UC Santa Barbara

The understanding and predicting of novel phenomena in magnetic materials is an important theme in condensed matter physics. The most interesting phenomena among them are the ones that exhibit intrinsic quantum behavior, where high degree of entanglement gives rise to macroscopic quantum effect not described in a traditional theory of symmetry breaking. This thesis is a collection of our efforts to combine the theoretical toolkit in analyzing exotic quantum states with recent experimental progress in realizing and finding quantum magnetic materials. We present our study in three parts:

The first part presents a study of the frustrated triangular lattice antiferromagnet NaYbO2. Both spin liquid signatures in zero field and quantum-induced ordering in intermediate fields are observed, suggesting the existence of an intrinsically quantum disordered ground state. Through symmetry analysis and spin wave calculations, we determine the microscopic model relevant to NaYbO2 and map out the phase diagram of magnetic orders in presence of a magnetic field. Our result indicates that NaYbO2 is a promising platform for exploring spin liquid physics with full tunability of field and temperature.

The second part presents an investigation of a chemically related compound LiYbO2, which has instead a stretched diamond lattice structure. Experiments reveal a rich magnetic phase diagram of LiYbO2 that includes a low field incommensurate spiral order and a high field commensurate order. We first show that the former is largely captured by a J1–J2 Heisenberg model, and then employ a phenomenological model to understand the incommensurate-to-commensurate transition at intermediate magnetic fields. Finally, several effects are addressed in order to understand a small variance between the observed and predicted phasing of Yb moments.

The last part is devoted to the classification of symmetric Z2 and U(1) spin liquids on the three-dimensional pyrochlore lattice. We first analyze the magnetic orders linked to specific Z2 quantum spin liquids. We find that under certain conditions, seemingly unrelated orders are intertwined and the conventional orders detected in experiments are accompanied by hidden orders. We then turn to the study of U(1) spin liquid classes and observe that, surprisingly, a large family of them is described by a U(1) gauge field coupled to symmetry protected gapless multi-nodal line spinons, hence uncovering a new prototype of quantum spin liquid beyond the standard example of pyrochlore quantum spin ice. The low temperature specific heat receives a T^{3/2} contribution with logarithmic corrections from the gauge–spinon coupling and the spinon bands, which serves as a simple criterion for the existence of these U(1) nodal line spin liquids.