Electrical Probing of Magnetic Phase Transition and Domain Wall Motion in Single-Crystalline Mn$_5$Ge$_3$ Nanowire*

We studied the magnetic phase transition and domain wall motion in single-crystalline Mn$_{5}$Ge$_{3}$ nanowires fabricated by thermally germaniding Ge nanowires with Mn contacts. The R-T curve showed a clear slope change near 300 K accompanied by a magnetic phase transition from ferro- to para-magnetism. Near this phase transition, the critical behavior was characterized by a power-law relation with a critical exponent of about 0.07. Besides, a cusp revealed in the dR/dT curve at about 67 K was attributed to a possible magnetic transition between non-collinear and collinear ferromagnetic states. Furthermore, temperature-dependent magneto-transport measurements demonstrated a hysteretic, symmetric and stepwise axial magnetoresistance. The interesting features of abrupt jumps indicated the presence of multiple domain walls in the Mn$_{5}$Ge$_{3}$ nanowire and the annihilation of domain walls driven by the magnetic field. The fitting on the temperature-dependent depinning fields yielded an energy barrier of 0.166 eV based on the Kurkijarvi model describing the domain wall depinning as thermally assisted escape from a single energy barrier.