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| where in $H^{\uparrow\uparrow}$ and $H^{\downarrow\downarrow}$ the kinetic energy of a plane wave component changes to | | where in <math>H^{\uparrow\uparrow}</math> and <math>H^{\downarrow\downarrow}</math> the kinetic energy of a plane wave component changes to: |
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Revision as of 13:14, 6 July 2018
Generalized Bloch condition
Spin spirals may be conveniently modeled using a generalization of the Bloch condition (set LNONCOLLINEAR=.TRUE. and LSPIRAL=.TRUE.):
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.
The generalized Bloch condition above 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.
Basis set considerations
redefining the Bloch functions
the Hamiltonian changes only minimally
where in and the kinetic energy of a plane wave component changes to: