Observation of breathing magnetic domain wall constrained at ferromagnetic nanowires

We investigated that the magnetization (M) consisting of a magnetic domain wall (MDW) is thermally fluctuated in the ferromagnetic nanowire at room temperature (300 K). M oscillations in the MDW are elucidated by considering the thermal fluctuation of the 2-dimensional magnetization, M(r, t) = mx (r, t) + my (r, t) at 300 K. We found that thermal fluctuation of the MDW exists at 4 kinds of specific frequencies—1.52 (mode 1), 2.28 (mode 2), 3.58 (mode 3) and 4.52 GHz (mode 4). Especially, the mx and my show stepwise reductions at mode 1 and mode 3 with increasing HT in the transverse direction (-y direction). As the strength of the thermal M fluctuations in the MDW depends on the specific modes of thermal M fluctuations in the MDW, it is clearly seen that it is related to the thermal fluctuation in transverse M of vortex-type MDWs at notches and the behavior of thermal fluctuation at mode 1 and mode 3 corresponds to that of oscillatory depinning field from notches. Thus, this depinning behavior is related to vibrations of the MDW width at the notches, called “breathing mode,” as confirmed by a micromagnetic simulation at 300 K.