Fluctuation-induced order and thermal transport in frustrated quantum magnets

Abstract

Order-by-disorder is a mechanism of "fluctuation-induced" ordering that occurs in many frustrated magnetic systems where magnetic moments, or spins, are subject to competing interactions. So far, this phenomenon has been discussed in systems where the quantum ground state is not a "classical" product state. In such a case, both thermal and quantum fluctuations act to lift the accidental classical degeneracy, raising the question of whether one mechanism of order-by-disorder is possible without the other.

In this thesis, we present results exposing a novel route to order-by-disorder, one without quantum zero-point fluctuations, in the ferromagnetic pyrochlore Heisenberg model with the Dzyaloshinskii-Moriya (DM) interaction as the leading perturbation. We show that any collinear ferromagnetic state is an exact eigenstate even in the presence of the anisotropic DM interaction, while thermal fluctuations give rise to a preferred magnetization direction. Using linear spin wave theory, we find that the anisotropy appears at lowest order as a sub-leading term in the low-temperature expansion of the free energy. Our results thus show that the phenomenon of thermal order-by-disorder can, in principle, occur even in the absence of quantum zero-point fluctuations driving quantum order-by-disorder. By extending our calculations to non-linear spin wave theory, we find that the ferromagnetic ground state becomes unstable for a spin-1/2 system when the DM interaction is large.

Next, we ask the question of how to adequately characterize order-by-disorder in real materials, and how to distinguish it from conventional energetic ordering. Currently, the only clear and universal signature that has been proposed is a characteristic temperature dependence of the fluctuation-induced pseudo-Goldstone gap. Thus far, this temperature dependence of the pseudo-Goldstone gap has only been characterized in the classical limit. Here, we use non-linear spin wave theory to characterize the pseudo-Goldstone gap in quantum magnets at low temperature, to leading order in 1/S. Using exact sum-rules for the magnon spectral functions, we find that the gap exhibits a distinct power-law temperature dependence. We examine the implications of our results for several candidate materials.

The final part of this thesis examines the thermodynamic and transport properties of the ferromagnetic pyrochlore Lu₂V₂O₇. Over the last decade, there has been immense interest in magnetic materials that host topologically non-trivial excitations. In ordered magnetic insulators, features analogous to those of topological insulators and semimetals can arise in the magnon band structure, and the associated Berry phases can manifest in observable heat and spin transport phenomena. This was unambiguously observed in Lu₂V₂O₇ in the form of a magnon thermal Hall signal, and proposed to arise from the DM interaction. A precise value of the DM interaction is not known, as the values obtained from fitting both thermal transport and inelastic neutron scattering data, as well as from density functional theory, are all mutually inconsistent. Motivated by this, we investigate the effect of additional symmetry allowed perturbations to the spin Hamiltonian of Lu₂V₂O₇ in an attempt to reconcile the different experimental probes of this material. We find that the thermal transport and neutron scattering measurements are consistent with the addition of a small second-nearest-neighbour DM interaction to the model. Conversely, we argue that existing specific heat measurements are inconsistent with neutron scattering experiments and cannot be reconciled with any additional exchange couplings to the bilinear spin-model in the perturbative regime. Our results motivate future thermal transport and specific heat measurements of this material.