Dynamics of domain walls in nanostrips via collective coordinates

The rich internal structure of domain walls in nanostrips [1-2] greatly affects the motion when an external magnetic field or electric current is applied, leading to reduced mobility when the driving force is strong. We generalize Thiele's equations [3] to describe arbitrary wall motion with any number of collective coordinates [4]. The formalism is sufficiently general as to allow the inclusion of spin current, and can be applied to films with in- or out-of-plane magnetic anisotropy. We examine a model wall [5] with two soft modes corresponding to the coordinates of a vortex core. As in a one-dimensional domain wall [6], the system has a steady-state regime below a critical field and an oscillatory regime above it. We calculate the drift velocity in both regions. The results are compared to numerical simulations and to available experimental data [7]. This work was supported in part by the NSF Grant DMR-0520491. [1] R. D. McMichael and M. J. Donahue, IEEE Trans. Magn. 33, 4167 (1997). [2] O. Tchernyshyov and G.-W. Chern, Phys. Rev. Lett. 95, 197204 (2005). [3] A. A. Thiele, Phys. Rev. Lett. 30, 230 (1973). [4] O. Tretiakov et. al, arXiv:0705.4463 [5] H. Youk et al., J. Appl. Phys. 99, 08B101 (2006). [6] N. L. Schryer and L. R. Walker, J. Appl. Phys. 45, 5406 (1974). [7] G. S. D. Beach et al., Nature Mater. 4, 741 (2005)