Cell-dependent higher-order topological charge in altermagnetic β-MnO₂

Altermagnets with non-relativistic band splitting have recently attracted widespread research interest. Via first-principles calculations and theoretical analysis, we reveal that three-dimensional (3D) β-MnO₂ is the first material example of an altermagnetic (AM) higher-order topological insulator (HOTI) with topologically protected hinge states. Unlike conventional magnetic topological materials, the AM β-MnO₂ has a cell-dependent topological charge Q_corner⁽²⁾, where the spin-up channel possesses a nontrivial Q_corner⁽²⁾ in one unit cell, while the spin-down channel exhibits a nontrivial Q_corner⁽²⁾ in another symmetry-related unit cell. Thus, the hinge states are fully spin-polarized, with the spin components of the hinge states being boundary-dependent, giving rise to an intriguing spin-hinge coupling. Our work provides an excellent platform for exploring the interaction between altermagnetism and topological states, while also offering new possibilities for the application of symmetry-protected topological states in AM spintronics.