View source for Incommensurate magnetic structure

<font color="blue">Structure magn&eacute;tique incommensurable</font> (''Fr''). <font color="red">Inkommensurable Magnetstruktur</font> (''Ge''). <font color="black">Struttura magnetica incommensurabile</font> (''It''). <font color="purple">非整合磁気構造</font> (''Ja''). <font color="green">Estructura magnética inconmensurable structure</font> (''Sp'').
 
== Definition ==
 
An  ''incommensurate magnetic structure'' is a [[crystal pattern|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 reciprocal lattice
of the atoms. Or, in the case of localized moments, the spin function  '''S'''('''n'''+'''r'''<sub>''j''</sub>)
(where the ''j''th atom has position '''r'''<sub>''j''</sub> in the [[unit cell]]) has Fourier components
with irrational indices with respect to the reciprocal lattice of the crystal.
 
== Details ==
 
When the atoms of the basic structure are at positions '''n'''+'''r'''<sub>j</sub>, where  '''r'''<sub>j</sub>
is the position of the ''j''th atom in the unit cell, then the spin function for
an incommensurate magnetic structure is

<center>
<math>S( n+ r_j) = \sum_ {k} \hat{S}( k)_j \exp \left[2\pi i  k.( n+
  r_j)\right], k=\sum_{i=1}^n h_i  a_i^* (h_i\,  \mathrm{integer})</math>.
</center>

This spin structure is incommensurate if one component of the basis vectors  '''a'''<sub>i</sub><sup>*</sup>
is irrational. Incommensurate magnetic structures may be linear, but occur as quite
complicated, like fan structures etc. as well. Especially, in rare-earth compounds very
complicated magnetic phase diagrams have been found.

[[Category:Fundamental crystallography]]