Remo V. Hügli

Artificial kagome spin ice: dimensional reduction, avalanche control and emergent magnetic monopoles

Artificial spin-ice systems consisting of nanolithographic arrays of isolated nanomagnets are model systems for the study of frustration-induced phenomena. We have recently demonstrated that monopoles and Dirac strings can be directly observed via synchrotron-based photoemission electron microscopy, where the magnetic state of individual nanoislands can be imaged in real space. These experimental results of Dirac string formation are in excellent agreement with Monte Carlo simulations of the hysteresis of an array of dipoles situated on a kagome lattice with randomized switching fields. This formation of one-dimensional avalanches in a two-dimensional system is in sharp contrast to disordered thin films, where avalanches associated with magnetization reversal are two-dimensional. The self-organized restriction of avalanches to one dimension provides an example of dimensional reduction due to frustration. We give simple explanations for the origin of this dimensional reduction and discuss the disorder dependence of these avalanches. We conclude with the explicit demonstration of how these avalanches can be controlled via locally modified anisotropies. Such a controlled start and stop of avalanches will have potential applications in data storage and information processing.

A geometric characterization of structural projections on a JBW∗-triple☆

A structural projection R on a Jordan∗-triple A is a linear projection such that, for all elements a, b and c in A, R{aRbc}={RabRc}. The L-orthogonal complement G◊ of a subset G of a complex Banach space E is the set of elements x in E such that, for all elements y in G, ||x±y||=||x||+||y||. A contractive projection P on E is said to be neutral if the condition that ||Px||=||x|| implies that the elements Px and x coincide, and is said to be a GL-projection if the L-orthogonal complement (PE)◊ of the range PE of P is contained in the kernel ker(P) of P. It is shown that, for a JBW∗-triple A, with predual A∗, a linear projection R on A is structural if and only if it is the adjoint of a neutral GL-projection on A∗, thereby giving a purely geometric characterization of structural projections.

Controlling vortex chirality in hexagonal building blocks of artificial spin ice

We exploit dipolar coupling to control the magnetic states in assemblies of single-domain magnetic nanoislands, arranged in one, two and three adjacent hexagonal rings. On tailoring the shape anisotropy of specific islands, and thus their switching fields, we achieve particular target states with near perfect reliability, and are able to control the chirality of the vortex target states. The magnetic states are observed during magnetization reversal with x-ray photoemission electron microscopy and our results are generally in excellent agreement with a numerical model based on point dipoles and realistic values of disorder. We conclude with a quantitative discussion of how our results depend on disorder and the chosen bias in shape anisotropy.

The identity is isolated among composition operators

Let H∞(B) be the Banach algebra of bounded holomorphic functions on the open unit ball B of a Banach space. We show that the identity operator is an isolated point in the space of composition operators on H°°(B). This answers a conjecture of Aron, Galindo and Lindstrom.