Public Reporting Burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Manuscript published: Nature 439, 303-306 (2006) Report Title ABSTRACT This is a report of a publication supported by the research grant:"Artificial 'spin ice' in a geometrically frustrated lattice of nanoscale ferromagnetic islands", R.

Frustration -the presence of competing interactions -is ubiquitous in the physical sciences and is a source of degeneracy and disorder, which in turn give rise to new and interesting physical phenomena. Perhaps nowhere does it occur more simply than in correlated spin systems, where it has been studied in the most detail. In disordered magnetic materials, frustration leads to spin-glass phenomena, with analogies to the behavior of structural glasses and neural networks. In structurally ordered magnetic materials, it has also been the topic of extensive theoretical and experimental studies over the past two decades. Such geometrical frustration has opened a window on a wide range of fundamentally new exotic behavior. This includes spin liquids in which the spins continue to fluctuate down to the lowest temperatures; and spin ice, which appears to retain macroscopic entropy even in the low temperature limit where it enters a topological Coulomb phase. In the past seven years a new perspective has opened in the study of frustration through the creation of artificial frustrated magnetic systems. These materials consist of arrays of lithographically fabricated single-domain ferromagnetic nanostructures that behave like giant Ising spins. The nanostructures' interactions can be controlled through appropriate choices of their geometric properties and arrangement on a (frustrated) lattice. The degrees of freedom of the material can not only be directly tuned, but also individually observed. Experimental studies have unearthed intriguing connections to the out-of-equilibrium physics of disordered systems and non-thermal 'granular' materials, while revealing strong analogies to (spin) ice materials and their fractionalized magnetic monopole excitations, lending the enterprise a distinctly interdisciplinary flavor. The experimental results have also been closely coupled to theoretical and computational analyses, facilitated by connections to classic models of frustrated magnetism, whose hitherto unobserved aspects have here found an experimental realization. We review the considerable experimental and theoretical progress in this field, including connections to other frustrated phenomena, and we outline future vistas for progress in this rapidly expanding field.

Artificial spin ice is a class of lithographically created arrays of interacting ferromagnetic nanometre-scale islands. It was introduced to investigate many-body phenomena related to frustration and disorder in a material that could be tailored to precise specifications and imaged directly. Because of the large magnetic energy scales of these nanoscale islands, it has so far been impossible to thermally anneal artificial spin ice into desired thermodynamic ensembles; nearly all studies of artificial spin ice have either treated it as a granular material activated by alternating fields or focused on the as-grown state of the arrays. This limitation has prevented experimental investigation of novel phases that can emerge from the nominal ground states of frustrated lattices. For example, artificial kagome spin ice, in which the islands are arranged on the edges of a hexagonal net, is predicted to support states with monopolar charge order at entropies below that of the previously observed pseudo-ice manifold. Here we demonstrate a method for thermalizing artificial spin ices with square and kagome lattices by heating above the Curie temperature of the constituent material. In this manner, artificial square spin ice achieves unprecedented thermal ordering of the moments. In artificial kagome spin ice, we observe incipient crystallization of the magnetic charges embedded in pseudo-ice, with crystallites of magnetic charges whose size can be controlled by tuning the lattice constant. We find excellent agreement between experimental data and Monte Carlo simulations of emergent charge-charge interactions.

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Frustrated arrays of interacting single-domain nanomagnets provide important model systems for statistical mechanics, because they map closely onto well-studied vertex models and are amenable to direct imaging and custom engineering. Although these systems are manifestly athermal, we demonstrate that the statistical properties of both hexagonal and square lattices can be described by an effective temperature based on the magnetostatic energy of the arrays. This temperature has predictive power for the moment configurations and is intimately related to how the moments are driven by an oscillating external field.

We study AC demagnetization in frustrated arrays of single-domain ferromagnetic islands, exhaustively resolving every (Ising-like) magnetic degree of freedom in the systems. Although the net moment of the arrays is brought near zero by a protocol with sufficiently small step size, the final magnetostatic energy of the demagnetized array continues to decrease for finer-stepped protocols and does not extrapolate to the ground state energy. The resulting complex disordered magnetic state can be described by a maximum-entropy ensemble constrained to satisfy just nearestneighbor correlations.

A double-walled carbon nanotube is used to study the radial charge distribution on the positive inner electrode of a cylindrical molecular capacitor. The outer electrode is a shell of bromine anions. Resonant Raman scattering from phonons on each carbon shell reveals the radial charge distribution. A self-consistent tight-binding model confirms the observed molecular Faraday cage effect, i.e., most of the charge resides on the outer wall, even when this wall was originally semiconducting and the inner wall was metallic.

We analyze the rotational demagnetization of artificial spin ice, a recently realized array of nanoscale single-domain ferromagnetic islands. Demagnetization does not anneal this model system into its antiferromagnetic ground state: the moments have a static disordered configuration similar to the frozen state of the spin ice materials. We demonstrate that this athermal system has an effective extensive degeneracy and we introduce a formalism that can predict the populations of local states in this icelike system with no adjustable parameters.