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 synchrotronbased 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 twodimensional. 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.

We study artificial spin ice with isolated elongated nanoscale islands arranged in a kagome lattice and solely interacting via long range dipolar fields. The artificial kagome spin ice displays a phenomenology similar to the microscopic pyrochlore system, where excitations at sub-Kelvin temperatures consist of emergent monopole quasiparticles that are connected via a solenoidal flux line, a classical and observable version of the Dirac string. We show that magnetization reversal in kagome spin ice is fundamentally different from the nucleation and extensive domain growth scenario expected for a generic 2D system. Here, the magnetization reverses in a strictly 1D fashion: After nucleation, a monopole-antimonopole dissociates along a 1D path, leaving a (Dirac) string of islands with reversed magnetization in its wake. Since the 2D artificial spin ice spontaneously decays into a 1D subsystem, magnetization reversal in kagome spin ice provides an example of dimensional reduction via frustration. V

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