Topological and magnetic properties of solids

In this dissertation, several spin models with connections to topological states of matter are investigated. In the second chapter, we study pyrochlore iridate bilayer and trilayer thin films grown along the [111] direction at strong coupling [Phys. Rev. Lett. 118, 177201 (2017)]. We obtain the ground state magnetic configurations on a mean field level and carry out a spin-wave analysis about them. In the trilayer case the ground state is found to be the all-in-all-out state, whereas the bilayer has a deformed all-in-all-out state. For all parameters we study, the lowest magnon band in the trilayer case has a nonzero Chern number. In the bilayer case we also find a parameter range with nonzero Chern numbers. We calculate the magnon thermal Hall response for both geometries, finding a striking sign change as a function of temperature. We also use a slave-boson mean-field theory to study the effects of doping on the trilayer system, and discover an unconventional time-reversal symmetry broken d+id superconducting state. In the third chapter, we investigate non-coplanar kagome antiferromagnets with Dzyaloshinskii-Moriya interactions that order in a canted, non-coplanar order, such as iron jarosites [arXiv:1804.09783]. We derive a new expression for the canting angle in the presence of an applied magnetic field, and use the resulting order as a starting point for a spin-wave analysis, finding topological magnon bands, with non-zero Chern numbers. We predict a large magnon thermal Hall effect for iron jarosites, and further show that it can be tuned by transverse magnetic fields, and by the Dzyaloshinskii-Moriya interaction strength. Our prediction suggests that the iron jarosites are a promising candidate material to observe the magnon thermal Hall effect in a noncollinear order. In the the fourth chapter, we study the momentum space entanglement spectrum of certain critical spin chains [Phys. Rev. B. 94, 08112(R) (2016)]. We advocate that the entanglement spectrum contains a gap that separates universal states, determined by the associated critical field theory, from a model specific non-universal part. Evidence from multicritical spin-1 chains described by SU(2)₂ and SU(3)₁ Wess-Zumino-Witten theories is provided.Physic