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.

中文翻译：

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多轨道−J 模型中的交替磁性和超导性


在探索相关多轨道交替磁体 （AlMs） 的激励下，我们研究了方形八边形晶格上的最小 t-J 模型，这有利于这种共线磁序。虽然反铁磁有序打破了平移和时间反转对称性，但 AlM 态（相当于“d 波铁磁体”）具有多极有序，它分别打破了时间反转和晶体旋转对称性，但保留了它们的产物，导致净磁化强度为零的自旋分裂带。当我们改变掺杂和相互作用时，我们研究了这些多轨道模型的平均场相位图，发现了两种类型的 AlM 有序：（i） 由准 1D van Hove 奇点驱动的流动弱耦合 AlM 金属，以及 （ii） 半填充时的强 AlM 有序。我们还发现了超导性状态，包括均匀的 s 波和 dxy 波配对状态、初期 dxy 波对密度波级以及单重态-三重态配对和 AlM 级共存的均匀相位。我们的非均匀平均场理论方法揭示了共存相对相分离不稳定，但更远距离的相互作用可能导致条带顺序。我们的结果可能与 AlM 材料上的掺杂和压力研究有关。