Spin spirals: Difference between revisions

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In the case of spin-spiral calculations the cutoff energy of the basis set is specified by means of the {{TAG|ENINI}}-tag.
In the case of spin-spiral calculations the cutoff energy of the basis set is specified by means of the {{TAG|ENINI}}-tag.
Additionally one needs to set {{TAG|ENMAX}} appropriately:
Additionally one needs to set {{TAG|ENMAX}} appropriately:
{{TAG|ENMAX}} (>{{TAG|ENINI}}) needs to be chosen large enough so that the plane wave components of both the up-spinors as well as the components of the down-spinor all have

Revision as of 13:37, 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

The generalized Bloch condition redefines the Bloch functions as follows:

This changes the Hamiltonian only minimally:

where in and the kinetic energy of a plane wave component changes to:

In the case of spin-spiral calculations the cutoff energy of the basis set is specified by means of the ENINI-tag.

Additionally one needs to set ENMAX appropriately: ENMAX (>ENINI) needs to be chosen large enough so that the plane wave components of both the up-spinors as well as the components of the down-spinor all have