| Description |
Low-dimensionality, magnetic frustration, and quantum fluctuations are three ingredients that give rise to nontrivial magnetic orders or exotic ground states, such as spin nematics and spin liquids. In this dissertation I discuss some efforts to find novel interesting magnetic phases by cooking up all these ingredients together. First, a large fraction of this dissertation is devoted to the behavior of quantum spin chains in the presence of a uniform Dzyaloshinskii-Moriya (DM) interaction. This problem is analyzed by the bosonization technique. Spin chain is the building block of many materials, such as K2CuSO4(Cl/Br)2 which strongly motivates our study. DM interaction originates from spin-orbit coupling, and is widely present in real materials. Theories of these systems are derived and described for both individual chain and weakly coupled ones at zero and finite temperature and in the presence of external magnetic field. A special geometry of DM interactions-staggered between chains, but uniform within a given chain-leads to a peculiar type of frustration that effectively cancels the transverse interchain coupling and strongly reduces the ordering temperature. By taking advantage of this special geometry of DM interaction, one can construct a chiral spin liquid, which shares some basic features of fractional quantum Hall effect, such as gapped bulk and gapless chiral edge states, in arrays of spin chains. The second part of this dissertation describes the investigation of the interplay between frustration, quantum fluctuations, and magnetic field in the phase diagram of quantum antiferromagnets on triangular lattice. For triangular antiferromagnets with spacial and/or exchange anisotropy and near the fully polarized field, the competition between classical degeneracies and quantum fluctuations leads to multiple phase transitions and highly nontrivial intermediate phases. As for a toy model of a zigzag chain, a spin chain with competing nearest and next-nearest exchange interactions, I investigate quantum fluctuations and geometric frustrations establish a 1/3 magnetization plateau and a bond-nematic state, which has a nonzero vector chirality on every lattice bond and circulating spin currents in every elementary triangle. |
