Fractionalized altermagnets: From neighboring and altermagnetic spin liquids to spin-symmetric band splitting

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We study quantum-fluctuation-driven fractionalized phases in the vicinity of altermagnetic order. First, the long-range magnetic orders in the vicinity of collinear altermagnetism are identified; these feature a noncoplanar orbital altermagnet, which has altermagnetic symmetries in spin-rotation-invariant observables. We then describe neighboring fractionalized phases with topological order reached when quantum fluctuations destroy long-range spin order, within Schwinger boson theory and an SU(2) gauge theory of fluctuating magnetism. Discrete symmetries remain broken in some of the fractionalized phases, with the orbital altermagnet becoming an altermagnetic spin liquid. We compute the electronic spectral function in the doped system, which is characterized by split Fermi surfaces with preserved spin-rotation symmetry.