Surface Magnetism Breakthrough Unlocks Robust Spin Control in Antiferromagnetic Materials

Researchers have discovered a novel mechanism for generating altermagnetism, a unique form of magnetism linked to spin transport, at the surfaces of antiferromagnetic materials. Valentin Leeb, from the Department of Physics at the University of Zurich, alongside Peru d’Ornellas and Fernando de Juan from the Donostia International Physics Center, and Adolfo G. Grushin et al., demonstrate that surface symmetry breaking can induce this effect even in conventional antiferromagnets. This is significant because surface altermagnetism represents a local phenomenon undetectable by conventional bulk measurements, offering a pathway to robust and symmetry-driven magnetism beyond established classifications. Their work defines the necessary symmetry conditions for this surface magnetism and provides a theoretical framework, exemplified by the Dirac semimetal CuMnAs, for realising and characterising it using techniques such as spin- and angle-resolved photoemission spectroscopy.

Surface symmetry breaking induces topologically protected altermagnetism in antiferromagnets

Scientists have uncovered a novel pathway to realise altermagnetism, a unique magnetic phase with potential spintronic applications, not within bulk materials, but at the surfaces of conventional antiferromagnets. This work demonstrates that symmetry-breaking at crystal surfaces can induce altermagnetism, even when the bulk material exhibits a spin-degenerate electronic band structure.
Researchers defined the specific symmetry conditions necessary for this surface altermagnetism and, crucially, revealed how it can be topologically protected, creating a robust magnetic effect. The study introduces a minimal model encompassing both trivial and topologically-protected examples of surface altermagnetism.

Calculations show that the spin spectral density, measurable via spin- and angle-resolved photoemission spectroscopy, can exhibit a d-wave-like altermagnetic character at the surface, despite complete spin degeneracy throughout the bulk band structure. This finding circumvents the typical requirement for spin-split band structures usually associated with altermagnetism.
Notably, the theoretical model accurately describes the behaviour of CuMnAs, a known Dirac semimetal, providing an existing material platform for realising this predicted surface magnetism. These results establish crystal surfaces as a promising avenue for developing robust, symmetry- and topology-driven unconventional magnetism, extending beyond the conventional classification of magnetic materials.

The research identifies that antiferromagnets, when considered as surface phenomena, can exhibit characteristics previously thought exclusive to altermagnets. This investigation details how symmetry prerequisites at the surface of a collinear antiferromagnet allow for the emergence of altermagnetic spin-split characteristics.

The work demonstrates that a spin-degenerate antiferromagnetic bulk can support local altermagnetic surface states, differing substantially from surface states found in bulk altermagnets or the influence of altermagnetic layers on non-magnetic surfaces. Researchers explored both trivial and topologically-protected surface states, developing a minimal model to encompass both scenarios.

Specifically, the study highlights a simple system exhibiting a spin-split surface alongside more complex topological phases characterised by altermagnetic drumhead states and Fermi arcs. The team demonstrated that room-temperature antiferromagnetic Dirac semimetals, such as CuMnAs and CuMnP, already known for their spintronic potential, provide a concrete realization of the proposed theory. The symmetry requirements for surface altermagnetism are linked to the breakdown of non-altermagnetic bulk symmetry groups at the surface, leading to a compensated even-wave spin-splitting in the spectral density.

Four-band tight-binding model construction and Hamiltonian parameterisation

A tight-binding model establishes the foundation for understanding the band structure, beginning without spin-orbit coupling. The nodal line, occurring at kz = 0, is protected by the mirror plane Mb, which maintains invariance of the kz = 0 plane. This nodal line resides within a subset of four bands, appearing in pairs with opposite Mb eigenvalues.

To accurately represent the nodal line, a model incorporating a single orbital at Wyckoff position 4c is insufficient, necessitating a four-band model with Wannier centres positioned at 4a. The model is layered along the b direction, utilising orbitals at (0, 0, 0), (1/2, 1/2, 0) in the first layer and (0, 0, 1/2), (1/2, 1/2, 1/2) in the second layer, as depicted in Figure 0.5(a).

Employing a coordinate system where (a, b, c) corresponds to (ky, kz, kx) and a basis of (c1, c2, c3, c4) representing the four sites, sublattice σi, layer τi, and spin si Pauli matrices are defined. The non-magnetic component of the Hamiltonian incorporates nearest-neighbour couplings both in-plane and out-of-plane, described by terms 2tσx(cos kx+ky/2 + cos kx-ky/2) and 2t⊥τx cos kz/2.

Spurious translation symmetries, potentially leading to forbidden altermagnetic splitting, are addressed through consideration of additional terms. These symmetries, including half-translations, are broken by the magnetic order, rendering them unnecessary for the current model, though their potential impact is discussed.

Further neighbour hoppings, as shown in Figure 0.5(b), can also break these symmetries. The magnetic component of the Hamiltonian assumes a collinear order along the z direction, expressed through spin-dependent nearest-neighbour hoppings, specifically 2∆0σysz(sin kx+ky/2 − sin kx-ky/2) and 2∆1σzτysz sin kz/2. These couplings are essential for generating the nodal line and creating a gap elsewhere, while also disrupting spurious surface rotation symmetries.

Surface altermagnetism arising from broken symmetry in spin-degenerate antiferromagnets

Researchers demonstrate that spin-degenerate antiferromagnets can exhibit altermagnetic spin-split characteristics at the crystal surface. This work defines the symmetry conditions necessary for surface altermagnetism and details how it can be protected, creating a robust effect. A minimal model is provided for one trivial case and two topological examples of surface altermagnetism, revealing a d-wave-like altermagnetic character in the spin spectral density accessible via spin- and angle-resolved photoemission spectroscopy.

The study identifies that even with a completely spin-degenerate full band structure, a surface can exhibit this altermagnetic behaviour. This surface magnetism emerges when bulk symmetries are broken, specifically through the loss of translational invariance and any point group symmetries incompatible with the surface normal.

Researchers explain that cutting a crystal plane to expose a single spin species generates a net surface magnetization, effectively creating a surface ferromagnet with a spin-split surface state. Furthermore, the research highlights that antiferromagnets possessing a non-vanishing surface octupolar moment exhibit altermagnetization.

The work demonstrates that the characteristic altermagnetic spin density can emerge as a local feature at the surface, undetectable by global bulk properties due to contributions from opposite surfaces cancelling each other out. Investigations into both trivial and topologically-protected altermagnetic surface states are reported, with a minimal model successfully realising both scenarios.

Specifically, the team studied systems in a slab geometry, employing periodic boundary conditions along the x and y directions and open boundary conditions in the z direction. The crystal structure examined features a four-site unit cell, with spin-up sites represented in red and spin-down sites in blue, highlighting the layer degree of freedom in the z direction. The room-temperature antiferromagnetic Dirac semimetals CuMnAs and CuMnP are identified as existing material realizations of this theory, potentially impacting spintronic applications.

Symmetry-driven altermagnetism and topologically protected surface states

Altermagnetism at crystal surfaces represents a previously overlooked pathway to unconventional magnetism in antiferromagnetic materials. Researchers have defined the symmetry conditions necessary for the emergence of surface altermagnetism, demonstrating how it can be stabilised as a robust effect even in materials with spin-degenerate band structures.

A minimal model and examples illustrate this phenomenon, predicting a wave-like altermagnetic character in the spin spectral density detectable through spin- and angle-resolved photoemission spectroscopy. This work establishes that surfaces offer a distinct platform for realising robust altermagnetism, driven by symmetry rather than bulk properties.

The key requirements for surface altermagnetism are the absence of combined spin-inversion and in-plane translation symmetries, alongside an out-of-plane time-reversal two-fold rotation axis. Two mechanisms for topologically protected surface altermagnetism were proposed: drumhead states in Dirac nodal line semimetals and Fermi arc states in Dirac semimetals.

While symmetry alone is insufficient for robust behaviour, topological protection guarantees its persistence against perturbations. The researchers acknowledge that spin-orbit coupling can affect the topological protection, but characteristics of the altermagnetic surface states remain. The findings suggest that existing materials satisfying the identified symmetry criteria, such as CuMnAs and potentially CuMnP, may already exhibit surface altermagnetism and warrant further investigation using surface-sensitive techniques like photoemission spectroscopy and spin-resolved transport measurements.

Future research could focus on exploring materials with spin-inverted altermagnetic layers or re-examining materials where altermagnetism was previously induced by breaking inversion symmetry, considering instead the role of local surface physics. This work expands the range of materials potentially exhibiting altermagnetism and highlights topology as a means of engineering robust spin-polarized states in antiferromagnets, potentially paving the way for advancements in antiferromagnetic spintronics and novel surface phenomena.