$p$-wave magnet and hedgehog-type Berry curvature in helimagnetic MnAu$_2$

Abstract: Recently discovered altermagnetism in collinear compensated magnets shows even-parity spin texture in momentum space. Beyond the collinear spin ordering, unique odd-parity spin textures emerge in noncollinear compensated magnets. The noncollinear candidates, however, remain unexplored toward a room-temperature metallic altermagnet. Here, we demonstrate that MnAu2 exhibits metallic p-wave magnetism and large spin splitting induced by helical spin ordering. By adapting the band-unfolding scheme based on the translation operators combined with spin rotations, first-principles calculations reveal an unconventional Fermi surface around the $\tilde{M}$-point composed of a single electron pocket with $p$-wave spin texture. Moreover, the spin twist in the helimagnet triggers topologically non-trivial hedgehog Berry curvature, which links to the nonlinear Hall effect and spin Hall effect. Considering the experimental T$_C$ = 335 to 370 K, MnAu$_2$ could establish itself as an ideal candidate for a room-temperature metallic $p$-wave magnet, promising for versatile spintronic applications.

• The paper demonstrates that helimagnetic MnAu₂ exhibits p-wave magnetism with significant spin splitting induced by pure spin-space twists.
• First-principles DFT and band-unfolding techniques reveal nonrelativistic, odd-parity spin textures and distinctive Fermi surface topologies.
• The study identifies tunable hedgehog-type Berry curvature and robust nonlinear/spin Hall effects, underlining its potential for spintronic devices.

Summary of $p$-Wave Magnetism and Berry Curvature in Helimagnetic MnAu$_2$

Altermagnetism: From Collinear to Noncollinear Paradigms

The phenomenon of altermagnetism, characterized by unique spin textures and band splitting in collinear compensated magnets, has garnered significant attention due to its implications for spintronic applications. In these systems, symmetry-induced even-parity spin textures yield anisotropic spin bands and novel transport effects. The present study extends the scope of altermagnetism from collinear to noncollinear compensated magnets, emphasizing the emergence of odd-parity spin textures and identifying room-temperature metallic candidates. The authors systematically demonstrate that MnAu$_2$, a helimagnetic compound, exhibits metallic $p$-wave magnetism and substantial spin splitting, facilitated by the helical spin ordering. Unlike collinear magnetism, this effect arises from purely spin-space twists, independent of lattice distortions.

Gauge Fields and $p$-Wave Spin Textures in Helimagnets

In helimagnetic MnAu$_2$, the $p$-wave spin texture is induced by the electron's traversal through a helical spin structure, generating a spin-dependent effective gauge field proportional to the $z$-component of the spin angular momentum. Continuum and tight-binding modeling reveal that nonrelativistic spin splitting emerges, accompanied by an odd-parity (antisymmetric) spin texture. Notably, the band-unfolding scheme, which incorporates translation and spin-rotation symmetries, exposes a single electron pocket at the M-point in the unfolded Brillouin zone, exhibiting the $p$-wave spin texture. Along the M$^*$–$_2$0–M line, two $_2$1-wave bands with opposite polarity are separated by approximately 1.5 eV, with one band crossing the Fermi level. This separation is robust, tied to the spin-space twist as opposed to traditional Zeeman-like exchange splitting.

Electronic Structure and Transport in MnAu$_2$2

First-principles DFT calculations, employing the supercell approach to accommodate helimagnetic ordering, confirm the body-centered tetragonal structure (space group $_2$3) with Mn layers displaying a 45° spin rotation between adjacent planes. The generalized band unfolding exposes non-degenerate bands and highly distinctive Fermi surface topologies (non-degenerate pockets, sheets, and torus), all with $_2$4-wave spin textures. Opposite spin textures are observed for partner planes ($_2$5), with the $_2$6 plane demonstrating null spin expectation value. Unlike collinear altermagnets, the spin-split-off bands display Sz-antisymmetric textures, and their spatial spin orientation aligns parallel or antiparallel to Mn local moments depending on band index and momentum.

Topological Berry Curvature and Nonlinear Transport

The helimagnetic ordering also triggers topologically non-trivial hedgehog-type Berry curvature (BC) distributions near the Z-point in k-space. The BC vectors radiate in the $_2$7–$_2$8 plane and point inward along $_2$9, forming a hedgehog (or anti-hedgehog) pattern contingent on the chirality of the spin spiral. The switchability of BC dipoles is directly linked to helical spin ordering and is measurable via nonlinear Hall experiments. Quantitatively, the BC dipole reaches values ($_2$0) comparable to those at topological phase transitions in BiTeI, indicating pronounced nonlinear Hall responses. Additionally, the system exhibits a substantial spin Hall conductivity, matching conductivities observed in heavy metals like Au and Ir.

Experimental Feasibility and Spintronic Implications

Experimental observations report a critical temperature ($_2$1) of 335–370 K for helimagnetic ordering in MnAu$_2$2, with robust local magnetic moments persisting at 300 K—about 80% of the low-temperature value. These results imply that MnAu$_2$3 is a viable candidate for room-temperature metallic $_2$4-wave magnetism with large spin splitting. The compound's combination of $_2$5-wave spin texture, switchable hedgehog Berry curvature, and strong nonlinear/spin Hall transport positions it as a promising platform for advanced spintronic devices, efficient spin generation, spin-charge conversion, and nonlinear transverse transport phenomena.

Theoretical and Practical Implications

The theoretical advance lies in demonstrating the emergence of odd-parity spin textures and topological BCs in noncollinear compensated magnets without reliance on lattice distortions or relativistic spin-orbit effects. The practical implication is the identification of MnAu$_2$6 as a highly promising material for spintronic applications operating at room temperature, with tunable transport properties via spin-spiral chirality manipulation. The result challenges and broadens conventional understanding of altermagnetic materials, suggesting future exploration of other helical magnets and their role in topological spintronic phenomena.

Conclusion

The exploration of helimagnetic MnAu$_2$7 establishes a compelling scenario: pure spin-space twists enable robust $_2$8-wave magnetism, large spin splitting, and unconventional hedgehog-type Berry curvature distributions. The compound's properties portend efficient nonlinear Hall effect and spin-charge conversion, and its room-temperature stability validates its candidacy as an ideal platform for altermagnetic and topological spintronics. Further experimental validation and the search for analogous materials with tailored spin textures and Berry curvatures are anticipated to advance both fundamental understanding and technological applications.