometry-controlled effective exchange in semiconductor nanowires, and surface- or interface-selective coupling governed by the projection of bulk altermagnetic partner momenta into the interfacial Brillouin zone (Sukhachov et al., 2024, Zhu et al., 8 Sep 2025, Hadjipaschalis et al., 30 Jun 2025, Sattigeri et al., 2023). Across these settings, the central distinction from ferromagnetic and conventional antiferromagnetic proximity is that the induced field is neither a uniform Zeeman term nor a fully compensated and band-degenerate background, but a symmetry-structured, often $d$-wave-like, momentum-anisotropic spin splitting inherited from a compensated magnetic order (Zhu et al., 8 Sep 2025, Qin et al., 7 Jan 2026).

1. Conceptual definition and distinction from other magnetic proximity effects

In altermagnets, opposite-spin sublattices are related by rotation or mirror symmetry rather than by inversion or translation, which yields zero net magnetization but nondegenerate spin bands even without spin-orbit coupling (Zhu et al., 12 Apr 2025). This makes altermagnetic proximity qualitatively different from both ferromagnetic and conventional antiferromagnetic proximity.

In ferromagnetic proximity, the induced exchange field is typically uniform in momentum space and resembles a Zeeman splitting. In conventional antiferromagnetic proximity, one may induce staggered real-space spin character or interfacial exchange effects, but if the opposite-spin sublattices are related by translation or inversion, the characteristic momentum-alternating spin splitting is absent (Zhu et al., 8 Sep 2025). By contrast, altermagnetic proximity transfers a reciprocal-space magnetic texture: the neighboring layer inherits a $k$-dependent spin splitting that preserves degeneracy on some symmetry lines and reverses spin polarization between symmetry-related momentum sectors (Zhu et al., 8 Sep 2025).

The literature uses several closely related formulations for this effect. In superconducting inverse proximity, the proximitized superconductor acquires a spin- and momentum-dependent self-energy rather than a homogeneous exchange field (Sukhachov et al., 2024). In semiconductor and nanowire heterostructures, the induced term is an even-in-momentum, orientation-dependent spin splitting that plays the role usually played by a Zeeman field, but with zero net magnetization (Hadjipaschalis et al., 30 Jun 2025). In van der Waals heterostructures, the induced state of the adjacent nonmagnetic layer is termed a proximitized altermagnet, and the interfacial imprinting process is termed altermagnetization (Zhu et al., 8 Sep 2025).

A recurring misconception is that bulk altermagnetism should automatically survive at any surface or interface. Surface-state analysis shows the opposite: whether a neighboring layer can feel altermagnetic spin splitting depends decisively on surface or interface orientation and on which bulk momenta carrying opposite-sign spin splitting collapse onto the same two-dimensional interfacial momentum (Sattigeri et al., 2023).

2. Microscopic mechanisms and symmetry selection rules

A common microscopic structure is a momentum-dependent exchange term inherited from the altermagnet. In a model altermagnet, the normal-state exchange field may take the $d$-wave form $J_a(\cos k_x-\cos k_y)\sigma_z$ or its continuum analogue, and this same form reappears in proximitized layers as an effective interfacial field or self-energy (Alam et al., 30 Oct 2025, Zhu et al., 8 Sep 2025). Because the sign changes across the Brillouin zone, the induced splitting is strongest away from nodal lines and vanishes along symmetry-enforced directions.

For interfaces and thin films, the governing symmetry principle is projection from the bulk three-dimensional Brillouin zone onto the two-dimensional surface Brillouin zone. If opposite-sign altermagnetic partner points project to different interfacial momenta, altermagnetism is preserved at the interface; if they project to the same interfacial momentum, the opposite splittings merge and annihilate, and the surface is blind to altermagnetism (Sattigeri et al., 2023). This rule explains why several surfaces of LaMnO$_3$, MnTe, and RuO$_2$ are blind while others preserve the bulk nonrelativistic spin splitting (Sattigeri et al., 2023).

The same symmetry selectivity appears in real-space model construction. A bottom-up spin-cluster scheme constructs altermagnetic order by fixing the symmetry operation $S$ that maps opposite-spin sublattices into one another, choosing a compatible Bravais lattice, generating a basis from a spin cluster, assigning opposite local exchange fields, and ensuring that $\mathcal{PT}$ and $t\mathcal{T}$ are broken (Zhu et al., 12 Apr 2025). For the canonical two-dimensional $d$-wave case, $k$0, and the resulting interface is not seen by a neighboring layer as a uniform Zeeman field but as a compensated, symmetry-odd, momentum-anisotropic exchange environment (Zhu et al., 12 Apr 2025).

This cluster-resolved viewpoint also shows that proximity can be highly sensitive to accidental restoration of $k$1. Enlarging the magnetic cluster may accidentally restore $k$2 through an inversion center between neighboring clusters, suppressing the desired altermagnetic band splitting; a simple geometric distortion can remove that restoration (Zhu et al., 12 Apr 2025). A plausible implication is that interfacial reconstruction, registry, and local distortion are not secondary details but primary control parameters for altermagnetic proximity.

3. Direct altermagnetization of adjacent nonmagnetic layers

The clearest explicit realization of direct altermagnetic proximity is the van der Waals framework based on V$k$3Se$k$4O, where a nonmagnetic layer inherits the hallmark momentum-alternating spin splitting of the altermagnet (Zhu et al., 8 Sep 2025). In monolayer PbO, the isolated layer is spin degenerate, whereas in the heterostructure the PbO-projected bands become spin split in a momentum-dependent way: spin degeneracy is preserved along $k$5–M, while opposite spin polarizations appear along M–X–$k$6 and $k$7–Y–M, consistent with the underlying order of V$k$8Se$k$9O (Zhu et al., 8 Sep 2025). Real-space spin density in PbO mirrors the substrate symmetry, and charge transfer occurs from PbO to V$d$0Se$d$1O (Zhu et al., 8 Sep 2025).

The dependence on interlayer spacing demonstrates that this effect is short ranged. The induced spin splitting $d$2 decreases monotonically as the interlayer separation $d$3 increases from the equilibrium distance $d$4, and the associated spin density decreases in parallel (Zhu et al., 8 Sep 2025). A decisive control case replaces the altermagnetic state of V$d$5Se$d$6O by a conventional antiferromagnetic configuration in a $d$7 supercell. In that case, the induced alternating spin splitting in PbO disappears, although PbO still acquires an antiferromagnetic real-space spin feature (Zhu et al., 8 Sep 2025). This establishes that the induced reciprocal-space texture is specifically altermagnetic.

The same platform extends to valleytronics. In PbS/V$d$8Se$d$9O, PbS inherits symmetry-paired spin-valley locking through altermagnetic proximity, and uniaxial strain lifts the $J_a(\cos k_x-\cos k_y)\sigma_z$0-$J_a(\cos k_x-\cos k_y)\sigma_z$1 valley degeneracy (Zhu et al., 8 Sep 2025). The resulting valley splitting $J_a(\cos k_x-\cos k_y)\sigma_z$2 grows monotonically under either compressive or tensile strain, and a $J_a(\cos k_x-\cos k_y)\sigma_z$3 tensile strain along $J_a(\cos k_x-\cos k_y)\sigma_z$4 yields a $J_a(\cos k_x-\cos k_y)\sigma_z$5 meV valence-band splitting (Zhu et al., 8 Sep 2025). This indicates that altermagnetic proximity can transfer not just spin splitting without net magnetization, but also a specific valley-resolved form of it.

A related but distinct interfacial effect arises in altermagnet/semiconductor Schottky contacts. There, the nonmagnetic semiconductor does not acquire an equilibrium proximity-induced exchange splitting; instead, the altermagnet injects a spin-polarized thermionic current because its spin-contrasting Fermi surface gives spin-dependent phase-space filtering at the interface (Ang, 2023). This is not altermagnetic proximity in the strict band-structure sense, but it demonstrates that zero-net-magnetization altermagnets can create strongly orientation-dependent interfacial spin selectivity (Ang, 2023).

4. Inverse proximity into superconductors

The inverse proximity problem asks how an adjacent altermagnet modifies a conventional superconductor. In an altermagnet–superconductor bilayer, integrating out the altermagnet yields a spin- and momentum-dependent self-energy in the superconducting layer rather than a uniform exchange field (Sukhachov et al., 2024). In the bilayer limit with momentum-conserving tunneling, the induced renormalized quasiparticle parameters are

$J_a(\cos k_x-\cos k_y)\sigma_z$6

where the altermagnetic splitting $J_a(\cos k_x-\cos k_y)\sigma_z$7 is momentum dependent (Sukhachov et al., 2024). Momentum-resolved spectral functions show clear spin splitting, but the fully momentum-integrated superconducting density of states remains spin degenerate because the splitting changes sign between momentum sectors (Sukhachov et al., 2024). Directional momentum selection is therefore essential for observing the effect.

This hidden spin splitting becomes functionally important in transport. In an AM-SC-AM junction with a momentum-conserving planar interface, the left altermagnet induces spin-resolved particle-hole asymmetry in the superconducting spectrum, while the right altermagnet acts as a directional, momentum-selective spin analyzer, producing a thermoelectric response without external magnetic fields or ferromagnetic stray fields (Sukhachov et al., 2024). The Seebeck coefficient and figure of merit are nonzero because the cancellation between opposite spin sectors is incomplete when the tunneling geometry resolves the altermagnetic lobes (Sukhachov et al., 2024).

A complementary thin-film study sharpens the distinction between metallic and insulating altermagnetic parents. In ballistic thin-film superconductor/altermagnet heterostructures, an altermagnetic insulator induces a well-defined effective altermagnetic exchange field in the superconducting film, with pure $J_a(\cos k_x-\cos k_y)\sigma_z$8-wave momentum symmetry, smooth dependence on subband index, and nearly homogeneous spatial profile across the thin superconducting layer (Bobkov et al., 20 Oct 2025). By contrast, a metallic altermagnet still induces spin-split spectra and pronounced triplet correlations, but the branch dependence becomes irregular in subband index, momentum, energy, and position, so a simple homogeneous effective-field model is generally not valid and no clean Zeeman-like splitting appears in the superconducting density of states (Bobkov et al., 20 Oct 2025). This establishes that altermagnetic proximity is governed not only by magnetic symmetry but also by whether the altermagnetic layer is metallic or insulating.

Altermagnetic inverse proximity also underlies memory functionality. In AM-SC bilayers and AM-SC-AM trilayers, the critical temperature $J_a(\cos k_x-\cos k_y)\sigma_z$9 of a conventional $_3$0-wave superconductor is controlled by the orientation of the Néel vector of the proximate altermagnet, with geometry-dependent modulation in bilayers and distinct parallel and antiparallel transition temperatures in trilayers (Giil et al., 2023). Because the control variable is the crystal-locked orientation of compensated order rather than a net magnetization, the proposed memory element is stray-field free (Giil et al., 2023).

5. Altermagnetic proximity and topological superconductivity

A major line of work uses altermagnetic proximity as the time-reversal-breaking ingredient in Majorana platforms. In one-dimensional semiconductor–superconductor heterostructures, a Rashba nanowire on an altermagnet with induced $_3$1-wave pairing acquires a momentum-dependent spin splitting that replaces the conventional Zeeman field (Ghorashi et al., 2023). The nanowire Bogoliubov–de Gennes Hamiltonian is

$_3$2

and the topological regime is

$_3$3

(Ghorashi et al., 2023). This yields Majorana zero modes at the wire ends with vanishing net magnetization. Because the induced altermagnetic term depends on wire orientation and vanishes on symmetry-enforced nodal directions, rotating the wire relative to the altermagnet provides a purely geometric tuning knob for the topological phase in $_3$4-, $_3$5-, and $_3$6-wave settings (Hadjipaschalis et al., 30 Jun 2025).

A related proximitized nanowire platform combines an altermagnet with a conventional $_3$7-wave superconductor to produce a meta-altermagnetic superconducting nanowire. There the effective Bogoliubov–de Gennes Hamiltonian contains the proximity-induced term $_3$8, which is the one-dimensional reduction of a parent $_3$9-wave altermagnetic splitting (Yi et al., 18 Jun 2026). In combination with induced $_2$0-wave pairing, this generates spin-triplet correlations and nonzero equal-spin Andreev reflection. With Rashba spin-orbit coupling, the system can enter a topological superconducting phase, with the gap-closing criterion

$_2$1

and a zero-bias spin conductance quantized at $_2$2 in the topological regime (Yi et al., 18 Jun 2026).

Two-dimensional and surface-state platforms use the same principle in other guises. On three-dimensional topological-insulator surfaces, a $_2$3-wave altermagnetic term can gap selected Dirac cones with opposite mass signs, producing chiral electronic modes at domain walls and, with superconductivity, chiral Majorana fermions (Ghorashi et al., 2023). In ferromagnetic topological-insulator Bi$_2$4Se$_2$5, a proximate $_2$6-wave altermagnet together with an in-plane magnetic exchange field generates surface-selective Dirac masses because the in-plane term shifts the Dirac point to a momentum where the $_2$7-wave altermagnetic mass is nonzero (Qin et al., 7 Jan 2026). A single gapped surface yields a half-quantized Hall conductance $_2$8, antiparallel Néel vectors on opposite surfaces produce an altermagnet-induced layer Hall effect with vanishing net Hall conductance, and parallel Néel vectors give a quantized Chern insulating state with $_2$9 (Qin et al., 7 Jan 2026).

Superconducting proximity into the altermagnet itself is equally nontrivial. A conventional $S$0-wave superconductor can induce superconductivity in a metallic altermagnet only if weak Rashba spin-orbit coupling is present at the interface (Heinsdorf et al., 3 Sep 2025). The induced pairing matrix contains both singlet and triplet components,

$S$1

and the resulting state is generically nodal, with eight Dirac point nodes per Brillouin zone in the minimal $S$2-wave altermagnet model (Heinsdorf et al., 3 Sep 2025). A related two-dimensional AM-SC framework based on self-energy integration finds even-frequency, even-parity singlet pairing and odd-frequency, even-parity triplet pairing without Rashba spin-orbit coupling, and even-frequency, odd-parity triplet components once Rashba coupling is included, enabling weak and strong topological superconducting phases characterized by winding number and Chern number (Alam et al., 30 Oct 2025).

6. Design principles, diagnostics, and open problems

The available literature converges on a set of design rules. First, the interface must preserve the momentum-space structure of the altermagnet rather than averaging it away. Surface-state calculations therefore identify which surfaces to cleave in order to preserve altermagnetism in surfaces or interfaces (Sattigeri et al., 2023). Second, interfacial orientation and registry matter because nodal directions are not accidental zeros but symmetry-forbidden directions where the induced term must vanish (Hadjipaschalis et al., 30 Jun 2025, Sattigeri et al., 2023). Third, when real-space motifs are important, one should preserve the cluster symmetry that generates the target $S$3-, $S$4-, or $S$5-wave altermagnetic harmonic and avoid accidental restoration of $S$6 at the interface (Zhu et al., 12 Apr 2025).

Fourth, transport or spectroscopy must often retain momentum selectivity. Full momentum integration can remove the visible spin splitting in inverse-proximitized superconductors, whereas directional tunneling, planar interfaces, and layer-resolved measurements reveal the hidden altermagnetic structure (Sukhachov et al., 2024, Qin et al., 7 Jan 2026). Fifth, the material class matters: proximity to an altermagnetic insulator gives a controllable, spectroscopically clean effective altermagnetic splitting in a superconducting film, whereas proximity to an altermagnetic metal gives irregular spectral reconstruction and triplet conversion without a robust density-of-states splitting (Bobkov et al., 20 Oct 2025).

The main experimental signatures proposed so far are momentum-resolved spin splitting in the proximitized layer, strong dependence on interface orientation, electrically or geometrically controlled gap closings at nodal angles, half-quantized or layer-resolved Hall responses on topological-insulator surfaces, equal-spin Andreev reflection and spin supercurrent in nanowires, and Néel-vector-controlled superconducting transition temperatures in AM-SC-AM memory structures (Zhu et al., 8 Sep 2025, Hadjipaschalis et al., 30 Jun 2025, Qin et al., 7 Jan 2026, Yi et al., 18 Jun 2026, Giil et al., 2023). Electric fields perpendicular to blind surfaces can even activate altermagnetism by breaking inversion symmetry and separating previously merged opposite-sign sectors in the projected surface Brillouin zone (Sattigeri et al., 2023).

Several limitations remain explicit. Many studies use idealized interface profiles, single-band or continuum models, and clean translationally invariant junctions; they do not yet provide quantitative interface Hamiltonians for disorder, charge transfer, orbital filtering, or lattice mismatch (Zhu et al., 12 Apr 2025, Qin et al., 7 Jan 2026, Ang, 2023). Even in first-principles van der Waals examples, the main text does not provide a complete mapping from interface chemistry to a universal effective altermagnetic self-energy (Zhu et al., 8 Sep 2025). This suggests that altermagnetic proximity is now established as a distinct interfacial mechanism, but its full materials-specific theory remains an open problem. A plausible implication is that the next stage of the field will be defined less by demonstrating that altermagnetic proximity exists than by determining how faithfully particular interfaces transmit the parent altermagnetic form factor into adjacent electronic, superconducting, valley, or topological degrees of freedom.