Micromagnetic Simulations Based On The Magnetic Skyrmion Bags

Magnetic skyrmion is a kind of magnetic texture with topological protection.Due to its small size,easy stability,and lower driven current density,it has been extensively studied.However,since skyrmion only has a single magnetic texture,its further development is affected.Therefore,plenty of topological magnetic texture based on the skyrmion have been proposed to facilitate their development,and magnetic skyrmion bags with arbitrary topological charge are one of them.With the prediction and discovery of magnetic skyrmion bags,we can pay attention to the related research on the new degree of freedom about topological charge.In this paper,the dynamics of skyrmion bags are studied mainly using micromagnetic simulation,which includes three parts: the dynamics of skyrmion bags driven by the spin-orbit torque,the skyrmion bags in a magnetic anisotropy gradient,and the spin eigenmodes of skyrmion bags.Firstly,we investigated the dynamics of skyrmion bags driven by the spin-orbit torque in an infinite ferromagnetic film and a nanostrip with a finite length using micromagnetic simulations,and theoretically derived their dynamics through the Thiele equation.In the case of an infinite ferromagnetic film,the velocity of skyrmion bag depends on its topological numbers,while in the case of motion in nanostrips with the skyrmion bag moving along the boundary,the velocity is independent of the topological charge number.The simulation results are in good agreement with the calculation results.Finally,we also drive the skyrmion bag through impurities and defects to study the topological protection of the skyrmion bag.Subsequently,to overcome the disadvantages of high energy consumption and low efficiency of spin-polarized currents,we investigated the skyrmion bags in a magnetic anisotropy gradient.Firstly,we investigate the stability of skyrmion bags under different magnetic anisotropy.Then,we eliminate the boundary potential to study the dynamics of skyrmion bags in a magnetic anisotropy gradient.It is found that the dynamics of skyrmion bags are dependent on the spin textures,and the velocity of skyrmionium with Q = 0 is faster than other skyrmion bags.However,when the skyrmion bags move along the boundary,the velocities of other skyrmion bags are the same as the skyrmionium.Then,we theoretically derived the dynamics of skyrmion bags in the two cases using the Thiele approach and discussed the scope of Thiele equation.Within a certain range,the simulation results are in good agreement with the analytically calculated results.In addition to spintronic devices such as racetrack memory,microwave devices have also recently attracted more attention.Hence,we systematically investigated the spin eigenmodes of skyrmion bags applied a perpendicular microwave magnetic field in a confined disk.A weak peak at lower frequency is found for the skyrmion bags rather than skyrmionium due to the reduced rotational symmetry.In addition,it is found that a lot of spin eigenmodes for skyrmion bags are more complex than the breathing mode of ordinary skyrmion due to the inner interaction between skyrmions.Afterward,a new spin eigenmode appears at larger magnetic field and larger disk size due to the uneven distribution of the interaction in the skyrmion bags.