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 ferromagnetic exchange coupling and long-range antiferromagnetic dipole-dipole interaction, and have opposite values of the out-of-plane magnetization. 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 shows that, while an isolated magnetic edge dislocation can be associated with a nonzero half-integer skyrmion charge (Qs=±1/2), the gyrotropic force Fgyro acting on the dislocation is obtained integrating the density of skyrmion charge over the whole film: therefore, Fgyro vanishes when 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 theabsence of the Dzyaloshinskii-Moriya interaction, the half-skyrmion topological defects investigated here do not have a given handedness. Their possible use in the field of spintronics is critically discussed.