Universal criteria for single femtosecond pulse ultrafast magnetization switching in ferrimagnets

Single-pulse switching has been experimentally demonstrated in ferrimagnetic GdFeCo and Mn$_2$Ru$_x$Ga alloys. Complete understanding of single-pulse switching is missing due to the lack of an established theory accurately describing the transition to the non-equilibrium reversal path induced by femtosecond laser photo-excitation. In this work we present general macroscopic theory for the magnetization dynamics of ferrimagnetic materials upon femtosecond laser excitation. Our theory reproduces quantitatively all stages of the switching process observed in experiments. We directly compare our theory to computer simulations using atomistic spin dynamics methods for both GdFeCo and Mn$_2$Ru$_x$Ga alloys. We provide explicit expressions for the magnetization relaxation rates in terms of microscopic parameters which allows us to propose universal criteria for switching in ferrimagnets.