Our project is a collaborative one between two Universities and a national laboratory working together across a combined theoretical and experimental programme. The experiments are based in both conventional laboratories and large-scale facilities. The work programme also involves continued international collaboration with colleagues in the US at Brookhaven National Laboratory, who have helped us make some of our most recent breakthroughs in creating and understanding nanostructured magnets, as well as adding new ones in the form of the unique expertise and facilities available for transmission x-ray imaging at the Advanced Light Source in Berkeley. Both of these are DOE-supported US national laboratories.

Our goal is to understand and control non-equilibrium dynamics in a new class of magnetic materials: strongly correlated arrays of sub-micron sized magnets. Examples have been studied recently, and given the name "artificial spin ice". These materials are important examples of new metamaterials with unique properties not realised in naturally occurring magnetic materials. The artificial magnetic ice are systems composed of strongly interacting magnetic moments, and the moments are arranged geometrically in order to produce metastable configurations with a high degree of degeneracy in energy. We will use artificial spin ice as a paradigm for a systematic exploration of non-equilibrium dynamics. This is a model system for which the free energy is specified by design and hence completely determined, and the exact microstate--and its evolution in time--can be observed directly for detailed comparison with mathematical predictions.

Inter-element interactions can be specified to a large extent by design through control of geometry. In this way it is possible to create competitions between ordering that result in geometrical frustrations responsible for complex response to applied magnetic fields. The resulting magnetic properties are analogous to those of traditional thin film or bulk magnetic systems, but with key differences that can be of especial importance for applications. For example, there are two ground state configurations in a square ice that form domains with zero net moment. These are separated by magnetised boundary walls along which magnetic charges can move.

Magnetic charges (sometimes called emergent monopoles) are of particular interest since they can be readily detected and can be moved through an array by applied magnetic fields. We will develop methods to inject and detect charges, and control their flow through array geometries. Our goal is to identify structures and techniques for the design of circuits through which "magnetricity" can flow and be usefully employed for technological applications. Our idea is to use thermal fluctuations to aid magnetic charge mobility. We can do this by using nanoscale particles in our arrays, such that the particles are near their superparamagnetic blocking temperature. An important distinction with prior work is that we shall use materials with phase transitions close to room temperature to allow us to tune simply between thermally equilibrated and athermal non-equilibrium states. This will mean that the individual moments can reverse spontaneously, thus enabling thermally driven motion of magnetic charges through a fluctuating array. Through a combination of applied fields and temperature control we will be able to start, stop, and direct magnetic charge dynamics. These systems may also give us new experimental models for studies of critical dynamics at phase transitions since they can be modelled by well known exactly soluble Ising systems, as well as providing new paradigms for information processing architectures.

Potential Impact:
The artificial magnetic ices that we shall study here are examples of systems engineered to display frustration, a phenomenon that is found throughout condensed matter physics and beyond. Aside from its traditional habitat of magnetism, it can, for instance, describe models of neural networks and protein folding and even social phenomena such as financial networks. Moreover, these nanostructures are a playground for exploring statistical mechanics in a unique way where all the parameters in a Hamiltonian can be tuned at will during the lithography, and the exact microstate of the system (and the way it evolves in time) can be inspected using advanced microscopy methods. Since these are systems that can be driven controllably between thermal and athermal states, they can be used to explore the physics of 'Emergence and matter far from equilibrium', an area highlighted by EPSRC as a Physical Sciences Grand Challenge topic. This special emphasis has been placed on the topic since impact can be expected in a number of areas arising both from the novelty of the experiments and the new classes of theory that will be developed.

New phenomena will be explored in this work through the nanotechnological metamaterials that we will create. Viewed as a new concept in magnetic materials, artificial spin ices represent a highly functional magnetic material with a highly degenerate set of possible magnetic states. Our concern will be the non-equilibrium dynamics that will arise from competing interactions when these complex systems are driven in the right way: both thermally, by fluctuations, and athermally, using applied fields, with the aim being to controllably inject, inspect, and manipulate individual magnetically charged excitations - the flow of these charged excitations under field has been dubbed 'magnetricity'. Some phenomena in these materials do not have analogues in traditional magnets, and we will investigate specific examples that show great promise for possible application for computer logic, data storage and retrieval, and realisations of neural networks.

As a new type of material, the most obvious impact areas for magnetric materials are in IT, both directly as information storage or processing systems, as well as indirectly in terms of the state-of-the-art nanofabrication and characterisation techniques that we shall develop and employ. However as a new property, magnetricity has potential to inspire new applications in industries that are traditionally far removed from microelectronics or data storage. Mobile magnetic charges might be of interest for microfluidics and biomagnetic medical applications, for example, or as models for complex networks. Hence the mathematical models and methods that we shall develop will have impact not only in the IT hardware sector, but in other areas of commerce and social policy such as financial services, traffic flow management, network design, and production line logistics.