Topological Magnetic Structures And Their Modulation By Magnetic Fields In Nanodisks With Multi-Magnetic Anisotropy

Topological magnetic order is a paradigm for studying topological properties of condensed matter.For example,in the last century,two-dimensional magnetic vortex was first studied.Subsequently,a variety of topological magnetic structures were discovered and studied,some are perpendicular magnetic anisotropy stabilized magnetic structures,the most famous one of them is skyrmion,and similar structures include nested skyrmions（skyrmionium）and kπ-skyrmions.There is also a class of in-plane anisotropy stabilized magnetic structures,such as magnetic meron,bimeron and nested bimerons（bimeronium）.The arrangement of the local magnetizations of the topological magnetic structures is consistent with the topological mathematical expressions,and these magnetic structures have important theoretic research and practical application value.For example,they can be used as logic units of new magnetic storage devices,increasing the memory capacity of the devices.Due to their small size,easy manipulation and high topological stability,these magnetic structures have the potential to become next generation of high-rate,low-energy information storage carriers.Previous studies have usually been carried out in materials with only one kind of magnetic anisotropy,and then the magnetic structures in the perpendicular or in-plane anisotropy systems described above were obtained,but there has been few researchs on systems where both perpendicular anisotropy and in-plane anisotropy coexist.Based on this situation,we focused on the influences of composite magnetic anisotropy on magnetic structures and conducted micromagnetic simulation researchs.We designed a special nanodisk with perpendicular magnetic anisotropy in the center and in-plane anisotropy at the edge,which may hold novel magnetic structures.In such a nanodisk,we carried out two simulations,the evolution of magnetic structures under zero field,and controling the topological transformations by magnetic field:In order to understand the influence of the coupling of composite magnetic anisotropy on magnetic structures,we first relaxed the magnetizations under zero field in nanodisks with different in-plane Dzyaloshinskii-Moriya interaction（DMI）magnitudes,starting from the initial state of skyrmion plus in-plane ferromagnetic background.From that,we obtained nine topological structures whose topological charges vary continuously with half integers,there are polymers of multiple merons found in them,which are called meron,bimeron,trimeron,quadrumeron and quintumeron;there are even combinations of skyrmion（or skyrmionium）and bimeron,as well as ₂⁵π-skyrmion with half-integer topological charge.Through this work,we theoretically verified the possibility of generating unique topological magnetic structures in extra thin nanodisks with both perpendicular anisotropy and in-plane anisotropy,that expands the scope of known magnetic structures.In order to useing these topological states to achieve information storage,we then further explored the mutual transformations between different topological states induced by external field.An ideal scheme is applying an external magnetic field,and we performed three simulations by applying different external fields:To obtain a continuous topological transformation process,uniform vertical increasing magnetic field were applied to magnetic structures previously obtained in nine different DMI magnitudes nanodisks.When a z+direction field is applied,there are gradual transformations from the initial state to central multi-skyrmions state,and then to the central polarized state,and the topological charge also changes.However,when the z-direction field is applied,the center of the nanodisks is rapidly polarized due to the negative polarity of various initial states,and no continuous topological phase transformation occurs.The magnetic structures containing multiple skyrmions have half-integer topological charges,can be used as a supplement to the skyrmion bags for multi-bit device design.After studying the influence of constant magnetic field on the magnetic structures,to achieve reversible transformations between different topological states,we assumed that the in-plane ferromagnetic structure is the initial state,and relaxed the system after applying pulsed microwave magnetic fields with different amplitudes and frequencies.From this,we obtained a series of final magnetic structures relating to the amplitude and the frequency,which contain a variety of other topological states mentioned earlier in addition to the ferromagnetic state.This work shows that microwave magnetic fields can be used as a good approach to induce the transformations of ferromagnetic initial states to other topological states,and that the states before and after the transition do not need an external field to be maintained.Finally,we chose a specific nanodisk,using the previously calculated magnetic structures as the initial state,applying pulsed magnetic fields with different frequencies and amplitudes,and obtained a series of unique stable states,and it was found that the alternating magnetic field can indeed achieve the transformations between a variety of topological states.Through analysising the selected different initial states and the corresponding results,we found that the appropriate selections of the frequency and the amplitude of the microwave magnetic field can realize the transition from one topological state to another topological state,and finally the closed-loop transitions between several topological states.In short,by manipulating the microwave magnetic field,we achieved controllable transformations between multiple topological states in nanodisks,which provides a theoretical reference for the design of memory devices.