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| G_{\rm ini}=\sqrt{\frac{2m}{\hbar^2}\mathtt{ENINI}} | | G_{\rm ini}=\sqrt{\frac{2m}{\hbar^2}\mathtt{ENINI}} |
| </math> | | </math> |
| | |
| | In most cases it is more than sufficient to set {{TAG|ENMAX}}={{TAG|ENMAX}}<tt>+100</tt>. |
Revision as of 13:51, 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 of the individual spinor components is specified by means of the ENINI-tag.
Additionally one needs to set ENMAX appropriately:
ENMAX needs to be chosen larger than ENINI, and large enough so that the plane wave components of both the up-spinors as well as the components of the down-spinor all have a kinetic energy smaller than ENMAX.
This is the case when:
where
In most cases it is more than sufficient to set ENMAX=ENMAX+100.