The magnetic skyrmion, i.e., the nanometric swirling spin vortexlike object with the topolgical charge, is broadly observed in chiral-lattice cubic magnets, typically MnSi; where the cylindrical-shape skyrmions form the two-dimensional hexagonal crystal, in a very narrow temperature-magentic field window for bulk crystals but in a much wider one for tens of nanometer thin films under the perpendicular magnetic field applied. We have investigated the stability of two-dimensional skyrmion states emerging in epitaxial thin films of Mn${}_{1-x}$Fe${}_x$Si with various thicknesses $t$ and iron contents $x$ ($t=10$, 15, and 20 nm; $x=0$, 0.02, and 0.04) by changing the magnetic-field direction. Topological Hall effect arising from the skyrmions is critically suppressed in the course of tilting the applied magnetic field from the normal vector, indicating the collapse of the skyrmion state. Utilizing this observation, the stable region of the skyrmions, which depends on the film thickness relative to the helimagnetic period, can be mapped out in the temperature-magnetic field plane.

• Received 10 December 2013

DOI:https://doi.org/10.1103/PhysRevB.89.064416