Spin spirals: Difference between revisions

From VASP Wiki
No edit summary
No edit summary
Line 16: Line 16:
</span>
</span>


''i.e.'', from one unit cell to the next the up- and down-spinors pick up an additional phase factor of <math>\exp(-i{\bf q}\cdot {\bf R}/2)</math> and <math>\exp(+i{\bf q}\cdot {\bf R}/2)</math>, respectively.
''i.e.'', from one unit cell to the next the up- and down-spinors pick up an additional phase factor of <math>\exp(-i{\bf q}\cdot {\bf R}/2)</math> and <math>\exp(+i{\bf q}\cdot {\bf R}/2)</math>, respectively,
Here, '''R''' is a lattice vector of the crystalline lattice, and '''q''' is the so-called spin-spiral propagation vector.
where, '''R''' is a lattice vector of the crystalline lattice, and '''q''' is the so-called spin-spiral propagation vector.
The latter is commonly chosen to lie within the first Brillouin zone of the reciprocal space lattice, and has to be specified by means of the {{TAG|QSPIRAL}}-tag.
 
The spin-spiral propagation vector is commonly chosen to lie within the first Brillouin zone of the reciprocal space lattice, and has to be specified by means of the {{TAG|QSPIRAL}}-tag.


This generalized Bloch condition gives rise to the following behavior of the magnetization density:
This generalized Bloch condition gives rise to the following behavior of the magnetization density:

Revision as of 12:53, 6 July 2018

Generalized Bloch condition

Spin spirals may be conveniently modeled using a generalization of the Bloch condition:

i.e., from one unit cell to the next the up- and down-spinors pick up an additional phase factor of and , respectively, where, R is a lattice vector of the crystalline lattice, and q is the so-called spin-spiral propagation vector.

The spin-spiral propagation vector is commonly chosen to lie within the first Brillouin zone of the reciprocal space lattice, and has to be specified by means of the QSPIRAL-tag.

This generalized Bloch condition gives rise to the following behavior of the magnetization density:

This is schematically depicted in the figure at the top of this page: the components of the magnization in the xy-plane rotate about the spin-spiral propagation vector q.