Free monopoles have fascinated and eluded researchers since their prediction by Dirac 1 in 1931. In spin ice, the bulk frustrated magnet, local ordering principles known as ice rules-two-in/two-out for four spins arranged in a tetrahedron-minimize magnetic charge. Remarkably, recent work 2-5 shows that mobile excitations, termed 'monopole defects', emerge when the ice rules break down 2 . Using a cobalt honeycomb nanostructure we study the two-dimensional planar analogue called kagome or artificial spin ice. Here we show direct images of kagome monopole defects and the flow of magnetic charge using magnetic force microscopy. We find the local magnetic charge distribution at each vertex of the honeycomb pins the magnetic charge carriers, and opposite charges hop in opposite directions in an applied field. The parameters that enter the problem of creating and imaging monopole defects can be mapped onto a simple model that requires only the ice-rule violation energy and distribution of switching fields of the individual bars of a cobalt honeycomb lattice. As we demonstrate, it is the exquisite interplay between these energy scales in the cobalt nanostructure that leads to our experimental observations.The dipolar interactions of a given spin with all of its nearest neighbours cannot be satisfied on a triangular lattice, resulting in a frustrated magnetic state with strong correlations and a local ordering principle, but no long-range order. Owing to its equivalence to the electrical charge distribution in water ice 6 , the materials are known as 'spin ices' and the local ordering scheme as the 'ice rules'. Spin-ice materials such as Dy 2 Ti 2 O 7 have been subject to an intense research effort 7,8 and frustrated magnetism has evolved into a deeply interdisciplinary field, providing model systems for complex biological problems and a mathematical basis for the neural network algorithm from the Sherrington-Kirkpatrick model 9 .A powerful way to understand spin ice is to consider the magnetic dipole as a positive and negative magnetic charge (±q) separated by one lattice spacing. The ice rule can then be described as the local minimization at each lattice site i of the total magnetic charge (Q i, = q i ). Predictions suggest that the magnetic properties can be fractionalized, with mobile excitations carrying magnetic charge, rather than spin, and their interactions being described by a magnetic Coulomb's law 2 (equation (1))where V 0 is the self-energy and r ij is the separation. Although these topological excitations are confined to the dipole lattice, and they are compatible with Maxwell's equations 10 , their free magnetic charge character has led to the nomenclature magnetic Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2AZ, UK. *e-mail: W.Branford@imperial.ac.uk.monopole defects. Recent studies 3-5,10 in rare-earth pyrochlores strongly suggest that monopole defects exist in bulk spin ice 10 .Creating an odd number of intersecting dipoles, as in 'kagome spin ice' 11 , is interesting becaus...

A relatively high critical temperature, T c , approaching 40 K, places the recently-discovered [1] superconductor magnesium diboride (MgB 2 ) intermediate between the families of low-and copper-oxide-based high-temperature superconductors (HTS). Supercurrent flow in MgB 2 is unhindered by grain boundaries [2, 3], unlike the HTS materials. Thus, long polycrystalline MgB 2 conductors may be easier to fabricate, and so could fill a potentially important niche of applications in the 20 to 30 K temperature range. However, one disadvantage of MgB 2 is that in bulk material the critical current density, J c , appears to drop more rapidly with increasing magnetic field than it does in the HTS phases [4]. The magnitude and field dependence of J c are related to the presence of structural defects that can "pin" the quantised magnetic vortices that permeate the material, and prevent them from moving under the action of the Lorentz force. Vortex studies [3] suggest that it is the paucity of suitable defects in MgB 2 that causes the rapid decay of J c with field. Here we show that modest levels of atomic disorder, induced by proton irradiation, enhance the pinning, and so increase J c significantly at high fields. We anticipate that chemical doping or mechanical processing should be capable of generating similar levels of disorder, and so achieve technologically-attractive performance in MgB 2 by economically-viable routes.A Type II superconductor undergoes the transition to the normal state at the upper critical field, H c2 . However, the ability to carry dissipation-free current ceases at a lower field, the irreversibility field, H irr . Above H irr the Lorentz force on the vortices is large enough for them to become detached from pinning defects, and virtually free to move. In MgB 2 powder (and also wires and tapes), H irr is approximately half of H c2 [5], so that there is an extended field domain where there might be a useful J c if only the pinning could be strengthened.Ion irradiation is a reproducible means of inducing crystalline disorder. Energetic ions displace atoms from their equilibrium lattice sites, creating a variety of defects, including vacancies and interstitials. Such defects tend to depress the superconducting order parameter locally, and thereby create pinning sites for the vortices. We chose protons for this initial study because at the maximum beam energy available to us of 2 MeV, they can penetrate 40 to 50µm into MgB 2 . A series of irradiations were performed in order to create significant defect densities. The probability of displacement per atomic site (dpa) can be simulated using commercial software [6], and we aimed to generate as uniform a profile as possible through the sample depth (Fig.1).As in our previous study [3], we selected fragments of about 100 µm size from commercial MgB 2 powder (Alfa Aesar Co., 98% purity). Several samples were prepared, each of 20 fragments embedded in silver-loaded epoxy and then polished, so that a defined geometry was obtained, with an estimated thickness of...

The recently discovered superconductor magnesium diboride, MgB2, has a transition temperature, Tc, approaching 40 K, placing it intermediate between the families of low- and high-temperature superconductors. In practical applications, superconductors are permeated by quantized vortices of magnetic flux. When a supercurrent flows, there is dissipation of energy unless these vortices are 'pinned' in some way, and so inhibited from moving under the influence of the Lorentz force. Such vortex motion ultimately determines the critical current density, Jc, which the superconductor can support. Vortex behaviour has proved to be more complicated in high-temperature superconductors than in low-temperature superconductors and, although this has stimulated extensive theoretical and experimental research, it has also impeded applications. Here we describe the vortex behaviour in MgB2, as reflected in Jc and in the vortex creep rate, S, the latter being a measure of how fast the 'persistent' supercurrents decay. Our results show that naturally occurring grain boundaries are highly transparent to supercurrents, a desirable property which contrasts with the behaviour of the high-temperature superconductors. On the other hand, we observe a steep, practically deleterious decline in Jc with increasing magnetic field, which is likely to reflect the high degree of crystalline perfection in our samples, and hence a low vortex pinning energy.

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Electromagnetic metamaterials 1 are a class of materials which have been artificially structured on a subwavelength scale. They are currently the focus of a great deal of interest because they allow access to previously unrealisable properties like a negative refractive index 2 . Most metamaterial designs have so far been based on resonant elements, like split rings 3 , and research has concentrated on microwave frequencies and above. In this work, we present the first experimental realisation of a non-resonant metamaterial designed to operate at zero frequency. Our samples are based on a recently-proposed template 4 for an anisotropic magnetic metamaterial consisting of an array of superconducting plates. Magnetometry experiments show a strong, adjustable diamagnetic response when a field is applied perpendicular to the plates. We have calculated the corresponding effective permeability, which agrees well with theoretical predictions. Applications for this metamaterial may include non-intrusive screening of weak DC magnetic fields. The first metamaterials 3,5 were designed to operate at microwave frequencies. Since then, while there has been some research on radio-frequency metamaterials 6 , most of the research effort has been focused on higher frequencies: technologically-important microwaves or visible light 7 . The low-frequency end of the spectrum has remained relatively unexplored. In addition, the majority of metamaterials devised to date consist of an arrangement of resonant components. There is a good reason for this: the response of a resonator varies greatly as a function of the frequency at which it is being driven. Close to the resonant frequency, the amplitude of the response can be very large, while the phase changes. The range of available values of the response function, or susceptibility, is therefore very wide. One of the crowning achievements of (and driving forces behind) metamaterials research is the realization of a negative refractive index 2,8 , and a simple argument shows that this cannot be achieved without relying on resonant structures. However, the price of working close to the resonant frequency is that losses and frequency dispersion are greatest here. When a negative response is not required then a non-resonant structure is advantageous. Another recent development means that there is new demand for metamaterials with nonnegative anisotropic parameters. Transformation optics 9 is a design paradigm that allows a new level of control over electromagnetic fields. For a given design, it provides a recipe for the material parameters as a function of position. The parameters generated in this way are always non-negative and anisotropic. A spectacular demonstration of the technique was provided by the construction of an electromagnetic cloak 10 using metamaterials. The interior of the cloak is shielded from microwaves with minimal disruption to the exterior fields.