Skating on spin ice: On the application of Lorentz microscopy and numerical techniques to characterise phase transitions and non-equilibrium phenomena in artificial spin ices

Artificial spin ices are arrays of nano-scale magnetic islands correlated by the interactions of their associated macrospins. They have proven an excellent playground in which to study phase transitions and non-equilibrium phenomena. Originally envisaged as a two-dimensional analogue to the frustrated rare-earth pyrochlores, they are now seen in their own right as promising candidates for a wide range of applications, including nanomagnetic computation and magnonics. At the same time, the capability of tuning their behaviour---whether by means of the constituent material, the fabrication pattern, or the application of external stimuli---enables the realisation of unusual aspects of statistical physics. This thesis comprises a combined numerical and experimental study of artificial spin ice. The aims are twofold. First, it seeks to address how magnetic order and defect textures are influenced by the choice of lattice geometry. Second, it considers one route towards making artificial spin ice configurable via a coupling to a site-specific exchange bias. In the initial segment of this thesis, the recently studied pinwheel form of artificial spin ice is described. This is created by rotating each island in the square lattice about 45 degrees through its centre. The rotation angle of the islands acts as a proxy for a mechanism to vary the interactions between spins. A transition between antiferromagnetism in the square lattice and ferromagnetism in the pinwheel lattice is predicted. The phase diagram and critical exponents of the transition are obtained numerically. The nature of this transition is confirmed experimentally using in-situ Lorentz transmission electron microscopy on thermally annealed cobalt arrays. Varying degrees of thermalisation are observed across the samples, as well as an apparent change in the nature of the defects: from one-dimensional strings in square ice to two-dimensional vortex-like structures for geometries similar to pinwheel. The numerical scaling of these quantities is consistent with that predicted by the Kibble-Zurek mechanism. Finally, a two-dimensional hybrid artificial spin ice is outlined. In this, exchange bias is inserted at specific sites to constrain the magnetisation dynamics of individual islands. By examining correlations, a model for the influence of this pinning is constructed. As the density of constrained spins is varied, different magnetic textures are observed following a simulated field demagnetisation. These simulations show good agreement with results obtained experimentally. In this manner, local control over individual islands provides a route to tuning the global response of the array, thus making the system configurable. This is an essential step towards device-based applications. Taken together, these results illustrate the interplay between topology and magnetic order in artificial spin structures, and enable the exploration of critical phenomena in frozen and glassy systems. The findings presented here demonstrate conclusively that artificial spin ice is an excellent test bed with which to probe out-of-equilibrium dynamics. They will also underpin its potential use in fields which are reliant on adressing specific microstates, such as neuromorphic computing.