Diffusion of a magnetic skyrmion in two-dimensional space

Anisotropic skyrmion mass induced by surrounding conduction electrons: A Schwinger-Keldysh field theory approach

“…( 1). This need is typically traced [25][26][27] to the change in the shape of the skyrmion and the corresponding energy cost, particularly in transient situations. In these explanations, the mass term [Eq.…”

Chiral Skyrmions Interacting with Chiral Flowers

“…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...…”

“…14,24,[61][62][63][64][65]68 In 2013, Mijalkov and Volpe demonstrated the possibility that particle-like chiral microswimmers performing circular active Brownian motion can be sorted in a chiral environment formed by using some static obstacle patterns on the substrate, 69,70 where the chirality of circular Brownian motion couples to chiral features present in the environment. As skyrmions also show circular Brownian motion due to their nontrivial topology, [36][37][38]40,41,43,[47][48][49][50]56 it is therefore envisioned that the thermally activated random-walk dynamics of skyrmions may also be modified in a chiral environment due to the skyrmion−substrate interactions, which is the focus of this work. However, it should be noted that active matter systems have some form of self-propulsion, 66,67,69,70 while the Brownian skyrmions are only undergoing thermal motion and are not self-propelled.…”