Van Hove singularity-induced multiple magnetic transitions in multi-orbital systems

Van Hove singularities (VHSs) amplify electronic correlations, providing a crucial platform for discovering novel quantum phase transitions. Here, we show that VHSs in multi-orbital systems can stabilize a variety of competing $\bm{Q}=0$ magnetic orders, including intrinsic altermagnetism emerging from spontaneous orbital antiferromagnetism. This intrinsic phase, in which antiparallel spins reside on distinct orbitals, is realized across all four 2D Bravais lattices. It is driven by orbital-resolved spin fluctuations enhanced by inter-orbital hopping and favors suppressed Hund’s coupling $J_H$, strong inter-orbital hybridization, and filling near a VHS from quadratic band touching. Through Hubbard-$U$-$J_H$ phase diagrams we map several magnetic phase transitions: (i) ferrimagnet to $d$-wave extrinsic altermagnet, (ii) $d$-wave intrinsic altermagnet to ferromagnet, and (iii) $g$-wave extrinsic altermagnet to either $d$-wave extrinsic altermagnet or ferromagnet. Our work identifies VHSs as a generic route to altermagnetism in correlated materials.

💡 Research Summary

The authors investigate how Van Hove singularities (VHSs) in multi‑orbital two‑dimensional systems can drive a rich set of collinear magnetic orders, focusing on the emergence of altermagnetism—a compensated magnetic state with momentum‑dependent spin splitting but zero net magnetization. Starting from a symmetry analysis of the four Bravais lattices (oblique, rectangular, centered‑rectangular, square, and hexagonal), they define two orbital‑antiferromagnetic operators O₁ and O₂ that place opposite spins on different orbitals (e.g., pₓ vs. p_y or dₓz vs. d_yz). These orders break both parity‑time (P·T) and translation‑time (t·T) symmetries, giving rise to “intrinsic altermagnetism.” In the square lattice, O₁ and O₂ generate d‑wave (dₓ²‑y²) spin‑splitting textures; in hexagonal lattices O₂ leads to a nematic altermagnetic state.

A minimal two‑orbital Hubbard model is constructed with intra‑orbital hopping (t₀, t₁, t₂) and inter‑orbital hybridization (t₃, t₅). The interaction part includes intra‑orbital Hubbard U, inter‑orbital V, and Hund’s coupling J_H, constrained by spin‑rotation symmetry (U = V + 2J_H). By varying U and the ratio J_H/U, the authors map out competing magnetic phases.

Using multi‑orbital random‑phase approximation (RPA), they compute the bare susceptibility tensor χ⁽⁰⁾(k) and project it onto six Q=0 order parameters (O₁–O₆). The static susceptibilities χ_RPA^α(k) reveal that the leading instability always appears at k=0, consistent with the Q=0 nature of the orders. Strong inter‑orbital hopping dramatically enhances orbital‑resolved spin fluctuations, favoring O₁ and O₂ when U is large and J_H is small. Conversely, a sizable J_H stabilizes conventional Néel or ferrimagnetic states.

Phase diagrams in the (U, J_H) plane display three characteristic transitions: (i) ferrimagnet → d‑wave extrinsic altermagnet (driven by sublattice asymmetry t₁≠t₂), (ii) d‑wave intrinsic altermagnet → ferromagnet (when Hund’s coupling is sufficiently suppressed and the filling is tuned near a VHS originating from quadratic band touching), and (iii) g‑wave extrinsic altermagnet → either d‑wave extrinsic altermagnet or ferromagnet (controlled by the strength of t₃, t₅). The presence of a VHS at the M point (logarithmic DOS divergence) amplifies these correlation effects, making the transitions highly sensitive to carrier doping or strain that shift the Fermi level.

The work concludes that VHSs provide a generic route to altermagnetism in correlated multi‑orbital materials. The key ingredients are (1) suppressed Hund’s coupling, (2) strong inter‑orbital hybridization, and (3) electron filling near a VHS from quadratic band touching. These findings offer concrete guidance for experimental searches—through doping, strain engineering, or heterostructure design—to realize intrinsic and extrinsic altermagnetic phases and exploit their spin‑splitting for spintronic applications.