Altermagnets with topological order in Kitaev bilayers

Building on recent advancements in altermagnetism, we develop a highly-frustrated magnetic model with Kitaev-like interactions that integrates key aspects of both quantum spin liquids and altermagnets. While the ground state is a gapless quantum spin liquid, our analysis indicates that an altermagnetic local order emerges upon the introduction of additional interactions that gap the excitation spectrum and give rise to a $\mathbb{Z}_2 $ topological order. This magnetically-fragmented topological altermagnet has fractionalized fermionic excitations with momentum-dependent splitting, in stark contrast to both standard altermagnets and Kitaev spin liquids. In addition, we discover two more altermagnetic phases, including a pseudo-altermagnet that exhibits splitting in the absence of a local order and a half-altermagnet that possesses only one type of fractionalized excitations, similar to a half-metal. We discuss experimental approaches for detecting these phases, including layer-dependent spin and heat transport. Our results highlight the rich physics that can arise due to the interplay between altermagnetism and fractionalized excitations in quantum magnets.