First Principles Calculation Of Magnetic Interaction

Condensed matter physics is one of the most active and widely applied branches of physics.Magnetism is a common and important property of matter.The intersection of condensed matter physics and magnetism,i.e.magnetism in condensed matter,has made many important achievements,such as spin liquid,spin glass and skyrmion,etc.In order to explain the properties of magnetic materials observed in experiments,such as specific heat,magnetic moment,magnetic susceptibility and magnetic excitation spectrum,it is necessary to build an appropriate magnetic model.Therefore,the quantitative determination of magnetic interactions in the magnetic model has aroused theoretical and experimental interest.In recent years,many first-principles methods have been developed to calculate magnetic interaction,such as energy mapping method,Green's function method and frozen megnon method.Based on the magnetic force theorem and linear response approach,we developed an efficient method to directly calculate the magnetic interaction,and successfully implemented this method in the first-principles calculation software WIEN2 k.This paper is divided into the following parts:In chapter 1,we first introduce the main types of material magnetism,and then introduce the formation mechanism of these magnetism,especially the Heisenberg exchange model.By introducing the spin orbit coupling,we obtain a more general Hamiltonian of exchange interaction.Finally,we introduce the spin wave theory.In chapter 2,we briefly introduce the development of first-principles.In chapter 3,we first introduce the linearized augmented plane wave method.Then we introduce a first-principles method to calculate the magnetic interaction,which is based on the magnetic force theorem and linear response approach.Then we introduce how to implement this method based on WIEN2 k software package.Finally,we give and discuss the results of some examples.In chapter 4,we use first-principles calculations to study the electronic and magnetic properties of quantum spin chain material K2 Cu SO4Cl2and K2 Cu SO4Br2.The first-principles linear response method is used to calculate the magnetic exchange parameters,and the theoretical values are in good agreement with the experimental values.According to signs and magnitudes of the interchain magnetic exchange parameters,we find that the magnetic order of K2 Cu SO4Br2along the b-axis is antiferromagnetic,while the magnetic order of K2 Cu SO4Cl2along the b-axis is strongly frustrated.According to the obtained magnetic exchange parameters,we successfully reproduce the experimental spin-wave dispersion.We also calculated Dzyaloshinskii–Moriya(DM)interaction and found that the DM interactions are stronger in these compounds compared to the interchain magnetic exchange interactions.Finally,the phase diagrams of the two materials are obtained by Monte Carlo simulations.Our results are consistent with previous experiments and give a complete explanation of the magnetic structure.In chapter 5,we systematically study the electronic and magnetic properties of Ca2Fe2O5 with first-principles calculations.Brownmillerite Ca2Fe2O5 has attracted much attention due to its novel properties and wide range of applications.The calculation results show that the valences of irons are + 3 in both octahedral and tetrahedral environments.Based on the first-principles linear response method,we calculate the magnetic exchange interaction.The magnetic exchange interactions are short-range and can be neglected for Fe-Fe atomic pair with bond length greater than 6 ?.Three large exchange interactions determine that the magnetic ground state is G-type antiferromagnetism,which is consistent with the experimental results.The magnetic transition temperature calculated using magnetic exchange parameters agrees well with the experimental results.According to the magnetic exchange parameters,we calculate the spin-wave dispersion.Due to the large exchange parameters,this compound has a large spin wave dispersion.The first-principles linear response method is also used to calculate the DM interaction.In chapter 6,we make a brief summary and give some future prospects.