This thesis presented magnetic characterisation results on four closely related materials. The first two discussed were the honeycomb and hyperhoneycomb polymorphs of . These have tricoordinated lattices of , moments, which have attracted recent theoretical interest as candidate platforms to host Kitaev physics. In both cases, this is the first time that single-crystal samples of the material have been magnetically characterised.
The second two materials discussed were the isostructural honeycomb transition metal titanites and , investigating the recent proposal that easy-plane antiferromagnet displays in-plane anisotropy driven by bond-dependent exchange interactions and a quantum zero-point fluctuations mechanism. Using single crystal torque magnetometry, I directly observe a six-fold in-plane anisotropy in the ordered phase, with an energy scale comparable with the value predicted from inelastic neutron scattering. I contrast this with the easy-axis antiferromagnet , where I observe the same effect in the ordered phase. In both cases, single-ion anisotropy can be rejected as the origin of the effect, leaving quantum zero-point fluctuations driven by bond-dependent exchange interactions as the most likely origin.
Honeycomb orders magnetically at into a canted antiferromagnetic structure, which has a clear fingerprint in the angular dependence of torque in three orthogonal crystal planes. I propose two minimal models which can stabilise this structure, one with XXZ Ising-like exchange interactions, and a second model with Heisenberg and symmetric off-diagonal exchange . In both cases, a symmetry-allowed unbalanced Dzyaloshinskii–Moriya interaction on the honeycomb bonds causes canting of the moments in the plane. Using torque magnetometry, I directly observe a spin-flop transition at high magnetic field, consistent with both magnetic models, and find a peculiar non-monotonic field dependence of crossover between spin-flop and paramagnetic phases.
Hyperhoneycomb orders at into a much more complex four sublattice non-collinear antiferromagnetic structure. I report temperature dependence of AC calorimetry and torque magnetometry consistent with a sharp transition to the magnetic structure observed in powder neutron diffraction. I explore a proposed minimal model which stabilises this structure consisting of Heisenberg and symmetric off-diagonal exchange on nearest-neighbour bonds. I show that this model predicts a spin-flop transition with a particular field orientation and use pulsed-field torque magnetometry to observe this spin-flop transition directly in single crystals.
Between the two proposed minimal models for , the model with XXZ interactions is arguably the simplest. However, given the evidence supporting a model in the polymorph , and the shared structural motifs between the two materials, it is worth considering if both materials may be described by very similar models of bond-dependent exchange interactions. Additionally, both materials were theoretically predicted to host strong bond-dependent Kitaev interactions, and in neither case is clear evidence of this seen. Understanding the origin of these interactions will be important to understanding the physics of cooperative magnetism in rare-earths.
To date, a huge amount of research effort has gone into investigating transition metal compounds as candidates for strong bond-dependent exchange in the search for experimental realisation of a Kitaev quantum spin liquid. This has been very successful in finding exotic magnetic phases of various types, however no conclusive evidence has been found for a true Kitaev-QSL. The results in this thesis show clear experimental evidence that magnetic rare-earths can also host strong bond-dependent exchange interactions, and provides further support that these may be fertile ground in the search for exotic magnetic phases driven by bond-dependent interactions.