Spin-wave Calculations For Helimagnets

Low-dimensional quantum antiferromagnetic systems have witnessed a great deal of interest for a long time due to their deep connection with magnetic properties of hightemperature superconductors.However,low-dimensional quantum spin systems are of interest in their own right as fruitful resources of novel and exotic quantum phases,such as valence bond solids and spin liquids.The most indispensable ingredient in terms of the emergence of these exotic quantum states is the quantum fluctuation caused by the SU(2)commutation relation of the spin operators.Frustration,on the other hand,acts as a very efficacious way of enhancing the quantum fluctuation effects and can even lead to the "melting"of magnetic long range order at zero temperature.If such magnetic long range order survives,it is expected that the quantum fluctuation effects will be suppressed and can have only weak influences on the thermodynamic properties of the system.Nevertheless,exceptions may occur,and as we shall see,quantum fluctuation can exhibit decisive consequences in noncollinear quantum antiferromagnets,despite the fact that the system is long range ordered.In this dissertation,we study several particular phenomena in the non-collinearly ordered quantum antiferromagnets including the magnon decay and the so called spin Casimir effect.The dissertation consists of six chapters:In chapter one,we give a brief introduction for the related theoretical background,spin wave expansion methods,and an outline of some fundamental conceptions.In chapter two,we present a theoretical overview of the phenomena of spontaneous magnon decays in non-collinearly ordered quantum antiferromagnets.The spontaneous decay of spin wave in quantum spin systems is a fascinating many-body effect,which has recently been observed in neutron-scattering experiments.An introduction to the effect of cubic and quartic magnon interactions and a discussion of their relations with magnon decay are provided.The dynamical properties of the quantum Heisenberg antiferromagnet on a triangular lattice are discussed intensively within the framework of spin-wave theory.Analytical results are compared with available experimental data and the experimental observations of the decay-related effects are briefly discussed.In chapter three,we present a detailed analysis of the spin-wave expansion on the spatial anisotropic triangular lattice Heisenberg antiferromagnets.The phenomenon that the classical ordering vector is modified by the quantum fluctuation is carefully studied and its Casimir nature is revealed.To describe these spin Casimir effects quantitatively we further define a spin Casimir torque,which describes a long-range torque effect generated by quantum spin fluctuation.Base on these results,it is shown that the presence of the spin Casimir effect can induce divergent results in a conventional spin-wave expansion even though the longrange order is stable.To solve this problem,we have developed a self-consistent approach in the frame of the spin-wave theory,which is applicable to regularize all the divergences in the 1/S expansion effectively.This accomplishment allows us to calculate many spinwave properties beyond linear approximation.Analytical results are compared with available numerical results and the possible experimental application of our theory is briefly discussed.In chapter four,we present a comprehensive study of the static magnetic properties of the long-range ordered quasi-one dimensional J1-J2 systems with a newly developed torque equilibrium spin-wave expansion approach,which can describe the spin Casimir and magnon decay effects in a unified framework.While the framework does not lose the generality,our discussion will be restricted to two representative systems,each of which has only one type of inter-chain coupling(J3 or J4)and is referred to the J3-or J4-system respectively.In spite of the long-range spiral order,the magnetic properties of these systems turn out to be highly nontrivial due to the incommensurate noncollinear spin configuration and the strong quantum fluctuation effects enhanced by the frustration and low-dimensionality.Both the systems show prominent spin Casimir effects induced by the vacuum fluctuation of the spin waves and related modification of the ordering vector,quantum critical point's position and sublattice magnetization.In chapter five,we present a comprehensive study of the dynamical magnetic properties of the long-range ordered quasi-one dimensional J1-J2 systems.Significant and spontaneous magnon decay effects are manifested in the quantum corrections to the excitation spectrum,including the broadening of the spectrum linewidth and downward renormalization of the excitation energy.Furthermore,the excitation spectrum appears to be very sensitive to the types of the inter-chain coupling and manifests three distinct features:(?)the magnon decay patterns between J3-and J4-system are very different,(?)the renormalized spectrum and the overall decay rate of the J3-and J4-systems show very different sensitivities to the magnetic anisotropy,and(?)there is a nearly flat mode in the renormalized magnon spectrum of the J4-system along the X-M direction.By adjusting the strength of magnetic anisotropy and varying the approximation scheme,it is revealed that these striking distinct features are quite robust and have deep connection with both the spin Casimir and the magnon decay effects.Thus these special consequences of the inter-chain coupling on the spin wave dynamics may be served as a set of probes for different types of inter-chain couplings in experiments.At last,to guide experimental measurements such as inelastic neutron scattering in realistic materials and complement our theoretical framework,we develop the analytical theory of the dynamical structure factor within the torque equilibrium formulism and provide the explicit results of the quasi-one dimensional J1-J2 systems.The last chapter presents a summary of this dissertation,and then gives some outlook for future investigation.