Altermagnets with topological order

We investigate the phase diagram of an exactly solvable model with Kitaev type interactions on a bilayer square-octagon lattice. On top of the spin liquid ground state, we introduce exchange interactions which lead to a local altermagnetic order that coexists with topological order. We show that this magnetically fragmented phase has momentum dependent fractionalized fermonic excitations. We also explore experimental consequences of the resulting spin-split Majorana quasiparticle bands.