Helimagnets

It is possible for ferromagnetic and antiferromagnetic interactions to be in conflict. A good example is a layer structure where ferromagnetic layers couple

Figure 1: Some incommensurate magnetic structures: (a) helical, (b) cycloidal, (c) helicoidal and (d) sinusoidally modulated. Only (b) has a net ferromagnetic moment.

ferromagnetically to the neighbouring layers, but antiferromagnetically to the next-neighbour layers. A helical spin structure is then possible. If ₁ and ₂ are the exchange constants for the first and second neighbour planes, the energy of a spin in the central plane,

is minimized when cos θ = −₁/4₂. The helimagnetic structure arises when
₁ > 0, ₁ < −4₂.
Other modulated structures that can arise from a balance of exchange and anisotropy are the helicoidal (easy cone) and cycloidal structures shown in Fig.1. The magnitude of the moment can sometimes be periodically modulated, rather than its direction. The best-known example of a sinusoidally modulated structure is chromium. When the modulation period is unrelated to the underlying periodicity of the lattice, as it is in pure Cr, the structure is incommensurate. Any commensurate magnetic order can equally well be described as a multisublattice structure in an enlarged unit cell.