Terahertz spectroscopy of quantum spin liquids

Abstract

The optical properties of the spin-1/2 kagome lattice antiferromagnetic Herbertsmithite, ZnCu₃(OH)₆Cl₂, are studied by means of Terahertz Time-Domain Spectroscopy. Herbertsmithite is proposed to exhibit Quantum Spin Liquid behavior, in which electron spins have strong antiferromagnetic interactions, but quantum fluctuations inhibit magnetic order even at 0 K, instead giving way to a Resonating Valence Bond state. Quantum Spin Liquids host exotic fractionalized excitations called spinons, which carry spin 1/2 but no charge. The low-energy behavior of these excitations are proposed to be governed by emergent gauge fields that depend on the quantum order of the macroscopically entangled ground state wavefunction. The nature of the quantum order of the ground state in Herbertsmithite has been the subject of great debate in the past decade. While computational work has suggested that a gapped Z 2 spin liquid is realized in Herbertsmithite, experimental work has seen no evidence of a spin gap, suggesting that a U(1) Dirac spin liquid might be realized instead. Recent theory work has proposed that a signature of the quantum order of the ground state of Herbertsmithite is manifested in its low-frequency optical conductivity as a result of the coupling of the charge and spin degrees of freedom through an emergent gauge field. In this dissertation, Terahertz Time-Domain Spectroscopy measurements on single crystals of Herbertsmithite will be used to test these theories, and provide evidence for the existence of a U(1) Dirac spin liquid state in Herbertsmithite.