| Magnetism is an old subject.With the development of condensed matter physic-s,the study of magnetism in condensed matter is becoming more and more impor-tant.Many exotic magnetic materials have been discovered,such as spin glass,spin ice,quantum spin liquid,skyrmion,Axion insulators,magnetic topological insulators,topological magnon insulators,and so on.Magnetic interactions are very important for the investigation of magnetic materials.Experimentally,people tend to construc-t suitable magnetic models to quantitatively describe the observed experimental data,such as magnetic moment,magnetic specific heat,magnetic susceptibility as a func-tion of temperature,and magnetic excitation spectrum measured by neutron scattering experiments.In recent years,the theoretical prediction of magnetic interaction based on first principles has attracted research interest.A common numerical calculation method is based on the energy mapping between different magnetic configurations and spin model.This energy mapping method is simple and effective,and has been widely used.However,the energy mapping method has several drawbacks that are difficult to overcome.Therefore,people have also developed several methods to calculate magnet-ic interactions directly from first-principles,such as Green function method and frozen magnon method.Based on the combining magnetic force theorem and linear-response approach,we have implemented this efficient method to calculate spin exchange in-teractions using first principles Wien2k,and it is already used to investigate magnetic materials.The overview of each chapter is listed as follows:In chapter 1,we briefly introduce the classification of magnetic materials and magnetic interactions firstly.Secondly,the spin-orbit coupling is introduced.Finally,we introduce magnetocrystalline anisotropy and Dzyaloshinskii-Moriya(DM)interac-tion.In chapter 2,we introduce the density functional theory and the linearized aug-mented plane wave method.In chapter 3,we first introduce the energy mapping method and how to use the en-ergy mapping method to calculate the Heisenberg interaction and the DM interaction.Then we introduce the first principles approach of calculating magnetic interactions based on the linear response theory,and we implemented it in the first-principles soft-ware Wien2k.Finally,we give the calculated results of some classical materials as examples.In chapter 4,using first-principles calculation and perturbation theory,we present a comprehensive investigation of the 5d transition-metal oxides Na4IrO4.In 5d tran-sition metal oxides,novel properties arise from the interplay of electron correlations and spin-orbit interactions.Na4IrO4,where 5d transition-metal Ir atom occupies the center of the square-planar coordination environment,has attracted research interest.We discuss its electronic structures,determine its magnetic ground state configuration,and find a giant MAE for this compound.We estimate the magnetic parameters in the generalized symmetry-allowed spin model,and find that the next nearest neighbor exchange interaction J2 is much larger than other intersite exchange interactions and results in the magnetic ground state configuration.The numerical results reveal that the anisotropy of interatomic spin exchange interaction is quite small and the huge MAE comes from the single-ion anisotropy.This compound has a large spin gap but very narrow spin-wave dispersion,due to the large single-ion anisotropy and quite small intersite exchange couplings.We clarify these remarkable magnetic features are orig-inated from its highly isolated and low-symmetry IrO4 moiety.We also explore the possibility to further enhance the MAE.In chapter 5,using first-principles calculation,we presented a comprehensive in-vestigation of Cu3TeO6.Recently topological aspects of magnon band structure have attracted much interest,and especially,the Dirac magnons in Cu3TeO6 have been ob-served experimentally.The calculations show that Cu3TeO6 is an insulator with a band gap about 2.07 eV and the calculated magnetic moment of the Cu ions is 0.81 ?B.Using magnetic force theorem and a first-principles linear-response approach,we es-timate the spin exchange parameters.The calculated exchange parameters are short-range and can be neglected for the distance more than 7A.The strongest terms J1 and J9 are compatible with the magnetic ground state,while the terms J2,J4,and J10 are much smaller and not compatible with the magnetic ground states,which is consistent with the modest frustration in this compound.We calculated the magnon spectra us-ing linear spin wave theory and the calculated spin wave is in good agreement with the experiment.The calculated neutron scattering cross section also agrees very well with the experiments.We also proved analytically that the "sum rule" only holds up to the 11th nearest-neighbour interactions.The calculated DM interactions lead to a very small canting angle about 1.3°of non-collinear antiferromagnetic order.The weak DMIs are the possible reason why the previous experimental work did not observe the nodal lines.In chapter 6,by applying the filling constraints,we discover several magnetic topological semimetals:XFe4Ge2(X=Y,Lu)and Mn3Pt.Magnetism,coupled with nontrivial band topology,can bring about many interesting and exotic phenomena,so that magnetic topological materials have attracted persistent research interest.Using a first-principles calculation,we presented a comprehensive investigation of XFe4Ge2(X=Y,Lu).The calculations show that YFe4Ge2 is a metal with a Dirac cone located at S point near the Fermi level,which is protected by the symmetry operations of magnetic stucture.We have varied the value of U from 0 to 4.0 eV,and the results show that Dirac point always exists,since the topological property is filling-enforced and independent on U.Moreover,when the magnetic moments have a small nonzero z-direction compo-nent through breaking PT symmetry,the Dirac point would split into Weyl nodes.We also perform the first-principles calculations based on the high-temperature collinear antiferromagnetic configuration of Mn3Pt.The calculation results and symmetry analysis show that 4-fold degenerate band crossings occur in the whole high symmetry path of A-Z,thus it is also a topological material.In chapter 7,we make a brief summary and give an outlook. |
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