When I was a kid, there were no toys I treasured more than magnets. I had dozens of them: horseshoes, bars, a couple of powerful alnico cylinders salvaged from old loudspeakers. The invisible but very palpable forces acting between these objects—pushing like poles apart, drawing unlike together—were signs to me that mystery still exists in the universe. And yet magnetism also taught me that mysteries can be unraveled and understood. In some book I borrowed from the public library (maybe it was a biography of William Gilbert?) I read an explanation of magnetism that seemed to make sense. Imagine an array of many thousands of magnetic compass needles, all packed tightly together, the book suggested. Each such needle will tug on its neighbors as the magnetic fields interact, and so the needles throughout the array will all tend to line up in parallel. This is how a permanent magnet (or ferromagnet) works, the book said; the imagined tiny compass needles represent individual atoms in magnetic materials such as iron.
There are two problems with this story. First, it fails to explain where the atomic magnetic fields come from. Are we to imagine inside each atom an array of even tinier compass needles? Second, the explanation is just plain wrong. The atomic-scale magnetic dipoles in a ferromagnet do not line up because of magnetic interactions like those between compass needles. The actual interatomic forces are quite different; they are short-range, quantum-mechanical interactions that have no direct counterpart in the world of macroscopic objects.
I have known the truth about ferromagnets for some time, but the debunking of the many-tiny-compass-needles story leaves another question still murky. If an array of compass needles is not a good model of a ferromagnet, what does happen when you bring a bunch of magnetic compasses close together? A recent paper by six authors in Japan, India and the U.S. answers this question in the most direct way possible—through experiments with real compasses. They used small, spherical, liquid-filled compasses meant for mounting on a car windshield.
Before reading on, you might try to guess the outcome of their experiments.
When the compasses are arranged in a line—a one-dimensional array—the needles do tend to line up head-to-tail, all parallel to the line. Even with as few as two compasses, this interaction is strong enough to overcome the influence of the earth’s magnetic field.
But a two-dimensional, square array behaves differently, and not at all like a ferromagnet. In fact, the square lattice of compasses is an antiferromagnet, with nearby elements pointing in opposite directions. Even more surprising, the antiferromagnetic lattice is twisted 45 degrees with respect to the underlying lattice of compass needles. If the edges of the compass array are parallel to the east-west and north-south axes, then the compass needles all point along the diagonals. Sets of four adjacent compasses form a sort of loop, with needles pointing northeast, southeast, southwest, northwest. The paper explains this curious structure as a superposition of two simpler antiferromagnetic states: In one of these states, alternating rows of the latttice are oriented east and west; in the other, alternating columns are directed north and south.
The paper, Ferroics: magnetic-compass lattice and optical phonon dispersions of dipolar crystals, is available from the arXiv and has been submitted to The American Journal of Physics. The authors are Takeshi Nishimatsu, Umesh V. Waghmare, Yoshiyuki Kawazoe, Benjamin Burton, Kazutaka Nagao and Yoshihiko Saito.