Theoretical Investigations On The Spin Dynamics Of Magnetic Frustrated Systems

In recent years,the investigations on magnetic frustrated systems have become the focus of intense research in condensed matter physics,since their frustrated interac-tions would result in enormous exotic quantum phase,such as quantum spin liquid.The quantum spin liquid was first proposed by Anderson and is a highly entangled magnetic disorder state.As an important branch of the quantum spin liquid,the Kitaev spin liq-uid starts with the exactly solvable Kitaev model with a spin of 1/2,which is proposed by Kitaev and is defined on a honeycomb lattice.This model hosts bond-directional exchange interactions which result in strong quantum frustration and induce a Z2 spin liquid ground state.Currently,?-RuCl3 has attracted much attentions as one of the most likely materials to achieve Kitaev spin liquid.It is a Mott insulator derived by the interplay of crystal field,spin-orbital coupling and Coulomb interactions,in which the exchange interactions required to achieve Kitaev spin liquid can be realised.Thus,it is extremely important to study the low-energy behavior of a-RuCl3 for the investi-gation of quantum spin liquids.On the other hand,fractionalized excitation is a major characteristic of quantum spin liquid,and for magnetic ordered phase in spin frustrated system,recent experiments have found that fractionalized excitations may also exist in high-energy region.Therefore,it is of great significance to theoretically study the spin excitation spectrum in frustrated spin system not only for search for quantum spin liq-uid but also for the comprehensive understanding of the spin dynamics of the magnetic frustrated system.In the first chapter of this thesis,we first review insulators induced by different mechanisms.Then we review quantum spin liquids caused by frustrations and quantum fluctuations,and finally introduce the related experimental measurement methods.In the second part,we introduce our theoretical models and methods in detail.In the third and fourth chapters,we investigate the spin dynamics of the material ?-RuCl3 and the square-lattice antiferromagnetic J1-J2 Heisenberg model:1.We derive a low-energy effective exchange model from electronic model in ?-RuC13,and study the spin-wave excitations by the linear spin-wave theory.The valance electrons in magnetic ion Ru3+have a 4d5 configuration,in which d orbitals are split into eg and t2g orbitals by the octahedral crystal field.Then the low-energy states t2g5 are divided into a low-energy Kramers doublet with an effective spin of 1/2 and a high-energy quartet.In previous studies,the effective exchange models were derived from the t2g orbitals model,in which the effects of eg orbitals on the low-energy behavior were ignored.Recent experiments have found that the energy gap between the eg and t2g orbitals is of the same order of magnitude as the Coulomb interaction,so we begin with the five-orbital model containing all d orbitals.Firstly,based on the energy-band structure calculated from the first-principle method,we obtain the five-orbital tight-bind model.Then,starting from perturbation theory,we derive an effective isospin-1/2 exchange model by projecting the five-orbital Hubbard model onto the lowest Kramers doublet in the large Coulomb interaction limit.By analysing the effective exchange terms,we find that the effective exchange model can be further reduced to the K-?model containing a ferromagnetic nearest-neighbor(NN)Kitaev interaction(K)and a NN off-diagonal exchange interaction(?).By working with the neutron-scattering-experiment group and using the linear spin-wave theory,we find that the excitation spectrum calculated from the K-? model can well describe the spin excitation spectrum of inelastic-neutron-scattering measurement,confirming that there is a strong Kitaev magnetic exchange interaction in ?-RuCl3.2.By employing the cluster-perturbation method and variational-Monte-Carlo method,we study the spin dynamics of the spin-1/2 J1-J2 Heisenberg model on square lattice.As J2 increases,the magnetic frustration is first enhanced and then weakened,which results in the ground state from the Neel antiferromagnetic phase into the quan-turn disordered state and finally into the stripe order.In Neel antiferromagnetic phase(J2/J1<0.4),we find that a continuum in high-energy region of magnon excitation appears near momentum(?,0),which is consistent with neutron scattering experiment.Near strongly frustrated point(J2=0.5J1),spin excitations become a very broad continuum,and the Goldstone excitation mode closely related to the Neel state disap-pears,indicating that the system become a nonmagnetic quantum phase.In stripe order(J2/J1>0.6),there is also a continuum similar to Neel phase in the high-energy re-gion of magnon excitation,but the continuum appears near(?/2,?/2).Moreover,by using the variational-Monte-Carlo and mean-field methods,we identify that the non-magnetic phase is a Z2 quantum spin liquid,and the high-energy continuum in both magnetic ordered phases is from the fractionalization of spin excitations,namely the deconfinement of spinons.In addition,we explain why fractionalized excitations in both magnetic ordered phases occur at different momentum points.