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ARTIFICIAL SPIN ICE
The unhappy wanderer
Frustration in spin systems can emerge geometrically in the absence of intrinsic energetic degeneracya topologically induced state that can be visualized in terms of a lattice walk. Now, evidence conrms that the exotic shakti lattice gives rise to such a topology.
Robert L. Stamps
There is an elegant simplicity to the geometrical design of articial spin-ice metamaterialsa simplicity that
belies their great utility in the realization and study of phenomena observed in particle systems far from equilibrium. Writing in Nature Physics, IanGilbert and colleagues1 provide a remarkable example of the potential for fresh insights aorded by articial spin ice. In their paper, the authors demonstrate that frustration can emerge in an intriguing manner that runs counter to common assumptions regarding degeneracy and residual entropy.
The rst articial spin ice was created by decorating a square lattice array with small magnetic islands placed along the edges of the squares dening the lattice2.
These islands were small enough tobehave approximately as block spins, yet large enough to be stable against thermal uctuations at room temperature. Their size also allowed for exact imaging of the spin congurations, and they were spaced such that they would interact strongly through stray magnetic elds produced by the uncompensated magnetic poles at the ends of eachisland.
In this context, it is convenient to discuss local spin congurations in terms of the magnetic congurations at each array vertex. The vertex denes the nearest- and next-nearest-neighbour interactions between magnetic poles at the ends of neighbouring elements a total of sixteen possibilitiesin the square lattice. High-level degeneracy exists for excited vertex states, but the ground-state energy is a well-dened antiferromagneticconguration.
A kagome geometry is realized by placing magnetic elements along the edges of a honeycomb lattice. This geometry supports a true six-fold degenerate ground state and this degeneracy is extensive3.
In contrast to the square lattice, the kagome lattice has a corresponding residual entropy at zero temperature arising directly from the degeneracy of ground-state vertexenergies.
By modifying the square lattice, Gilbert etal.1 demonstrated a way to
generate residual entropy that does not follow from a degeneracy of vertex energies. The result forms a subtly dierent pictureof how frustration can emerge through geometrical constraints even when...