| This dissertation presents analytic and numerical studies of magnetism in strongly correlated solid-state systems. In diverse probes such as neutron scattering, scanning tunneling microscope (STM), muon spin rotation (musR) and nuclear magnetic resonance (NMR), strongly correlated systems often exhibit evidence of local electronic inhomogeneity. Competing tendencies in these systems can lead to spontaneous nanoscale structures, such as stripes and checkerboards. Strongly correlated systems also exhibit a wide variety of homogeneous phases and transitions among these phases. In the three chapters of this dissertation, some of the consequences of these complex features are explored.; First, spin waves and magnetic excitations for well-ordered spin structures are studied by using a suitably parametrized Heisenberg model. Both site-centered and bond-centered antiphase domain walls are considered for a range of spacings between stripes and checkerboard antiphase domain walls. The dynamical structure factor of spin waves for weakly coupled vertical stripes strongly resembles recent high energy neutron scattering data in cuprate superconductors. At low energy, spin wave cones may not always be resolvable experimentally because their intensity depends strongly on the coupling across the stripes. Spin wave theory is very successful at describing the spin-ordered systems.; Second, quasi-two-dimensional spin systems are explored by using the Stochastic Series Expansion Quantum Monte Carlo method. The order-disorder phase transitions are studied for both static and dynamic bond-diluted Heisenberg spin systems. The quantum critical point is found to be sensitive to the nature of the bond configurations. A study of the ground state energy shows possible phase separation. Varying the interlayer coupling J', the Neel temperature TN and universal scalings are studied for weakly coupled Heisenberg antiferromagnetic layers consisting of coupled ladders. This system can be tuned to different two-dimensional scaling regimes for T > TN.; Third, a two-dimensional Heisenberg antiferromagnet with nearest-neighbor and four-spin ring exchange is studied, which exhibits a quantum phase transition from the Valence Bond Solid (VBS) phase to Neel order. Using singlet-triplet basis, the triplon spectrum starting from the VBS phase is calculated and strong quantum fluctuations are found. The features are consistent with a critical point exhibiting so-called deconfined quantum criticality. |
