R. F. Wang

Artificial ‘spin ice’ in a geometrically frustrated lattice of nanoscale ferromagnetic islands

Frustration, defined as a competition between interactions such that not all of them can be satisfied, is important in systems ranging from neural networks to structural glasses. Geometrical frustration, which arises from the topology of a well-ordered structure rather than from disorder, has recently become a topic of considerable interest. In particular, geometrical frustration among spins in magnetic materials can lead to exotic low-temperature states, including ‘spin ice’, in which the local moments mimic the frustration of hydrogen ion positions in frozen water. Here we report an artificial geometrically frustrated magnet based on an array of lithographically fabricated single-domain ferromagnetic islands. The islands are arranged such that the dipole interactions create a two-dimensional analogue to spin ice. Images of the magnetic moments of individual elements in this correlated system allow us to study the local accommodation of frustration. We see both ice-like short-range correlations and an absence of long-range correlations, behaviour which is strikingly similar to the low-temperature state of spin ice. These results demonstrate that artificial frustrated magnets can provide an uncharted arena in which the physics of frustration can be directly visualized.

Energy minimization and ac demagnetization in a nanomagnet array.

We study ac demagnetization in frustrated arrays of single-domain ferromagnetic islands, exhaustively resolving every (Ising-like) magnetic degree of freedom in the systems. Although the net moment of the arrays is brought near zero by a protocol with sufficiently small step size, the final magnetostatic energy of the demagnetized array continues to decrease for finer-stepped protocols and does not extrapolate to the ground-state energy. The resulting complex disordered magnetic state can be described by a maximum-entropy ensemble constrained to satisfy just nearest-neighbor correlations.

Ground state lost but degeneracy found: The effective thermodynamics of artificial spin ice

We analyze the rotational demagnetization of artificial spin ice, a recently realized array of nanoscale single-domain ferromagnetic islands. Demagnetization does not anneal this model system into its antiferromagnetic ground state: the moments have a static disordered configuration similar to the frozen state of the spin ice materials. We demonstrate that this athermal system has an effective extensive degeneracy and we introduce a formalism that can predict the populations of local states in this icelike system with no adjustable parameters.

Demagnetization protocols for frustrated interacting nanomagnet arrays

We report a study of demagnetization protocols for frustrated arrays of interacting single-domain permalloy nanomagnets by rotating the arrays in a changing magnetic field. The most effective demagnetization is achieved by not only stepping the field strength down while the sample is rotating, but also by combining each field step with alternation in the field direction. By contrast, linearly decreasing the field strength or stepping the field down without alternating the field direction leaves the arrays with a larger remanent magnetic moment. These results suggest that nonmonotonic variations in field magnitude around and below the coercive field are important for the demagnetization process.