Reseach

 

 

Spin-orbit enabled unconventional Stoner magnetism

At Brillouin zone edges hosting spinless pseudospin, SOC splits the 8-fold degenerate band into 4 doubly degenerate bands, leaving all spin operators inter-band.


Intra-band g-factors in UCoGe calculated along the k line (π + k, π + k, 0.2π). These g-factors quantify the energy splitting between Kramers’ doublets for fields applied along the x, y, and z directions. The value g = 1 corresponds to usual spin-1/2. Inset: Fermi surface of UCoGe. The g calculations are done along the arrow and for the bands producing the inner (pale red) Fermi surface.

The Stoner instability remains a cornerstone for understanding metallic ferromagnets. This in- stability captures the interplay of Coulomb repulsion, Pauli exclusion, and two-fold fermionic spin degeneracy. In materials with spin-orbit coupling, this fermionic spin is generalized to a two-fold degenerate pseudospin which is typically believed to have symmetry properties as spin. We identify a distinct symmetry of this pseudospin that forbids it to couple to a Zeeman field. This ‘spinless’ property is required to exist in five non-symmorphic space groups and has non-trivial implications for superconductivity and magnetism. With Coulomb repulsion, Fermi surfaces composed primarily of this spinless pseudospin feature give rise to Stoner instabilities into magnetic states that are qualitatively different than ferromagnets. These spinless-pseudospin ferromagnets break time-reversal symmetry, have a vanishing magnetization, are non-collinear, and exhibit altermagnetic-like energy band spin-splittings. In superconductors, for all pairing symmetries and field orientations, this spinless pseudospin extinguishes paramagnetic limiting.

 

Altermagnetism from coincident Van Hove singularities

Realizing two-dimensional (2D) altermagnets is important for spintronics applications. We propose a microscopic template for stabilizing 2D altermagnetism through van Hove singularities that are coincident in both energy and momentum. These coincident van Hove singularities are a generic consequence of non-symmorphic symmetries in 8 2D space groups. They allow new hopping interactions between the van Hove singularities that do not appear in analogous van-Hove singularity based patch models for cuprates and graphene. These new interactions can give rise to various weak coupling and BCS-based instabilities, including altermagnetism, nematicity, interband d-wave superconductivity, and orbital altermagnetic order.These results are applied to quasi-2D organic κ-Cl in which altermagnetism is known to appear.

 

Minimal Models for Altermagnetism

Three-dimensional Berry curvature obtained from the the one-orbital minimal model normal state band structure for RuO2. The large values near the Brillouin zone face arise from pseudospin.

Altermagnets feature vanishing net magnetization, like antiferromagnets, but exhibit time-reversal symmetry breaking and momentum-dependent spin-split band structures. Motivated by the prevalence of altermagnetic materials with non-symmorphic symmetry-dictated band degeneracies, realistic minimal models for altermagnetism are constructed starting from tight-binding models for nonsymmorphic space groups with a sublattice defined by two magnetic atoms. These models can be applied to monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic materials and can describe d-wave, g-wave, and i-wave altermagnetism. By examining the altermagnetic susceptibility and mean field instabilities within a Hubbard model, these models are found to have altermagnetic ground states and yield a Berry curvature that is linear in the spin-orbit coupling.

 

 

Model System: TM-intercalated NbSe2

STM/STS and ARPES of MBE grown 1H-NbSe2.

To connect to these models to real systems, we consider
(Fe|Co)1/4Nb(S|Se)2 motivated by our modeling that links the 2a Wyckoff position of Fe/Co in the non-symmorphic space group 194 to an altermagnetic state, As a first step towards the synthesis of transition-metal Nb(S|Se)2, the growth of single-layer 1H-NbSe2 on graphene and SrTiO3(001) substrates using molecular beam epitaxy (MBE) has been demoonstrated. in situ ARPES measurements of the valence band structure at 77 K reveal that the 1H variant exhibits metallic behavior with a hexagonal Fermi surface around the Γ point. This is
consistent with band dispersions along the Γ-Μ direction. For the 1H phase, one band crosses EF midway between Γ and M, with two other hole-like bands with binding energies at Γ of -0.90 and -1.15 eV. STM imaging reveals the well-ordered (3×3) charge density wave (CDW) on single-layer 1H films, similar to that observed on the surface of bulk 2H-NbSe2.

Calculated bands and simulated STM image for 1H-NbSe2, and spin resolved bands along Γ-L in bulk Fe1/4NbSe2.

The electronic properties of the 1H phase are also characterized by tunneling spectroscopy and directly compared with the ARPES dispersion taken at 77 K. The energy positions of two peaks in the dI/dV spectrum below EF coincide with the tops of the ARPES bands. A soft gap of 4.1 meV is evident in the dI/dV spectrum due to the (3×3) CDW. DFT calculations of the band structure and simulated STM images are in good agreement with the experiments. Further calculations for ordered intercalated Fe1/4NbSe2 demonstrate that in this antiferromagnet the bands are spin-split, i.e., is an altermagnet.