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The study of topological magnetic excitations has attracted widespreadattention in the past few years. In this thesis, I have studied some examplesof novel topological magnonic phases/phenomena in low-dimensional quantummagnets. The first chapter motivates the research based on the research gap inthis field of study. The second chapter is written to make the thesisself-sufficient and the concepts are explained through examples. In the secondchapter, the following formalisms and physical observables are described:Holstein-Primakoff, bond operator, Schwinger boson, Bogoliubov-Valatin, Grouptheory, Berry-phase, Berry-curvature, Chern number, thermal Hall conductance,Nernst conductivity, dynamical spin structure factor, edge-current. The mainresults of the thesis are shown in the third, fourth, and fifth chapters. Inthe third chapter, I have shown that anti-chiral edge states (co-propagatingedge states) arise in the ferromagnetic Heisenberg model on the honeycomblattice with Dzyaloshinskii-Moriya (DM) interactions. My results suggest thatsuch anti-chiral edge states may be induced in certain realistic models ofquantum magnets. In the fourth chapter, I have found the emergence of manymagnon band-topological phases in the flux state of the Shastry-Sutherlandmodel. I have derived a simple analytical form of the temperature dependence ofderivative of thermal Hall conductivity near the band topological transitionpoint which I propose to be experimentally useful. In the fifth chapter, I haveinvestigated the emergence of Weyl triplons due to inter-layer DM-interactionin a microscopic model of SrCu2(BO3)2, a widely studied frustrated quantummagnet. I have shown that the thermal magnon Hall conductivity has aquasi-linear dependence as a function of the magnetic field in a Weyl-triplonregion.

Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions