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Difference between revisions of "Incommensurate magnetic structure"

From Online Dictionary of Crystallography
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[[Incommensurate magnetic structure]]
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<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'').
 
   
 
   
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== Definition ==
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<Font color="blue">Structure magn&eacute;tique incommensurable</font> (Fr.)
 
 
   
 
   
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  '''Definition'''
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An ''incommensurate magnetic structure'' is a [[crystal pattern|structure]] in which the magnetic moments are
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ordered, but without periodicity that is commensurate with that of the nuclear structure
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of the crystal. In particular, the magnetic moments have a spin density with wave vectors
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that have at least one irrational component with respect to the reciprocal lattice
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of the atoms. Or, in the case of localized moments, the spin function  '''S'''('''n'''+'''r'''<sub>''j''</sub>)
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(where the ''j''th atom has position '''r'''<sub>''j''</sub> in the [[unit cell]]) has Fourier components
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with irrational indices with respect to the reciprocal lattice of the crystal.
 
   
 
   
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An  ''incommensurate magnetic structure'' is a structure in which the magnetic moments are
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== Details ==
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ordered, but without  periodicity that is commensurate with that of the nuclear structure
 
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of the crystal. In particular, the magnetic moments have a spin density with wave vectors
 
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that have at least one irrational component with respect to the reciprocal lattice
 
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of the atoms. Or, in the case of localized moments, the spin function  '''S'''( '''n'''+'''r'''<sub>j</sub>)
 
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(where the $j$th atom has position {\bf r}$_j$ in the unit cell) has Fourier components
 
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with irrational indices with respect to the reciprocal lattice of the crystal.
 
 
   
 
   
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  '''Details'''
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When the atoms of the basic structure are at positions '''n'''+'''r'''<sub>j</sub>, where  '''r'''<sub>j</sub>
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is the position of the ''j''th atom in the unit cell, then the spin function for
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When the atoms of the basic structure are at positions '''n'''+'''r'''<sub>j</sub>, where  '''r'''<sub>j</sub>
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an incommensurate magnetic structure is
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is the position of the ''j''th atom in the unit cell, then the spin function for
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an incommensurate magnetic structure is
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<center>
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<math>S( n+ r_j) = \sum_ {k} \hat{S}( k)_j \exp \left[2\pi i  k.( n+
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  r_j)\right], k=\sum_{i=1}^n h_i  a_i^* (h_i\,  \mathrm{integer})</math>.
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</center>
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This spin structure is incommensurate if one component of the basis vectors  '''a'''<sub>i</sub><sup>*</sup>
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is irrational. Incommensurate magnetic structures may be linear, but occur as quite
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complicated, like fan structures etc. as well. Especially, in rare-earth compounds very
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complicated magnetic phase diagrams have been found.
  
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<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>
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[[Category:Fundamental crystallography]]
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This spin structure is incommensurate if one component of the basis vectors  '''a'''<sub>i</sub><sup>*</sup>
 
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is irrational. Incommensurate magnetic structures may be linear, but occur as quite
 
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complicated, like fan structures etc. as well. Especially, in rare-earth compounds very
 
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complicated magnetic phase diagrams have been found.
 

Latest revision as of 17:15, 14 November 2017

Structure magnétique incommensurable (Fr). Inkommensurable Magnetstruktur (Ge). Struttura magnetica incommensurabile (It). 非整合磁気構造 (Ja). Estructura magnética inconmensurable structure (Sp).

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+rj) (where the jth atom has position rj 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+rj, where rj is the position of the jth atom in the unit cell, then the spin function for an incommensurate magnetic structure is

[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].

This spin structure is incommensurate if one component of the basis vectors ai* 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.

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