Geometrical Frustration - Artificial Geometrically Frustrated Ferromagnets

Artificial Geometrically Frustrated Ferromagnets

Although many properties of spin ice materials have been studied experimentally, little has been revealed about the local accommodation of spin to frustration within the system, since that individual spins cannot be probed without altering the state of the system. Fortunately, with the help of new nanometer techniques, it is possible to fabricate nanometer size magnetic islands analogous to those of the naturally occurring spin ice materials, and they can be probed without altering the moment configuration.

In 2006 R.F.Wang et al. reported the discovery of an artificial geometrically frustrated magnet composed of arrays of lithographically fabricated single-domain ferromagnetic islands. These islands are manually arranged to create a two-dimensional analog to spin ice. As shown in Figure 7a, to mimic the frustration of spin ice, a two-dimensional analog is created by frustrated arrays consisting of square lattices, in which a single lattice is represented by four ferromagnetic islands meeting at a vertex. For a pair of moments at one vertex, it is favorable to have one pointing in and the other pointing out, while unfavorable to have both pointing out or pointing in, due to energy minimization (Figure 7b). For the four moments at one vertex, there are 16 kinds of configurations, as in Figure 7c. The lowest energy vertex configurations is Type I and II, which have two moments pointing in toward the centre of the vertex, and two pointing out. The percentage of Type I and II are 12.5% and 25% respectively.

Using lithographically fabricated arrays, it is possible to engineer frustrated systems to alter the strength of interactions, the geometry of the lattice, the type and number of defects, and other properties which impact the nature of frustration. The lattice parameters range from 320 nm to 880 nm, with a fixed island size of 80 nm × 220 nm laterally and 25 nm thick, which is small enough for magnetic moments to point lengthwise along the islands and big enough to be stable at 300 K. Figure 8 is AFM (Atomic force microscopy) and MFM (Magnetic force microscopy) images of the frustrated lattice. The black and white halves in Figure 8b indicate the north and south poles of the ferromagnetic island. From the MFM images, the moment configuration of array can be easily determined. The vertex types can be directly observed as described in Figure 7c: the pink vertex is Type I, the green vertex is Type III and the blue vertex is Type II. Thus the artificial spin ice is demonstrated.

In this work on a square lattice of frustrated magnets, Wang et al. observed both ice-like short-range correlations and the absence of long-range correlations, just like in the spin ice at low temperature. These results solidify the uncharted ground on which the real physics of frustration can be visualized and modeled by these artificial geometrically frustrated magnets, and inspires further research activity.