Geometric frustration in high spin orbit coupling magnetic materials

Frustrated magnetic materials have long been a topic of intense research interest due to the variety of exotic states found in such systems. Here I present a study of the role of the local environment on two families of frustrated materials. The ferrimagnetic spinel $\mathrm{CoV_2O_4}$ has been a topic of recent interest, both as a frustrated insulator with unquenched orbital degeneracy and as a near-itinerant magnet which can be driven metallic with moderate applied pressure. Here, we report on our recent neutron diffraction and inelastic scattering measurements on powders and epitaxial thin films. In both samples we observe a phase transition at $T = 90$~K. In the bulk sample a weak ($\frac{\Delta a}{a} \sim 10^{-4}$), first order structural phase transition at $T^* = 90$~K is found. This transition is characterized by a short-range distortion of oxygen octahedral positions, and inelastic data further establish a weak $\Delta\sim 1.25 meV$ spin gap at low temperature. Together, these findings provide strong support for the local orbital picture and the existence of an orbital glass state at temperatures below $T^*$. The strain from lattice mismatch with the substrate causes the thin film sample to be in a lower symmetry state and is found to have an orthorhombic structure. Neutron scattering results show that there is a large spin re-ordering transition at $T_{N2} = 90$~K, where the initially collinear ferrimagnetic Co and V spins rotate from pointing along the (001) above 90~K to being entirely in the a-b plane below 90~K. The low temperature magnetic phase has collinear Co spins that point along the (110) and V moments that remain in the plane, but are canted away from the (110) by a large angle. This magnetic phase is consistent with orbital ordering transition at 90~K which is strengthened by the strain from the lattice mismatch. The second family of materials studied here is the family of compounds MgRE$_2$Se$_4$ (RE $\in$ $\{$Ho, Tm, Er and Yb$\}$). Particular attention is given to the case of RE = Er where it is shown that this material is a spin ice. In spin ice research, small variations in structure or interactions drive a multitude of different behaviors, yet the collection of known materials relies heavily on the `227' pyrochlore structure. Here, we present thermodynamic, structural and inelastic neutron scattering data on a new spin-ice material, MgEr$_2$Se$_4$. X-ray and neutron diffraction confirm a normal spinel structure, and places Er$^{3+}$ moments on an ideal pyrochlore sublattice. Measurement of crystal electric field excitations with neutron inelastic scattering confirms that the moments have perfect Ising character, and further identifies the ground state Kramers doublet as having dipole-octupolar form with a significant multipolar character. Heat capacity and magnetic neutron diffuse scattering have ice-like features, but are inconsistent with Monte Carlo simulations of the nearest-neighbor and next-nearest-neighbor dipolar spin-ice (DSI) models. A significant remnant entropy is observed as T$\rightarrow$0 K, but again falls short of the full Pauling expectation for DSI, unless significant disorder is added. We show that these observations are fully in-line with what is recently reported for CdEr$_2$Se$_4$, and point to the importance of quantum fluctuations in these materials. For all of the other compounds in the MgRE$_2$Se$_4$ series we present inelastic neutron scattering (INS) measurements of the CEF excitaions on the family of compounds MgRE$_2$Se$_4$ (RE $\in$ $\{$Ho, Tm, Er and Yb$\}$). These compounds form in the spinel structure, with the rare earth ions comprising a highly frustrated pyrochlore sublattice. Within the symmetry constraints of this lattice, we fit both the energies and intensities of observed modes in the inelastic neutron scattering spectra to determine the most likely CEF Hamiltonian for each material and comment on the ground state wavefunctions in the local electron picture. In this way, we experimentally confirm MgTm$_2$Se$_4$ has a non-magnetic ground state, and MgYb$_2$Se$_4$ has effective $S=\frac{1}{2}$ spins with $g_\parallel = 5.188(79)$ and $g_\perp = 0.923(85)~\mu_B$. The spectrum of MgHo$_2$Se$_4$ indicates a ground state doublet containing Ising spins with $g_\parallel = 2.72(46)$, though low-lying CEF levels are also seen at thermally accessible energies $\delta_E = 0.591(36)$, 0.945(30) and 2.88(7)~meV, which can complicate interpretation. Additionally neutron powder diffraction measurements show that MgHo$_2$Se$_4$ does not exhibit any magnetic order down to temperatures of 300 mK