Crystal Structure of LaVOSiO4. The magnetic V4+ ions occupy the centres of the tetrahedra.

The elementary textbook view of a magnetic solid is one in which neighbouring atomic spins are preferentially aligned parallel to each other (ferromagnet) or antiparallel to each other (antiferromagnet) at low temperatures. The latter is observed in the CuO₂ planes of the undoped cuprate high-temperature superconductors, for instance. The full rotational symmetry of the underlying Hamiltonian is broken in such a state, as the system spontaneously selects a preferred axis of orientation.

In some materials and model systems, the presence of competing interactions can produce a transition from a state with long range magnetic order to one with no magnetic order. Such a phase has been termed a “spin liquid”, since there is no local rigidity against spin fluctuations, unlike the ordered case, which might be termed a “spin solid”. The whole picture is complicated by the presence of “quantum fluctuations”, which make it very difficult to compute what will happen.

Our group has been studying such problems for a number of years, both to discover general features of frustrated low-dimensional magnetic systems and to model particular materials. We have recently been awarded an ARC grant of $750K over 5 years to continue this and other work.

An archetypical model system is the spin-1/2 J₁-J₂ Heisenberg antiferromagnet, illustrated below. The axial interactions with strength J₁ compete with, or “frustrate”, the diagonal interactions with strength J₂. This model has a spin-liquid phase at zero temperature in the intermediate coupling range 0.38 J₂/J₁ 0.6. Our work has shown that the spin-liquid phase is not in fact structureless, but appears to be a dimerized correlated state where local symmetry breaking is preserved for short times, but disappears on averaging over the system. Recent work, by our group and others, has demonstrated the relevance of the model to the recently synthesized materials LaVOSiO₄ and Li₂VOGeO₄. We have studied a somewhat similar model which appears to provide a good description of another material SrCu₂(BO₃)₂. While interesting, none of these materials lies in the spin-liquid region of the model phase diagram. Experimentalists are eagerly searching for materials which are spin liquids or, an even more exciting possibility, could be tuned through a quantum critical point into a spin liquid phase.