The ancient Greeks were aware of the phenomenon of magnetic order in lodestone, a type of rock containing the ferromagnet magnetite Fe3O4. Magnetic moments in a ferromagnet tend to align and thereby sum to an easily observed macroscopic magnetic moment. The absence of such a moment even in ordered antiferromagnets is the reason their discovery is comparatively recent. It had to await the development of Louis Néel’s microscopic theory of spin interactions in the 1930s and the neutron diffraction measurement of MnO in 1949 by Clifford Shull and Stuart Smart.
There are magnets, however, that today present greater experimental and theoretical challenges than those posed by simple antiferromagnets in the 1930s. 1 The origin of their complex and varied behavior is remarkably simple and can be illustrated by as few as three spins on a triangular lattice. Once two of the spins on an elementary triangle...
