Topological and magnetic properties of solids

Laurell, Pontus Bengt Johan
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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.