Non-Hermitian phase transition in a bulk magnetoelectric system

In phase transitions, a small parameter change near a critical point leads to a qualitative change of system properties. Conventionally, the system remains in thermal equilibrium in this time-reversal-symmetric transfer and, therefore, experiences a change of static properties. An example is the emergence of a magnetization when cooling a ferromagnet below the Curie temperature. When driving a system far from equilibrium, however, the relaxation dynamics itself can go through a distinct, qualitative change, and otherwise inaccessible quantum states of matter may arise. This evolution is typically non-Hermitian, breaking time-reversal symmetry. Phase transitions in non-Hermitian systems are therefore of fundamentally new nature in that the dynamical behavior rather than static properties undergo a qualitative change at a so-called exceptional point. Here we present a non-Hermitian phase transition in a bulk magnetoelectric system. Optical excitation creates electric-charge carriers in a ferromagnetic semiconductor. In a temperature-dependent interplay with the ferromagnetic order, a non-Hermitian change of the relaxation dynamics occurs, manifesting in our time-resolved reflection data as a transition from bi-exponential real to single-exponential complex decay at the exceptional point. Our theory models this behavior and predicts non-Hermitian phase transitions for a large class of magnetoelectric or potentially even multiferroic systems.