Magnetic monopoles as a collective phenomenon

Moessner and his colleagues use an astonishingly simple model to explain magnetic monopoles as a collective phenomenon in spin ice. The starting point of the model are the magnetic moments at the corners of the tetrahedra of which spin ice is composed. Moessner compares each magnetic moment to a dumbbell, with a north pole at one end and a south pole at the other. Two north and two south poles thus meet in the middle of each tetrahedron. The opposing magnetic charges of the poles in this configuration cancel.

When one bar magnet in achain (a) flips, two monopoles (b and c) are created. In the spin ice model, such chains are jumbled up (coloured lines, d). The monopoles can move along these chains (e).

If one of the dumbbells is now turned by 180 degrees, an imbalance arises in the middle of two adjacent tetrahedra. Three poles with the same polarity meet one with the opposite polarity: in one tetrahedron, three north poles face a single south pole, and in the adjacent tetrahedron, three south poles a north pole. So overall, there are surplus north poles in one tetrahedron, and surplus south poles in the other. This disturbs the magnetic neutrality at a local level, and thus requires the use of a tiny energy quantum.

The poles can now move apart; this requires only a little additional energy to overcome the attraction between the magnetic monopoles. As the distance between the poles increases, the energy required drops progressively. When an adjacent dumbbell flips, one of the poles migrates one tetrahedron further. Since the procedure can be repeated indefinitely, the magnetic monopoles are effectively freely mobile. In conventional magnetic substances, such as iron, this is not the case. Although these substances contain magnetic moments, the reversal of each moment requires the same amount of energy, since it is surrounded by opposing moments. For this reason, in ferromagnets, the attraction between two magnetic defects does not become weaker as they move apart; rather, the energy required increases without bound, almost as if they were at opposite ends of a spring being stretched apart. In spin ice, by contrast, chains of moments are tangled like spaghetti on a plate that can be pushed around at will. So monopoles are linked, as it were, not by a spring, but by a loose thread.

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