Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions - Bhowmick, Dhiman (Nanyang Technological University, 2021)
The study of topological magnetic excitations have attracted widespread attention in the past few years. The wide variety of ground state phases realized in different two-dimensional magnets have emerged as versatile platforms for realizing magnetic analogues of topological phases uncovered in electronic systems over the past two decades. Dzyaloshinskii-Moriya(DM) interactions, that are ubiquitous in many quantum magnets, and has been demonstrated to induce a non-trivial topology in the magnetic excitations in many quantum magnets. In particular, signatures of DM-interaction induced topological features observed in the dispersion of magnetic excitations in the geometrically frustrated Shastry-Sutherland compound SrCu2(BO3)2 and honeycomb ferromagnet CrI3 have provided the motivation behind the bulk of the research presented in this thesis. In the first chapter we introduce the background and motivation of our study. We showed that the vastly available materials with a possibility of non-zero symmetry allowed DM-interaction motivate us to study the minimal models of interacting spins related to the materials. In the second chapter we have described the methods that is used to study the spin systems. To describe the spin excitations in the long-range ordered system and dimerized system, we use Holstein-Primakoff transformation and bond-operator formalism respectively. The Schwinger Boson mean field theory is applicable for any generic magnetic ground state and useful to study the system at high temperatures compared with Holstein-Primakoff transformation. After transforming the Hamiltonian into a quadratic bosonic Hamiltonian, it is diagonalized by using Bogoliubov-Valatin transformation. Different observables like Berry-curvature, Chern-number, Dynamical Spin structure factor etc. are calculated by using the single particle wave-function obtained from Bogoliubov-Valatin transformation. A non-zero Berry curvature is a signature of topologically protected edge states in a stripe geometry of a lattice and a systematic way of calculating edge states is also explained in the second chapter. Moreover, in the second chapter the usefulness of symmetry in obtaining band degeneracies and the allowed spin-spin interaction terms are also described. The past theoretical studies show the presence of topological magnons in honeycomb ferromagnetic models due to presence of DM-interaction on a next-nearest neighbour bonds. Recently this kind of DM-interaction is detected in the honeycomb ferromagnet CrI3. This type of DM-interaction induces chiral edge states of magnon in the system and so we named it as chiral DM-interaction. In the third chapter we show that breaking of inversion symmetry at the center of honeycomb structure gives rise to a extra DM-interaction which we named as anti-chiral DM-interaction. We studied the system by using Schwinger Boson mean field theory and Holstein-Primakoff transformation and show that when the antichiral DM-interaction dominates over the chiral DM-interaction, the direction of velocity of the edge states become in the same direction (antichiral edge states). Due to conservation of total number of spins in the system a bulk current flows in the opposite direction relative to the antichiral edge current. In this study we suggested the way to break the inversion symmetries in the materials CrSrTe3, CrGrTe3, AFe2(PO4)2 (A=Ba, Cs, K, La) to achieve antichiral DM-interaction. The presence of antichiral edge states can be detected by using inelastic neutron scattering by detecting the band tilting at K and K' points of magnon bands. Moreover we showed that spin Hall noise spectroscopy at the edges is useful measurements to detect the presence of antichiral edge modes. Magnetic force microscopy is also a promising tool to detect the antichiral magnons at edges. The underlying spin-Hamiltonian of the antiferromagnetic systems in the materials like rare-earth tetraborides (RB4, R=Er,Tm) and U2Pd2In can be described by using extended Shastry-Sutherland models. In previous theoretical studies it is shown that there is a non-collinear spin-state known as flux state exists in the Shastry-Sutherland model in presence of out of plane DM-interaction. Although the presence of perpendicular component of DM-interactions in the rare-earth materials are not known, it can be induced artificially by using circularly polarized light or using heavy-metal alloys. In the fourth chapter, we studied the magnetic excitations in the flux state on Shastry-Sutherland lattice incorporating realistic in-plane DM-interactions (using the DM-interactions present in the low symmetry crystal structure of SrCu2(BO3)4) by using Holstein-Primakoff transformation and showed the presence of topological magnon bands with non-zero Chern-numbers in the system. We found a variety of band topological transitions and showed that each band-topological transition is associated with the logarithmic divergence in the derivative of the thermal Hall conductance. We derived a analytical expression for the temperature dependence of the derivative of thermal Hall conductivity near band topological transition point for a generic spin model. This is useful to extrapolate the energy of band touching point during the band topological phase transition by using thermal Hall effect experiment. In the fifth chapter the spin systems related to Shatry-Sutherland lattice is described. There are three possible phases in Shastry-Sutherland model and those are (i) dimer-phase, (ii) plaquette order phase and (iii) Nèel phase. The dimer-phase material SrCu2(BO3)4 possesses two crystal symmetries; one is low symmetry phase (at low temperature) in which case both the in plane and out of plane DM-interactions are allowed; another is high symmetry phase (at high temperature) in which only the out of plane DM-interaction is allowed. We use bond operator formalism to show the existence of Weyl-triplons in low crystal symmetry structures of Shastry-Sutherland lattice. We predict that the low symmetry phase of SrCu2(BO3)4 at low temperature should contain Weyl-triplons in presence of any finite interlayer perpendicular DM-interactions and at low temperature the Weyl-triplon phenomenon is not altered in presence interlayer in-plane DM-interaction and Heisenberg interaction. There are several band topological transitions happen by changing the external magnetic field and interlayer DM-interaction (which might be varied by applying a pressure). The topological nature of Weyl triplons are confirmed by the presence of the non-zero Berry-curvature and monopole charge of Weyl-point in the bulk system. Again, topological non-triviality is further confirmed by showing that at the surface of the material the Weyl-points are connected by Fermi-arc like surface states which is possible to detect by neutron scattering. Using Kubo-formula of thermal conductivity it is shown that the thermal Hall conductivity of the triplons has a quasi-linear dependence as a function of magnetic field in the Weyl-triplon region and this functional feature is absent in topologically trivial or non-trivial gapped triplon bands.