The long road to an ideal realization of the kagome lattice antiferromagnet: a few pertubations met along the way...

When geometric frustration – the inability of a spin system to satisfy all of its internal interactions – is combined with strong quantum fluctuations, exotic states called spin liquids can result. One of the enduring mysteries in quantum frustrated magnetism is the nature of the spin liquid state in the kagome lattice antiferromagnet model, which describes a two-dimensional tiling of corner-sharing triangles is populated by antiferromagnetically coupled spins. Despite significant recent theoretical progress towards this goal, unequivocal evidence of the predicted states has not been found in experiments. This is partly due to the imperfections of the materials – typically Cu²⁺ minerals – used to study the model. These include chemical disorder, lattice distortions, anisotropic exchange, and further neighbour exchange, all of which conspire to relieve the frustration and generate more conventional magnetic states.

In this talk, I will aim to give an overview of the materials studied as realizations of the kagome lattice antiferromagnet, focusing on three in particular: herbertsmithite (Cu₃Zn(OH)₆Cl₂), volborthite (Cu₃V₂O₇(OH)_2.2H₂O), and KCu₃As₂O₇(OH)₃. I will aim to show how the crystallography and chemistry of these materials lead to the above imperfections, and discuss their implications in each case. Throughout, the main probe used will be neutron scattering. Although the study of kagome lattice materials shows that realizing the intrinsic properties of the model is extremely difficult, it also demonstrates the rich variety of physics created by combining quantum fluctuations and magnetic frustration.