Quantum altermagnetic instability in disordered metals

The possibility of a zero temperature, altermagnetic instability in anisotropic two dimensional electron systems in the diffusive regime is analyzed, in the presence and absence of spin-orbit coupling. Allowing for ferromagnetism, a phase diagram is built as a function of the parameter that controls anisotropy and the strength of the interactions. It is found that, at zero spin orbit coupling, ferromagnetism only dominates at small values of anisotropy and coupling constant. Larger values of these parameters favour the formation of altermagnetism. At finite spin-orbit coupling, a paramagnetic phase competes with the other two, and a quantum critical point appears. The phase transition from the paramagnetic to the magnetically ordered phases is of second order, while the phase transition between ferromagnet and altermagnet states is first order. The altermagnetic phase is robust under small magnetic fields, displaying a coexistence with a field-induced magnetization.