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Abstract:

α-��ܰ��₃ is a major candidate for the realization of the Kitaev quantum spin liquid, but its zigzag antiferromagnetic order at low temperatures indicates deviations from the Kitaev model. We have quantified the spin Hamiltonian of α-��ܰ��₃ by a resonant inelastic x-ray scattering study at the Ru L₃ absorption edge. In the paramagnetic state, the quasi-elastic intensity of magnetic excitations has a broad maximum around the zone center without any local maxima at the zigzag magnetic Bragg wavevectors. This finding implies that the zigzag order is fragile and readily destabilized by competing ferromagnetic correlations. The classical ground state of the experimentally determined Hamiltonian is actually ferromagnetic. The zigzag state is stabilized by quantum fluctuations, leaving ferromagnetism - along with the Kitaev spin liquid - as energetically proximate metastable states. The three closely competing states and their collective excitations hold the key to the theoretical understanding of the unusual properties of α-��ܰ��₃ in magnetic fields.

Abstract:

Spin liquids, not showing a spontaneous-symmetry-breaking order down to low temperatures, serve as a platform for unconventional spin-correlated phenomena beyond the Landau paradigm. Numerous varieties of classical and quantum spin liquids (QSL) motivate the experimental identification of different spin liquid states. However, the lack of an unambiguous signature makes the identification attempts often unsuccessful. A new experimental approach is clearly needed, and an emerging concept is to use spin noise as fingerprints of spin liquid states.

In this thesis, I perform spin noise spectroscopy on spin liquid compounds whose specific states have not been established. Chapter 1 presents an introduction to different classes of spin liquid states and the difficulty in their identification, motivating a new experimental approach. Chapter 2 explains the principle of spin noise spectroscopy, together with more conventional AC susceptometry. I also introduce a spin noise spectrometer that employs a Superconducting QUantum Interference Device (SQUID). In Chapter 3, I present the SQUID spin noise spectrometers that I designed and assembled during my DPhil. They have an extreme sensitivity approaching 10⁻¹⁴ T/√Hz, broad bandwidth of DC to 100 kHz, and a temperature range of 10 mK to 6000 mK. I utilize them to study QSL candidate compounds with controversial spin liquid states. Chapter 4 presents the spin noise study of Ca₁₀Cr₇O₂₈, which has been hypothesized to be either a QSL or a spiral spin liquid (SSL). Powerful spin noise spanning a frequency range from 0.1 Hz to 50 kHz is discovered in Ca₁₀Cr₇O₂₈, and its overall correspondence with the prediction of SSL noise simulation evidences Ca₁₀Cr₇O₂₈ as an SSL. Lastly, Chapter 5 presents the spin noise study of ZnCu₃(OH)₆Cl₂, an iconic QSL candidate with a spin-1/2 kagome lattice. Spins substituted in the interlayer are discovered to generate powerful spin noise spanning from 0.1 Hz to 100 Hz and to undergo a sharp transition at 260 mK. The experimental observations are consistent with spinon-mediated interactions between the interlayer spins, via the spinon spectrum in a quantum spin liquid state within the kagome layer.