Topological defects carrying half-integer skyrmion charge in FeN magnetic films

Thin films of nitrogen-implanted iron (FeN), epitaxially grown on a single crystal of ZnSe/GaAs(001), were investigated using atomic and magnetic force microscopy (AFM and MFM) imaging techniques. Using an opportune dose of N2+ ions for implantation, a magnetic domain pattern was observed, consisting of long and straight stripes with a few topological defects in the form of magnetic edge dislocations. In the presence of a uniaxial magnetic anisotropy favoring the z direction, normal to the film plane xy, the stripes are generated by the competition between short-range exchange coupling and long-range magnetic dipole-dipole interaction, and have opposite values of the out-of-plane magnetization [1]. Topological magnetic edge dislocations are randomly distributed in the sample and compensate for local mismatches of the periodic structure. In this work, we studied the driving effect exerted on a magnetic edge dislocation by an external magnetic field applied in plane parallel to the stripes axis. Combining MFM observations in a real FeN film and Landau-Lifshitz-Gilbert (LLG) micromagnetic simulations of the dynamics of a pair of magnetic edge dislocations we show that, for moderate intensity of the applied field, the defects are subjected to a straight displacement along the stripes axis. A theoretical model based on the Thiele equation [2] shows that a magnetic edge dislocation is associated with a nonzero local density of skyrmion charge (Qs=1/2, as for a half-skyrmion). However, the gyrotropic force [2] acting on the dislocation (which is obtained integrating the skyrmion charge density over the whole film) is found to vanish because the defect is embedded in a stripe domain pattern. Consequently, for moderate intensity of the magnetic field, the displacement of the defect is predicted to occur along a straight line, either in the direction of the applied field or in the opposite direction, depending on the in-plane magnetization distribution in the magnetic edge dislocation, but irrespective of the z-polarization. Note that in the absence of the Dzyaloshinskii-Moriya interaction, the half-skyrmion topological defects do not have a given handedness. Finally, their possible use for spintronics applications is critically discussed. [1] A. Hubert and R. Schaefer, Magnetic Domains: The Analysis of Magnetic Microstructures (Springer, Berlin, 1998) [2] A. A. Thiele, J. Appl. Phys. 45 (1974) 37