# Incommensurate magnetic structure

An *incommensurate magnetic structure* is a structure in which the magnetic moments are ordered, but without periodicity that is commensurate with that of the nuclear structure of the crystal. In particular, the magnetic moments have a spin density with wave vectors that have at least one irrational component with respect to the **S**(**n**+**r**_{j}) (where the *j*th atom has position **r**_{j} in the unit cell) has Fourier components with irrational indices with respect to the reciprocal

### Details

When the atoms of the basic structure are at **n**+**r**_{j}, where **r**_{j} is the position of the *j*th atom in the unit cell, then the spin function for an incommensurate magnetic structure is

This spin structure is incommensurate if one component of the basis vectors **a**_{i}^{*} is irrational. Incommensurate magnetic structures may be linear, but occur as quite complicated, like fan structures etc. as well. Especially, in rare-earth