Exotic phenomena in rare-earth based geometrically frustrated magnets

2022 Spring.Includes bibliographical references.Rare-earth (RE) based frustrated magnets are ideal systems to explore quantum effects in materials, which are paramount for the development of quantum computers, MRAM, and other next-generation technology. RE based materials are of specific interest due to the strong spin-orbit coupling and crystal electric field effects, which split the degenerate 4f angular momentum states, often leading to an effective spin-1/2 doublet with anisotropic effective exchange models. For this reason, RE materials are paramount to investigating the effects of anisotropic exchange on exotic ground states or quantum phases. Exchange frustration refers to when a system cannot simultaneously satisfy competing interactions, which can lead to a macroscopic degeneracy in the ground state of the system. Materials with geometric frustration, where competing interactions occur due to the crystal geometry alone, have been shown to host a wealth of exotic phenomena, including spin ice phases, quasi-particle excitations, order-by-disorder, and the highly entangled quantum spin liquid (QSL) state, to name a few. In this thesis, we will discuss three RE systems that exhibit geometric frustration in addition to exchange frustration: two RE pyrochlore oxides (RE2TM2O7) and a 2D isosceles triangular lattice material K3Er(VO4)2. Spin-1/2 antiferromagnetic (AFM) 2D triangular lattice magnets are an archetype of geometric frustration. While these materials are theorized to host a variety of different ground states and exotic phases depending on the anisotropies of the system, only a handful of RE material examples have been explored. We report the first deep dive into one such system, K3Er(VO4)2. We have determined the ordered magnetic structure of K3Er(VO4)2, finding an unusual structure with alternating layers comprised of AFM aligned and zero moment. We theorize this unique structure is due to the strong XY single-ion anisotropy, suggested from magnetometry measurements, which acts to suppress (to the point of vanishing completely) the out-of-plane pseudo-spin-1/2 magnetic moments. Next, we explored the effects of phase competition in a well-studied effective spin-1/2 RE pyrochlore oxide, Er2Sn2O7. Previous polycrystalline work has found Er2Sn2O7 to possess a suppressed critical temperature and an AFM Palmer-Chalker ground state. The determined exchange and single-ion anisotropy of Er2Sn2O7 find the ground state lies in close proximity to a competing AFM phase. Through extensive single crystal heat capacity measurements, we discovered a reentrant field vs. temperature phase diagram, where a system that has developed order returns to the original, less ordered (paramagnetic) state as some external parameter (field) is tuned continuously. We investigated the underlying mechanisms behind the reentrance by utilizing Monte Carlo simulations, mean field theory, and classical linear spin-wave calculations. This theory suggests that reentrance is linked to soft modes arising from phase competition, either from enhanced competition of the proximal AFM phase or from competing T=0 field-evolved ground states, depending on the specific applied field direction. In both cases, the soft modes enhance thermal fluctuations which cause the specific ordered phase to be entropically stabilized, thus forming a reentrant phase diagram. Finally, we report recent elastic neutron diffraction results on a RE pyrochlore oxide and candidate octupolar spin-ice, Ce2Sn2O7. The pseudo-spin-1/2 moments in Ce2Sn2O7 are known to possess dipolar-octupolar character and a large parameter space within the phase diagram is theorized to host novel QSL states. Previous powder neutron diffraction found diffuse scattering at high scattering vectors associated with magnetic octupoles. However, our undertaking of a similar measurement on nominally the same sample, found strikingly different results. Our neutron diffraction resulted in a broad, diffuse signal at low scattering vectors, reminiscent of a dipolar spin-ice. Neutron diffraction and atomic PDF measurements have not turned up obvious sample deformities or evidence of oxidation that could explain the differences in the diffuse signals. Further atomic studies and significant theory work is necessary to fully understand the results of this measurements, but the similarities to sister compound Ce2Zr2O7 suggest that Ce2Sn2O7 could lie on a phase boundary that is sensitive to minor distortions