Difference between revisions of "Incommensurate magnetic structure"
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Incommensurate magnetic structure
Structure magnétique incommensurable
Definition 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 reciprocal lattice of the atoms. Or, in the case of localized moments, the spin function S( n+r_{j}) (where the $j$th atom has position {\bf r}$_j$ 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_{j}, where r_{j} is the position of the jth atom in the unit cell, then the spin function for an incommensurate magnetic structure is
[math]{\bf S}({\bf n}+{\bf r}_j)~=~\sum_{\bf k} \hat{\bf S}({\bf k})_j \exp \left(2\pi i {\bf k}.({\bf n}+{\bf r}_j)\right),~~{\bf k}=\sum_{i=1}^n h_i {\bf a}_i^*~~(h_i ~~{\rm integer}).[/math]
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 rareearth compounds very
complicated magnetic phase diagrams have been found.