Frustrated magnetism studies in NaCaNi$_2$F$_7$, Er$_3$Ga$_5$O$_{12}$ and ErMgGaO$_4$

Abstract

This dissertation details studies of three different frustrated magnet families: NaCaNi$_2$F$_7$, Er$_3$Ga$_5$O$_{12}$, and ErMgGaO$_4$, using a variety of techniques, including magnetization, specific heat, neutron scattering and muon spin rotation/relaxation ($\mu$SR).

NaCaNi$_2$F$_7$ belongs to the fluoride pyrochlores family. In this thesis, we study the effect of the randomness on the A site on the magnetic property of B site. This chemical disorder randomness was caused by the mixture of two different elements from Group 1 and 2 (Na and Ca). DFT calculation and computation simulations indicates a possible non-centred $F-\mu -F$ muon stopping site. Zero field (ZF) and longitudinal field (LF) $\mu$SR shows that the $Ni^{2+}$ spins undergo spin freezing into a disordered ground state below 4K, with persistent spin dynamics to our lowest temperature 75 mK.

We obtained high quality single crystal of Er$_3$Ga$_5$O$_{12}$ by utilizing the optical floating-zone (OFZ) technique. We performed inelastic neutron scattering measurements to determine the crystalline electric field (CEF) Hamiltonian, eigenvalues and eigenvectors, indicating an Ising-like anisotropy ground state which is also consistent with our specific heat experiment with entropy approaching $Rln(2)$. All seven crystalline electric field excitations from the ground state Kramers doublet were identified. In addition, Rietveld refinement of neutron powder diffraction data reveal that Er$_3$Ga$_5$O$_{12}$ orders into the $\Gamma_3$ magnetic structure, with ordered magnetic moment $\mu_{ord} = 5.24(4)~\mu_{B}$, in agreement with $\mu_{Ising}$ = 5.61 $\mu_{B}$ from our deduced CEF Hamiltonian. Our $\mu$SR measurements also reveals the presence of fluctuating local fields on the muon timescale, indicating exotic slow spin dynamics in the ground state.

The objective of the work on ErMgGaO$_4$ was to identify a new quantum spin liquid candidate. Single crystals of ErMgGaO$_4$ were obtained through (OFZ) technique as well, and the structure was refined and confirmed by powder X-ray diffraction and Laue diffraction after a repeated refinement of our synthesis process. Susceptibility measurements reveal no evidence of a magnetic transition down to 0.5 K, in agreement with specific heat measurement which exhibit no anomalies which would have been evidence of an ordering transition. ZF-$\mu$SR measurements reveal no sign of coherent long range order or spin freezing down to 25 mK, while LF-$\mu$SR measurements shows persistent spin dynamics at 25 mK. Our observations provides evidence for a quantum spin liquid ground state in this compound.