In this PhD thesis two geometrically frustrated classical Heisenberg antiferromagnets on the paradigmatic triangular and kagomé lattices are studied. The two compounds, hexagonal yttrium manganite (h-YMnO3) and chromium jarosite (KCr3(OD)6(SO4)2), are investigated using magnetometry and neutron spectroscopy, and their behaviour is set in relation to the concept of classical spin liquids.
h-YMnO3 is a spin-2 frustrated and multiferroic antiferromagnet on the
stacked triangular lattice. The antiferromagnetic phase transition at TN = 72 K
was investigated with neutron spectroscopy on a single-crystal and shown to have an anomalous critical exponent of β = 0:207(3). This critical exponent does not match any known universality class, and we suggest the existence of a separate universality class for frustrated pseudo-two-dimensional triangular lattice Heisenberg antiferromagnets.
Furthermore, significant correlated disorder was observed in h-YMnO3 both
far above and below TN as diffuse, directional, and quasielastic scattering. This
was measured using neutron spectroscopy, including the newly-commissioned
multiplexing triple-axis spectrometer CAMEA at the Paul Scherrer Institute.
The diffuse dynamic scattering is two-dimensional in the triangular plane with a
correlation length that seems to diverge as the temperature approaches zero. We
model this scattering with critical two-dimensional spin correlations existing in
a vastly extended critical region due to the frustration. We argue that this is a
manifestation of classical spin liquid behaviour, and suggest critical scattering as
a broader framework for understanding frustrated antiferromagnets.
Cr-jarosite, KCr3(OD)6(SO4)2, is a spin-3=2 kagomé antiferromagnet. Past
studies has been plagued by significant non-stoichiometry. In this thesis, the
most comprehensive structural characterisation of polycrystalline Cr-jarosite is
presented. The hydrothermal-redox synthesis is shown to have problems with
significant K+ substition for D3O+ in Cr-jarosite, which causes stacking faults in
the c direction. The most stoichiometric sample with Cr occupancy of 98.2(2)%
and K occupancy of 84 - 89% is concluded to order antiferromagnetically at
TN = 3:8(1) K in a q = 0 structure with a small ferromagnetic canting due to the
Dzyloshinkii-Moriya interaction.
Subsequently, the dynamics of polycrystalline, deuterated Cr-jarosite was studied using time-of-fight neutron spectroscopy. This revealed spin waves below TN with diffuse broadening due to finite life-times. The spin waves were modelled using linear spin wave theory. Above TN, distinct diffuse excitations were observed that indicated short-ranged, two-dimensional magnetic scattering subsisting until 35 K. The excitations were modelled using a heuristic model for powder-averaged two-dimensional features in three-dimensional (hkl) space. This cluster-like approach revealed an increasing correlation length for decreasing temperature, very similar to the extended critical scattering observed in h-YMnO3.