Theoreticacl Study Of Magnetic Anisotropy And Flat Band Systems

Magnetic anisotropy is an important branch in the field of magnetic research.In general,magnetic anisotropy is manifested in the fact that the magnetic properties of an object have a direction-dependent response to an external field.It describes how materials are more or less magnetized along certain directions.According to different mechanisms,magnetic anisotropy is mainly divided into four categories:magnetocrys-talline anisotropy,shape anisotropy,induced anisotropy,and stress anisotropy.Among them,magnetocrystalline anisotropy occupies a core position in the magnetic anisotropy of many magnetic materials,especially permanent magnets,and depends on the specific lattice structure.It is also the center of this work.Today a hot spot in the field of magnetic research is magnetic thin films and mul-tilayer film materials.This type of material with significant perpendicular magnetic anisotropy promotes the development of magnetic devices,especially magnetic ran-dom access memory,and facilitates the application of multiple magnetic subdisciplines including spintronics and nanomagnetism.Experimental and theoretical studies have shown that spin-orbit coupling is the key source of perpendicular magnetic anisotropy.In particular,the perpendicular magnetic anisotropy of 3d transition metal films is only determined by the second-order perturbation of spin-orbit coupling.The perpendicu-lar anisotropy of most 3d transition metal thin film materials is about 1 me V,which is an order of magnitude smaller than the spin-orbit coupling strength in these systems.Therefore,it is an important research direction to explore the relationship between spin-orbit coupling and magnetic anisotropy and to find materials with strong perpendicular magnetic anisotropy.In addition to being an ideal platform for strong magnetocrystalline anisotropy,the flat band is also an ideal system for the study of various many-body correlation phenom-ena,and recent studies have shown that the singularity of the flat band can also lead to some novel quantum states of matter.For this reason,the co-authors and I proposed an exchange field model with two orbitals for the theoretical study of magnetocrystalline anisotropy.I calculated this model’s magnetocrystalline anisotropy energies and mag-netic susceptibilities on the triangular lattice,Kagome lattice,and pyrochlore lattice.The results show that magnetocrystalline anisotropy energies of Kagome lattice and py-rochlore lattice have a linear relation to spin-orbit coupling due to their band structures containing flat bands as ground states,and magnetic susceptibilities also exhibit notice-able anisotropy in the vertical and in-plane directions.As a comparison,the calculation on the triangular lattice shows that the magnetocrystalline anisotropy near the Dirac points can be linearly related to the spin-orbit coupling,while in most other regions of the Brillouin zone,due to the influence of the energy bandwidth,the magnetocrystalline anisotropy energies are a second-order perturbation of spin-orbit coupling,and the over-all results deviate from the quadratic relationship.In addition,I replaced the spin-orbit coupling inside the atoms on the lattice with the Kane-Mele type spin-orbit coupling and calculated the magnetocrystalline anisotropy energy on the Kagome lattice.The Kane-Mele spin-orbit coupling comes from the Coulomb interaction caused by elec-trons’hoppings between lattice points,which affects the energy band structure of the system,making the original flat band appear wide,resulting in a relationship between first-order and second-order perturbations between magnetocrystalline anisotropy and spin-orbit coupling.The inspiration brought by these results is that the flat-band system may be an important direction to find strong magnetic anisotropy materials.Therefore,my collaborators and I have established a systematic method for con-structing a flat-band system.By constructing geometric units with destructive inter-ference,they are spliced into compact localized states with boundaries,and then lat-tice structures with flat bands are obtained through translation operations.Using this method,my collaborators and I obtained a series of two-dimensional flat-band systems in the single-orbital model and the two-orbital{,}model.Notably,the image of destructive interference is richer in the two-orbital model.According to the relative strength of the（）bond and（）bond,the electronic wave functions of adjacent lat-tice points inside the compact localized state jointly affect the destructive interference through amplitude,phase,etc.In addition,the compact localized states correspond-ing to the flat bands have physical images beyond destructive interference.Taking the graphene lattice as an example,since the（）bonds are frozen,the electrons con-fined to the compact localized state cannot make outward hoppings.I generalized this physical picture to more 2D structures with flat bands.In addition,I also discussed the flat-band system including the next-nearest neighbor and the third-nearest-neighbor hopping terms.I found that when the relative strength of thebond andbond is ap-propriate,the introduction of high-order hopping terms can still guarantee the existence of compact localized states and destructive interference images,which has reference significance for finding stable flat-band systems.The results of the study on the flat band system laid the foundation for the further study of magnetic anisotropy.