Coercivity Mechanisms And 3D Skyrmions In The Soft/Hard Spherical Core/Shell Material

Soft/hard composites magnetic materials have the large magnetization saturation and the strong coercivity field,contributed by the soft and hard magnetic materials,respectively.Therefore,the composites have the large magnetic energy products academically.However,there's a big discrepancy between the experimental and theoretical data due mainly to the smaller coercivity which is called Brown's Paradox.As it was proposed,a lot of research has been carried out to elucidate the coercivity mechanisms of various materials and hence to solve the coercivity paradox.Previous research on the coercivity mechanism focus on the hard/soft multilayers,where the mathematics is relatively simple.In this work,the soft/hard spherical core/shell model is built to explore the coercivity mechanisms by the analytical way and micromagnetic simulation.This model can also shed light on the coercivity mechanism in so-called single-phased permanent magnets where the soft phase can be regarded as a defect.In particular,a new mountain-curling nucleation mode has been found,which can evolve to three-dimensional(3D)skyrmions in the demagnetization process.Traditionally,the skyrmions are regarded as the two-dimensional nanometer-scale quasi-particles,whose topological protection and low-current mobility make them prospective candidates for spintronic devices.Recently,the 3D skyrmions as the emerging spins are proposed theoretically and experimentally,whose spin structures are more complicated than those of two-dimensional skyrmions.Here the exotic 3D skyrmions are founded in the demagnetization process of the soft/hard spherical core/shell composites for the first time,whose formation,evolution and annihilation play important roles in the magnetization reversal process.The 3D skyrmions are characterized by a skyrmionic core and a pair of Bloch points,of which skyrmionic core are stacked by two-dimensional intermediate skyrmions in the direction of the applied field.Specially,the Bloch points attached to the 3D skyrmion,whose radius can be adjusted freely,are related to the magnetization reversal process.Both calculated nucleation and coercive fields in the spherical composites are sensitive to the size of the soft phase,similar to the hard/soft multilayer systems.As the radius of the soft core R^sincrease,the simulated nucleation and coercive fields decrease monotonically and the coercivity mechanism changes from nucleation to pinning,consistent with the analytical results.The dominant coercivity mechanism is pinning due to the small value of the critical radius,where the coercivity mechanism changes.Such a pinning is closely related to the nucleation and is called self-pinning,as has been done in hard/soft multilayer systems.In particular,the self-pinning of a 3D skyrmion is first found in the spherical composite material,which enriches the understanding of the coercivity mechanism and offers new materials hosting 3D skyrmions.Such a self-pinning of 3D skyrmion is a general phenomenon in both composite and single-phased permanent magnets with defects,where skyrmions can exist in various spherical composites with large range of the radius of the soft phase.