Pyrochlore oxides where A is a rare-earth ion and B is a transition metal ion form a network of corner -sharing tetrahedra in both the A and the B sites. These compounds are examples of geometrically frustrated magnets where the natural tendency to form long-range ordered ground states is suppressed, resulting in novel exotic quantum states of matter: spin glass, spin liquid, and spin ice. Classical spin ice materials are realized in Dy2Ti2O7 and Ho2Ti2O7. The effective Ising spins interact via a dominant ferromagnetic coupling. Quantum fluctuations imposed on the classical spin ice state introduce spin-flipping processes. The presence of these additional interactions transform a classical spin ice into a quantum spin ice system. The most promising quantum spin ice candidates investigated experimentally are Tb2Ti2O7, Pr2(Sn, Zr)2O7, and Yb2 Ti2O7.

Image created by Curtislee Thornton (undergraduate research student)

A comprehensive analysis of the bimagnon resonant inelastic x-ray scattering (RIXS) intensity spectra of the spatially frustrated Heisenberg model on a square lattice in both the antiferromagnetic and the collinear antiferromagnetic phase revealed RIXS spectrum splitting. Utilizing an interacting spin wave theory study within the ladder approximation Bethe-Salpeter scheme, we found the appearance of a robust two-peak structure over a wide range of the transferred momenta in both magnetically ordered phases. The unfrustrated model has a single-peak structure with a two-peak splitting originating due to spatial anisotropy and frustrated interactions.

Power dissipation in spintronic devices can be minimized through the use of insulating quantum magnets. We investigated the effects of spin and spatial anisotropy on spin conductivity in an insulating Heisenberg magnet. We computed the spin conductivity in both the antiferromagnetic and the collinear antiferromagnetic phase. Based on our studies we conclude that materials with spatial anisotropy are better spin conductors than those with spin anisotropy at both zero and finite temperatures.

We studied the spin dynamics in a 3D quantum antiferromagnet on a face-centered cubic (FCC) lattice. The effects of magnetic field, single-ion anisotropy, and biquadratic interactions were investigated using linear spin wave theory with spins in a canted basis about the Type IIA FCC antiferromagnetic ground state structure which is known to be stable. We calculated the expected finite frequency neutron scattering intensity and give qualitative criteria for typical FCC materials MnO and CoO. The magnetization reduction due to quantum zero point fluctuations was also analyzed.

We studied the spin dynamics in a 3D quantum antiferromagnet on a face-centered cubic (FCC) lattice. The effects of magnetic field, single-ion anisotropy, and biquadratic interactions were investigated using linear spin wave theory with spins in a canted basis about the Type IIA FCC antiferromagnetic ground state structure which is known to be stable. We calculated the expected finite frequency neutron scattering intensity and give qualitative criteria for typical FCC materials MnO and CoO. The magnetization reduction due to quantum zero point fluctuations was also analyzed.

We studied the effects of next-nearest neighbor (NNN) interactions in the two-dimensional ferromagnetic kinetic Ising model exposed to an oscillating field. By tuning the interaction ratio (p = JNNN/JNN) of the NNN (JNNN) to the nearest-neighbor (NN) interaction (JNN) we found that the model undergoes a transition from a regime in which the dynamic order parameter Q is equal to zero to a phase in which Q is not equal to zero. From our studies we concluded that the model can exhibit an interaction induced transition from a deterministic to a stochastic state. Furthermore, we demonstrated that the systems' metastable lifetime is sensitive not only to the lattice size, external field amplitude, and temperature (as found in earlier studies) but also to additional interactions present in the system.

A novel route to a one-dimensional Fulde-Ferrell-Larkin-Ovchinnikov (1D-FFLO) state in the absence of broken time-reversal symmetry was proposed in this paper. At present such a state may be encouraged in a clean AlAs quantum wire. Using the AlAs quantum wire as an example it was shown using bosonization and the renormalization group approach that the 1D-FFLO state can arise due to a combination of Coulomb interactions and the unique bandstructure arrangement of the AlAs quantum wire. The present theoretical proposal is very general and is applicable to other systems with similar fermionic interaction terms.