Topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, display rich behaviours not found elsewhere in nature. Artificial spin ice takes a materials-by-design approach to studying frustration, where lithographically patterned bar magnets mimic the frustrated interactions in real materials but are also amenable to direct characterization. Here, we introduce controlled topological defects into square artificial spin ice lattices in the form of lattice edge dislocations and directly observe the resulting spin configurations. We find the presence of a topological defect produces extended frustration within the system caused by a domain wall with indeterminate configuration. Away from the dislocation, the magnets are locally unfrustrated, but frustration of the lattice persists due to its topology. Our results demonstrate the non-trivial nature of topological defects in a new context, with implications for many real systems in which a typical density of dislocations could fully frustrate a canonically unfrustrated system.Comment: 12 pages, 6 figures, 3 supplemental figures. For supplemental movies, see http://dx.doi.org/10.13016/M25H7

Thermal activation, long-range ordering, and topological frustration of artificial spin ice

Frustrated systems, typically characterized by competing interactions that cannot all be simultaneously satisfied, are ubiquitous in nature and display many rich phenomena and novel physics. Artificial spin ices (ASIs), arrays of lithographically patterned Ising-like single-domain magnetic nanostructures, are highly tunable systems that have proven to be a novel method for studying the effects of frustration and associated properties. The strength and nature of the frustrated interactions between individual magnets are readily tuned by design and the exact microstate of the system can be determined by a variety of characterization techniques. Recently, thermal activation of ASI systems has been demonstrated, introducing the spontaneous reversal of individual magnets and allowing for new explorations of novel phase transitions and phenomena using these systems. In this work, we introduce a new, robust material with favorable magnetic properties for studying thermally active ASI and use it to investigate a variety of ASI geometries. We reproduce previously reported perfect ground-state ordering in the square geometry and present studies of the kagome lattice showing the highest yet degree of ordering observed in this fully frustrated system. We consider theoretical predictions of long-range order in ASI and use both our experimental studies and kinetic Monte Carlo simulations to evaluate these predictions. Next, we introduce controlled topological defects into our square ASI samples and observe a new, extended frustration effect of the system. When we introduce a dislocation into the lattice, we still see large domains of ground-state order, but, in every sample, a domain wall containing higher energy spin arrangements originates from the dislocation, resolving a discontinuity in the ground-state order parameter. Locally, the magnets are unfrustrated, but frustration of the lattice persists due to its topology. We demonstrate the first direct imaging of spin configurations resulting from topological frustration in any system and make predictions on how dislocations could affect properties in numerous materials systems

Topology by Design in Magnetic nano-Materials: Artificial Spin Ice

Artificial Spin Ices are two dimensional arrays of magnetic, interacting nano-structures whose geometry can be chosen at will, and whose elementary degrees of freedom can be characterized directly. They were introduced at first to study frustration in a controllable setting, to mimic the behavior of spin ice rare earth pyrochlores, but at more useful temperature and field ranges and with direct characterization, and to provide practical implementation to celebrated, exactly solvable models of statistical mechanics previously devised to gain an understanding of degenerate ensembles with residual entropy. With the evolution of nano--fabrication and of experimental protocols it is now possible to characterize the material in real-time, real-space, and to realize virtually any geometry, for direct control over the collective dynamics. This has recently opened a path toward the deliberate design of novel, exotic states, not found in natural materials, and often characterized by topological properties. Without any pretense of exhaustiveness, we will provide an introduction to the material, the early works, and then, by reporting on more recent results, we will proceed to describe the new direction, which includes the design of desired topological states and their implications to kinetics.Comment: 29 pages, 13 figures, 116 references, Book Chapte

Topological frustration of artificial spin ice supplemental movies

Supplemental movies for the manuscript entitled "Topological frustration of artificial spin ice."This work was supported by NSF CAREER Grant No. DMR-1056974. We also acknowledge the support of the Maryland NanoCenter and its AIMLab and FabLab

How to extract distributed circuit parameters from the scattering parameters of a transmission line

Distributed circuit parameters parameterize the transmission and reflection off a given transmission line in terms of a distributed resistance, inductance, capacitance, and conductance, which are per-unit-length, frequency-dependent quantities. While there are analytical models for extracting the distributed circuit parameters, these models are discontinuous as a function of frequency when the argument approaches a branch cut. Here, we develop a nonlinear least-square regression algorithm that accurately extracts the distributed circuit parameters. Compared to existing approaches and finite element models, our algorithm successfully extracts the distributed circuit parameters as a function of frequency, all while being less sensitive to these phase conditions. Such an algorithm is useful for understanding how to deembed transmission lines, and how to extract electrical properties of the materials used in a circuit.Peer ReviewedPostprint (published version

How to extract distributed circuit parameters from the scattering parameters of a transmission line

Distributed circuit parameters parameterize the transmission and reflection off a given transmission line in terms of a distributed resistance, inductance, capacitance, and conductance, which are per-unit-length, frequency-dependent quantities. While there are analytical models for extracting the distributed circuit parameters, these models are discontinuous as a function of frequency when the argument approaches a branch cut. Here, we develop a nonlinear least-square regression algorithm that accurately extracts the distributed circuit parameters. Compared to existing approaches and finite element models, our algorithm successfully extracts the distributed circuit parameters as a function of frequency, all while being less sensitive to these phase conditions. Such an algorithm is useful for understanding how to deembed transmission lines, and how to extract electrical properties of the materials used in a circuit.Peer Reviewe