  The study of topological magnetic excitations has attracted widespread
attention in the past few years. In this thesis, I have studied some examples
of novel topological magnonic phases/phenomena in low-dimensional quantum
magnets. The first chapter motivates the research based on the research gap in
this field of study. The second chapter is written to make the thesis
self-sufficient and the concepts are explained through examples. In the second
chapter, the following formalisms and physical observables are described:
Holstein-Primakoff, bond operator, Schwinger boson, Bogoliubov-Valatin, Group
theory, Berry-phase, Berry-curvature, Chern number, thermal Hall conductance,
Nernst conductivity, dynamical spin structure factor, edge-current. The main
results of the thesis are shown in the third, fourth, and fifth chapters. In
the third chapter, I have shown that anti-chiral edge states (co-propagating
edge states) arise in the ferromagnetic Heisenberg model on the honeycomb
lattice with Dzyaloshinskii-Moriya (DM) interactions. My results suggest that
such anti-chiral edge states may be induced in certain realistic models of
quantum magnets. In the fourth chapter, I have found the emergence of many
magnon band-topological phases in the flux state of the Shastry-Sutherland
model. I have derived a simple analytical form of the temperature dependence of
derivative of thermal Hall conductivity near the band topological transition
point which I propose to be experimentally useful. In the fifth chapter, I have
investigated the emergence of Weyl triplons due to inter-layer DM-interaction
in a microscopic model of SrCu2(BO3)2, a widely studied frustrated quantum
magnet. I have shown that the thermal magnon Hall conductivity has a
quasi-linear dependence as a function of the magnetic field in a Weyl-triplon
region.
