Spin-Orbital Altermagnetism

Altermagnet is a newly discovered magnetic phase, characterized by non-relativistic spin-splitting that has been experimentally observed. Here, we introduce a framework dubbed {\it spin-orbital altermagnetism} to achieve spin-orbital textures in altermagnetic materials. We identify two distinct classes of spin-orbital altermagnetism: intrinsic and extrinsic. The intrinsic type emerges from symmetry-compensated magnetic orders with spontaneously broken parity-time symmetry, while the extrinsic type stems from translational-symmetry breaking between sublattices, as exemplified by the Jahn-Teller-driven structural phase transition. In addition to directly measuring the spin-orbital texture, we propose spin conductivity and spin-resolved orbital polarization as effective methods for detecting these altermagnets. Additionally, a symmetry-breaking mechanism induces weak spin magnetization, further revealing the peculiar feature of spin-orbital altermagnetism. We also utilize the staggered susceptibility to illustrate a potential realization of this phase in a two-orbital interacting system. Our work provides a new platform to explore spin-orbital locked physics, extending the materials classes that may display complex spin textures from the standard $4d-5d$ compounds to $3d$ compounds.