Brownian Motion of Magnetic Skyrmions in One- and Two-Dimensional Systems

Chiral Skyrmions Interacting with Chiral Flowers

“…The skyrmion motion guided by the square edges is similar to that guided by grain boundaries, which may enhance the skyrmion diffusion. The Brownian gyromotion of a skyrmion is a feature of its topological nature, which is due to the Magnus force associated with the net skyrmion number. − ,,,,− , We note that the Magnus force is absent in the antiferromagnetic system, where a skyrmion may not show Brownian gyromotion. , …”

“…34−58 For example, a skyrmion driven by the spin−orbit torques may show the skyrmion Hall effect, 39,42,59,60 where the skyrmion moves at an angle with respect to the applied current direction. On the other hand, a skyrmion driven by thermal effects may show the Brownian gyromotion, [36][37][38]40,41,43,[47][48][49][50]56 where the skyrmion tends to move in circular trajectories during the random walk. Skyrmions can also be driven into directional motion by thermal gradients.…”

“…The Brownian gyromotion of a skyrmion is a feature of its topological nature, which is due to the Magnus force associated with the net skyrmion number. [36][37][38]40,41,43,[47][48][49][50]56 We note that the Magnus force is absent in the antiferromagnetic system, where a skyrmion may not show Brownian gyromotion. 38,56 The time-dependent velocities of the skyrmions with Q = −1 and Q = +1 interacting with the square are given in Figure 2(e) and 2(f), respectively.…”

“…The dynamics of chiral skyrmions stabilized by chiral exchange interactions , in ferromagnets include two aspects, i.e., the motion driven by applied forces − , and the spontaneous diffusion induced by thermal fluctuations. − For example, a skyrmion driven by the spin–orbit torques may show the skyrmion Hall effect, ,,, where the skyrmion moves at an angle with respect to the applied current direction. On the other hand, a skyrmion driven by thermal effects may show the Brownian gyromotion, − ,,,,− , where the skyrmion tends to move in circular trajectories during the random walk. Skyrmions can also be driven into directional motion by thermal gradients. ,,, Both the skyrmion Hall effect and skyrmion Brownian diffusion in the ferromagnetic and ferrimagnetic systems depend on the topological charge carried by the skyrmion (i.e., the skyrmion number), which is defined as Q = 1 4 π ∫ bold-italicm · ( ∂ m ∂ x × ∂ m ∂ y ) normald italicx normald italicy with m being the redu...…”

“…We first show the typical Brownian gyromotion of a ferromagnetic skyrmion within a square obstacle in a two-dimensional model, which results in the confinement of the skyrmion. ,, The length, width, and thickness of the ferromagnetic layer equal 256, 256, and 1 nm, respectively. The square pattern is made of four obstacle bars, which are rectangle regions locally modified to have enhanced PMA K 0 .…”