Hysteretic Dynamics of Domain Walls at Finite Temperatures

Theory of domain wall motion in a random medium is extended to the case when the driving field is below the zero-temperature depinning threshold and the creep of the domain wall is induced by thermal fluctuations. Subject to an ac drive, the domain wall starts to move when the driving force exceeds an effective threshold which is temperature and frequency dependent. Similar to the case of zero temperature, the hysteresis loop displays three dynamical phase transitions at increasing ac field amplitude $h_0$. The phase diagram in the 3D phase space of temperature, driving force amplitude, and frequency is investigated.