Magnetic and Topological Aspects of Spin Liquid Candidates with Strong Spin-orbit Coupling

Correlated transition metal compounds with strong spin-orbit coupling have been the subject of great interest to condensed matter physicists recently. They provide an excellent playground in which to explore various quantum phases of matter ranging from exotic magnetism to topological orders. In this thesis, we specifically focus on materials that can be effectively described by a total angular momentum j = 1/2 pseudospin degree of freedom owing to strong spin-orbit coupling. This j = 1/2 pseudospin degree of freedom serves as a building block with which it can be made possible to realize different quantum phases of matter. In particular, we study magnetic and topological aspects of Ir- and Ru-based transition metal compounds that are candidates for a material realization of the long-sought quantum spin liquid phase - a highly entangled state of matter in which the electrons’ spin do not magnetically order, or “freeze,” at low temperature. We begin by investigating possible quantum magnetic orderings arising in layered 2D triangular materials effectively described by j = 1/2 spins, and apply our findings to Ba_3IrTi_2O_9 . We then turn our attention to potential symmetry protected topological phases in single layers of α-RuCl_3 and A_2IrO_3 (A = Li, Na). Finally we show how it is possible to stabilize topological order in correlated honeycomb materials such as the Kitaev spin liquid candidate α-RuCl_3 . We conclude by considering potential avenues for future research.Ph.D