Systems of interacting nanomagnets known as artificial spin ice 1-4 have allowed the design, realization and study of geometrically frustrated exotic collective states 5-10 that are absent in natural magnets. We have experimentally measured 11,12 the thermally induced moment fluctuations in the Shakti geometry of artificial spin ice. We show that its disordered moment configuration is a topological phase described by an emergent dimer-cover model 13 with excitations that can be characterized as topologically charged defects. Examination of the lowenergy dynamics of the system confirms that these effective topological charges have long lifetimes associated with their topological protection, that is, they can be created and annihilated only as charge pairs with opposite sign and are kinetically constrained. This manifestation of classical topological order 14-19 demonstrates that geometrical design in nanomagnetic systems can lead to emergent, topologically protected kinetics that can limit pathways to equilibration and ergodicity. Artificial spin ices are lithographically fabricated systems of interacting single-domain nanomagnets. These systems can be used to investigate the collective magnetic behaviour of interacting moments as effective models for understanding the complex phenomena of frustration. Each nanomagnet moment aligns along the edges of a lattice and points towards or away from the lattice vertices. In their low-energy collective states, the moments enter a so-called ice-manifold; an ensemble in which, at each vertex, the difference between the number of moments pointing in and out is minimized, leading to the ice-rule (2-in/2-out 20 at vertices where four moments meet or 1-in/2-out, 2-in/1-out at vertices where three moments meet). Originally inspired by rare-earth pyrochlore spin ice materials, these artificial spin ice systems evolved towards new geometries 5,6 , with exotic phases absent in natural magnets 2,3,7,8,21. Recent experimental works have characterized the thermal fluctuations of the individual magnetic moments, opening new vistas in the real-time, real-space analysis of frustration 11,12,22-25. The Shakti lattice geometry 5-7 (Fig. 1) is a decimation of the square ice lattice geometry. In Fig. 1e, we show the possible moment configurations at vertices and label them by the number of islands at each vertex (the coordination number, z) and by their relative energy hierarchy. The collective ground state is a configuration in which the z = 2 and z = 4 vertices are all in their lowest energy state (that is, type I 4 for the four-island vertices and type I 2 for the twoisland vertices) while only half of the z = 3 vertices lie in their lowest
The change in electrical resistance associated with the application of an external magnetic field is known as the magnetoresistance (MR). The measured MR is quite complex in the class of connected networks of single-domain ferromagnetic nanowires, known as 'artificial spin ice', due to the geometrically-induced collective behavior of the nanowire moments. We have conducted a thorough experimental study of the MR of a connected honeycomb artificial spin ice, and we present a simulation methodology for understanding the detailed behavior of this complex correlated magnetic system. Our results demonstrate that the behavior, even at low magnetic fields, can be well-described only by including significant contributions from the vertices at which the legs meet, opening the door to new geometrically-induced MR phenomena.
Artificial spin ices (ASIs) are interacting arrays of lithographically-defined nanomagnets in which novel frustrated magnetic phases can be intentionally designed. A key emergent description of fundamental excitations in ASIs is that of magnetic monopoles -mobile quasiparticles that carry an effective magnetic charge. Here we demonstrate that the archetypal square ASI lattice can host, in specific regions of its magnetic phase diagram, high-density plasma-like regimes of mobile magnetic monopoles. By passively "listening" to spontaneous monopole noise in thermal equilibrium, we reveal their intrinsic dynamics and show that monopole kinetics are minimally correlated (that is, most diffusive) in the plasma phase. These results open the door to on-demand monopole regimes having field-tunable densities and dynamic properties, thereby providing a new paradigm for probing the physics of effective magnetic charges in synthetic matter.
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