Altermagnetism and superconductivity in a multiorbital𝑡−𝐽model

Motivated by exploring correlated multiorbital altermagnets (A⁢ℓ⁢Ms) we study minimal 𝑡−𝐽 models on the square-octagon lattice, which favors such a collinear magnetic order. While antiferromagnetic order breaks translational and time-reversal symmetries, the A⁢ℓ⁢M state (equivalently, a “𝑑-wave ferromagnet”) features multipolar order, which separately breaks time-reversal and crystal rotation symmetries but preserves their product leading to spin-split bands with zero net magnetization. We study the mean-field phase diagram of these multiorbital models as we vary doping and interactions, discovering two types of A⁢ℓ⁢M order: (i) itinerant weak-coupling A⁢ℓ⁢M metals driven by quasi-1D van Hove singularities, as well as (ii) strong A⁢ℓ⁢M order at half-filling. We also find regimes of superconductivity including uniform 𝑠-wave and 𝑑𝑥⁢𝑦-wave pairing states, incipient 𝑑𝑥⁢𝑦-wave pair density wave order, and uniform phases with coexisting singlet-triplet pairing and A⁢ℓ⁢M order. Our inhomogeneous mean-field theory approach reveals that the coexistence phases are unstable to phase separation, but longer-range interactions could lead to stripe order. Our results may be relevant to studies of doping and pressure on A⁢ℓ⁢M materials.