Quantum magnetism in the rare-earth pyrosilicates

2021 Spring.Includes bibliographical references.In recent years, both physicists and non-physicists have shown immense interest in the burgeoning field of quantum computing and the possible applications a quantum computer could be used for [1]. However, current quantum computers suffer from issues of decoherence: where the quantum state used for computation is broken by external noise. A new possible avenue for quantum computation would be to use systems that are intrinsically protected from some level of noise, such as topologically protected states. Topological states are inherently protected from small perturbations due to their topological nature. However, to exploit this feature of topologically protected systems more experimental realizations are needed to better understand the underlying mechanisms. This has motivated a surge in interest of condensed matter systems with topologically protected states, such as the quantum spin liquid or fractional quantum Hall systems. A current focus in the subfield of quantum magnetism has focused on using the anisotropic exchange properties of the rare-earth (La - Lu) ions to find quantum spin liquid states, such as the Kitaev spin liquid that is predicted for systems exhibiting a honeycomb lattice. The Kitaev model is an exactly solvable model with a quantum spin liquid ground state, allowing for precise comparison between experiment and theory. Currently, no system has been rigorously proven to be a Kitaev spin liquid but developing our understanding of the underlying physical mechanisms in these systems may allow for the "engineering" of systems that are likely to be Kitaev spin liquids. The desire to understand the underlying mechanisms for quantum spin liquids and other quantum ground states led to the study of the three-honeycomb rare-earth pyrosilicate compounds discussed in this dissertation. The first compound, Yb2Si2O7, is a quantum dimer magnet system with the first evidence for a rare-earth based triplon Bose-Einstein condensate. Inelastic neutronscattering, specific heat, and ultrasound velocity measurements showed a characteristic (for triplon Bose-Einstein condensates) dome in the field-temperature phase diagram and provided evidence for predominantly isotropic exchange, something that is not typically expected for rare-earth systems. Following this work on Yb2Si2O7, our focused turned to two of the Er3+ rare-earth pyrosilicates. The first of these Er3+-based pyrosilicates measured was D-Er2Si2O7. Previous work on D-Er2Si2O7 discovered a highly anisotropic g-tensor, an antiferromagnetic ground state, and modeled some of the magnetic field induced transitions via Monte-Carlo simulations [2]. Our work followed up on this with AC susceptibility, powder inelastic neutron scattering, and powder neutron diffraction measurements to further investigate the ground state of this quantum magnet. Through this we discovered that the system enters an antiferromagnetic state with the spins almost aligned along the previously determined local Ising-axis [2]. The inelastic neutron scattering spectrum show a gapped excitation at zero field - consistent with Ising-like exchange. Transverse field AC susceptibility shows a change in the susceptibility at 2.65 T. These signatures indicate that D-Er2Si2O7 exhibits predominantly Ising-like exchange and that a transition can be induced by a field applied transverse to the Ising axis. This allows for the possibility of D-Er2Si2O7 bein g a new experimental realization of the Transverse Field Ising Model (TFIM). The TFIM is a simple, anisotropic exchange, theoretically tractable model exhibiting quantum criticality with few experimental examples, making new experimental examples of this model highly desired. These intriguing results on D-Er2Si2O7 and Yb2Si2O7 led to an interest in the polymorph formed at lower synthesis temperatures, C-Er2Si2O7, which happens to be isostructural to Yb2Si2O7. Measurements of the neutron diffraction, specific heat, and magnetization/susceptibility in this system allowed for us to determine that C-Er2Si2O7 magnetically orders at 2.3 K into an antiferromagnetic Néel state. While this is the expected ground state for an isotropically exchange coupled honeycomb system, C-Er2Si2O7 does not form a "perfect" honeycomb lattice and it is interesting that C-Er2Si2O7 magnetically orders while Yb2Si2O7 does not. Understanding the ground state for C-Er2Si2O7 will allow for bettering our understanding of Yb2Si2O7 and rare-earth quantum magnet ground states by comparing the properties of the two systems. Overall, the work on these three compounds required numerous experimental techniques, models, and theoretical understanding. It is my hope that the preliminary understanding for these three pyrosilicates will motivate future work within the rare-earth pyrosilicate family and provide a family of rare-earth quantum magnets that can be studied to improve our understanding of novel quantum states