Vestigial altermagnetism
Interaction effects and fluctuations govern the phase diagram of systems with multiple competing phases. In particular, as individual phases are destroyed by increasing temperature, fluctuations can still produce a composite `vestigial' order given by a product of individual order parameters. Here, we describe vestigial Altermagnetism (AM) from the thermal melting of antiferromagnetic (AFM) and orbital orders (OO) on the square lattice. The coexistence of AFM and OO can give rise to conventional AM with ordering wave vector $\mathbf{Q}=(π,π)$. We show that a distinct `vestigial AM' phase with $\mathbf{Q}=0$ can arise from thermal melting of AFM and OO, and investigate its generic phase diagram. We find that the transition from the high-temperature disordered phase into the vestigial AM phase can be either first or second order, depending on the AFM and OO bare susceptibilities and their interactions. We then investigate the unique experimental signatures by calculating the electron spectral function for a minimal two-orbital model. Despite the fact that the vestigial AM order parameter does not couple to electrons directly, fluctuations dominate the self-energy corrections giving rise to a spin- and orbital-dependent quasi-particle lifetime with the AM symmetry.