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-spinor 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.
Here, '''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.
The latter is commonly chosen to lie within the first Brillouin zone of the reciprocal space lattice.

Revision as of 12:46, 6 July 2018

Generalized Bloch condition

Spin spirals may be conveniently modeled using a generalisation 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. Here, 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.

This condition gives rise to the following behaviour 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.