Title: Laser-driven 1st order spin reorientation and Verwey phase transitions in the magnetite Fe$_3$O$_4$ beyond the range of thermodynamic equilibrium

Abstract: Ultrafast photo-induced phase transitions occurring under the impact of femtosecond laser pulses provide versatile opportunities to switch solids between distinctly-different crystalline, electronic, and spin states and thus modify their functional properties in a significant manner. In this paper, we report on the laser-induced spin reorientation and Verwey phase transitions in a ferrimagnetic single crystalline magnetite Fe$_3$O$_4$. Using femtosecond optical and magneto-optical pump-probe techniques, we define the range of initial sample temperatures and laser fluences when partial or complete photo-induced phase transitions occur from a monoclinic insulating to a cubic metallic state with concomitant switching of magnetic anisotropy from the uniaxial to the cubic one. We thus reveal a connection between these phase transitions when driven by femtosecond laser pulses. Using transient linear and quadratic magneto-optical effects, we examine magnetization dynamics launched by the magnetic anisotropy axis switching, and unveil the presence of the domains undergoing the laser-induced phase transitions even below the established thershold fluence for the transitions, as well as when the material is initially in the cubic phase. This is the manifestation of the 1st order of these laser-induced phase transitions beyond the range of thermodynamic equilibrium.