Spin relaxation in geometrically frustrated pyrochlores

• Main Author: Dunsiger, Sarah Ruth
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/12990

This thesis describes µSR experiments which focus on systems where the magnetic ions occupy the vertices of edge or corner sharing triangular units, in particular the pyrochlores A₂B₂O₇. The scientific interest in pyrochlores is based on the fact that they display novel magnetic behaviour at low temperatures due to geometrical frustration. The ground state of these systems is sensitively dependent on such factors as the range of the spin-spin interactions, disorder, anisotropy, thermal and quantum fluctuations. For example, Y₂Mo₂O₇ shows many features reminiscent of a conventional spin glass, even though this material has nominally zero chemical disorder. It is found that the muon spin polarisation obeys a time-field scaling relation which indicates that the spin-spin autocorrelation function has a power law form in time, in stark contrast with the exponential form often assumed for conventional magnets above their transition temperature. Gd₂Ti₂O₇ shows long range order, but only at a temperature much lower than its Curie-Weiss temperature, a signature of a frustrated system. In the paramagnetic regime, it is well described by an isotropic Heisenberg Hamiltonian with nearest neighbour couplings in the presence of a Zeeman interaction, from which the spin-spin autocorrelation function may be calculated as a power series in time. The muon spin relaxation rate decreases with magnetic field as the Zeeman energy becomes comparable with the exchange coupling between Gd spins. Thus, an independent measure of the exchange coupling or equivalently the Gd spin fluctuation rate is extracted. By contrast, Tb₂Ti₂O₇ has been identified as a type of cooperative paramagnet. Short range correlations develop below 50 K. However, there is no long range ordering down to very low temperatures (0.075 K). The Tb³⁺ ion is subject to strong crystal electric field effects: point charge calculations indicate that this system is Ising like at low temperatures. Thus this system may be analogous to water ice, a system theoretically predicted to have finite entropy at zero temperature. It is possible to qualitatively explain the unusual changes in T₁⁻¹ as a function of applied magnetic field which are also observed using µSR.