Neutron scattering and magnetization studies of the spin correlations on the kagomé lattice antiferromagnet KFe₃(Oh)₆(SO₄)₂

Includes bibliographical references (p. 203-222).Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, February 2008.(cont.) The former represents a continuous planar rotational symmetry corresponding to the SO(2) symmetry, while the latter is a discrete symmetry associated with the Z2 symmetry. Depending on which measurements are performed, the critical behavior of the system can belong to either SO(2) or Z2 universality classes with two distinct critical temperatures; one is associated with the spontaneous breaking of the Z2 symmetry, and the other corresponds to a topological order (BKT transition) due to vortex- antivortex binding. The former occurs at a slightly higher temperature than the latter. Neutron scattering measurements show a signature of the BKT transition, while specific heat measurements show a feature of the 2D Ising transition. Above TN, the in-plane spin gap vanishes, and the system retains the SO(2) symmetry when measured with neutron scattering. On the other hand, specific heat measurements show a feature of the 2D Ising transition, since the underlying symmetry of the spin Hamiltonian is the time-reversal or Z2 symmetry.The collective behavior of interacting magnetic moments can be strongly influenced by the topology of the underlying lattice. In geometrically frustrated spin systems, interesting spin dynamics and chiral correlations may develop that are related to the spin arrangement on triangular plaquettes. We report studies of the spin-wave excitations and spin chirality on a two-dimensional geometrically frustrated lattice. Our new chemical synthesis methods allow us to produce large single crystal samples of KFe3(OH)6 (SO4)2, an ideal kagom6 lattice antiferromagnet. The spin-wave excitations have been measured using high-resolution inelastic neutron scattering. We directly observe a flat mode which corresponds to a lifted "zero energy mode," verifying a fundamental prediction for the kagome lattice. A simple Heisenberg spin Hamiltonian provides an excellent fit to our spin-wave data. The antisymmetric Dzyloshinskii-Moriya interaction is the primary source of anisotropy and explains the low-temperature magnetization and spin structure. In addition, combined thermodynamic and neutron scattering measurements reveal that the phase transition to the ordered ground-state is unusual. At low temperatures, application of a magnetic field induces a transition between states with different non-trivial spin- textures. The transition indicated by the sudden increase in the magnetization arises as the spins on alternating layers, which are previously oppositely canted due to the ferromagnetic interplane coupling, rotate 1800 to align the canting moment along the c-axis. These observations are consistent with the ordering induced by the Dzyloshinskii-Moriya interaction. Elastic neutron scattering measurements in high field verify the 180' spin rotation at the transition. The critical behavior in jarosite cannot be categorized by any known universality classes. We propose a scenario where both 2D XY and 2D Ising symmetries are present.by Kittiwit Matan.Ph.D