Neutron-scattering studies of frustrated magnetic materials

Frustrated spin systems exhibit a very large number of low-energy states which can lead to the suppression of conventional magnetic order. They are nevertheless distinguished from classical paramagnets by the presence of unconventional spin correlations or “local rules”. These local correlations have been linked to systems of fundamental importance, including high-temperature superconductors and multiferroics, and are widely studied using neutron-scattering experiments. Whereas the neutron-scattering pattern of a periodic spin structure shows sharp reflections (Bragg peaks), scattering patterns of frustrated systems show only broad diffuse features. Consequently, conventional crystallographic methods cannot be used to solve these systems. Instead, the neutron scattering pattern anticipated from a predetermined interaction model is typically compared with experimental single-crystal neutron-scattering data. This approach relies on anticipating the nature of the magnetic interactions; it is also inherently unfeasible for the many interesting materials for which large single crystal samples do not exist.
In this thesis I examine whether these two problems can be addressed using reverse Monte Carlo (RMC) refinement, a method in which the orientations of spins in a large configuration are refined to match experimental diffuse-scattering data. I first assess whether RMC refinement to magnetic powder diffuse-scattering data can allow three-dimensional (3D) information to be recovered. I show that the information lost during powder averaging of the full 3D diffuse-scattering pattern is actually surprisingly minimal, and the compete 3D scattering pattern can be recovered from RMC refinement to simulated powder data. In addition, information is obtained about the presence and type of magnetic anisotropy and (in favourable cases) about higher-order correlations. I go on to develop a fast RMC algorithm to refine to large 3D diffuse-scattering datasets (⇠106 data points) in reasonable time (⇠days). These results show that RMC refinement represents a successful alternative to traditional methods of interaction modelling, allowing quantitative refinement of disordered spin structures in complex magnetic materials.
I use the RMC approach to refine to experimental diffuse-scattering data for five frustrated magnetic materials. I first consider the interplay of frustration and low-dimensional magnetism in the paramagnetic phase of the spin-chain compound Ca3Co2O6, in which Ising-like spin chains are arranged on a triangular lattice. Both intra-chain and interchain correlations persist above the magnetic ordering temperature TN, but are essentially decoupled. Intra-chain correlations resemble the ferromagnetic (FM) Ising model, while inter-chain correlations resemble the frustrated triangular-lattice antiferromagnet (AFM). Using previously-published bulk property measurements in addition to powder neutron-scattering data, I obtain values of the FM and AFM exchange interactions and the single-ion anisotropy, which provide the first consistent explanation of thermodynamic anomalies observed above TN.
I next use powder diffuse-scattering data to obtain an atomic-scale model of the spinliquid state in the canonical frustrated magnet Gd3Ga5O12. I showthat this state exhibits a hidden (non-dipolar) order which has three unusual properties. First, it is a collective phenomenon, in which multipoles are formed from ten-spin loops. Second, it is long-range, with a diverging correlation length. Third, it is a consequence of the interplay between AFM spin correlations and local magnetic anisotropy, which allows it to be indirectly observed in neutron-scattering experiments.
In a final study using powder data, I consider the partially-ordered low-temperature magnetic structure of the frustrated AFM Gd2Ti2O7. This structure is currently believed to involve multiple magnetic propagation vectors in a so-called 4k model, based on analysis of powder diffuse-scattering data. I present three pieces of evidence against this 4k structure. First, I use single-crystal neutron-diffraction measurements to observe a redistribution of magnetic intensity between Bragg peaks when a small magnetic field is applied. This result is consistent with the selective population of magnetic domains for the alternative 1k structure, but is inconsistent with the 4k structure unless a fieldinduced phase transition occurs which is silent in thermodynamic measurements. Second, I find evidence from high-resolution neutron powder-diffraction measurements that shortrange rhombohedral strains are present at low temperature, which may be generated by magneto-elastic coupling only for the 1k structure. Third, I demonstrate that the powder diffuse-scattering intensity can be modelled quantitatively by a 1k structure.
I then present two studies of RMC refinement to single-crystal magnetic diffusescattering data. First, I consider the paramagnetic (PM) phase of the canonical AFM, MnO, which is only weakly frustrated. I compare the local magnetic structure in the PM phase with the well-known ordered AFM structure of MnO, and find significant differences between the two over short length-scales. This result indicates that the spin correlations of weakly-frustrated paramagnets do not necessarily resemble the incipient ordered magnetic structure over short length-scales. This result may have implications for other weaklyfrustrated systems (e.g., high-temperature superconductors such as La1-x SrxCuO4).
Finally, I identify the presence of emergent spin structures in Co-doped !-Mn, a metal which has a crystal structure noted for its complexity. Single-crystal polarised-neutron scattering experiments on beta-Mn0.8Co0.2 reveal the persistence of highly-structured magnetic diffuse scattering and the absence of magnetic order to T = 0.05 K. I employ RMC refinements and mean-field theory calculations to construct an effective Hamiltonian which accounts for the magnetic diffuse scattering. The interactions I identify describe an emergent spin structure which mimics the triangular-lattice AFM, one of the canonical models of frustrated magnetism.

Advisor: Goodwin, A
Stewart, R