spinw.fourier method#

Syntax#

F = fourier(obj,Q,Name,Value)

Description#

F = fourier(obj,hkl,Name,Value) calculates the following Fourier sum:

\[J(\mathbf{k}) = \sum_{i,j} J_{i,j} * \exp(i \mathbf{k}\cdot \mathbf{d}_{i,j})\]

The code is optimised for calculating the sum for large number of wave vectors and alternatively for a large number of \(d_{i,j}\) vectors (large system size). The single ion anisotropy is not included in the sum.

Input Arguments#

obj

spinw object.

Q

Defines the \(Q\) points where the spectra is calculated, in reciprocal lattice units, size is \([3\times n_{Q}]\). \(Q\) can be also defined by several linear scan in reciprocal space. In this case Q is cell type, where each element of the cell defines a point in \(Q\) space. Linear scans are assumed between consecutive points. Also the number of \(Q\) points can be specified as a last element, it is 100 by defaults.

For example to define a scan along \((h,0,0)\) from \(h=0\) to \(h=1\) using 200 \(Q\) points the following input should be used:

Q = {[0 0 0] [1 0 0]  50}

For symbolic calculation at a general reciprocal space point use sym type input.

For example to calculate the spectrum along \((h,0,0)\) use:

Q = [sym('h') 0 0]

To calculate spectrum at a specific \(Q\) point symbolically, e.g. at \((0,1,0)\) use:

Q = sym([0 1 0])

Name-Value Pair Arguments#

'extend'

If true, the Fourier transform will be calculated on the magnetic supercell, if false the crystallographic cell will be considered. Default is true.

'isomode'

Defines how Heisenberg/non-Heisenberg Hamiltonians are treated. Can have the following values:

'off' Always output the \([3\times 3]\) form of the Hamiltonian, (default).
'auto' If the Hamiltonian is Heisenberg, only output one of the diagonal values from the \([3\times 3]\) matrices to reduce memory consumption.

'fid'

Defines whether to provide text output. The default value is determined by the fid preference stored in swpref. The possible values are:

0 No text output is generated.
1 Text output in the MATLAB Command Window.
fid File ID provided by the fopen command, the output is written into the opened file stream.

Output Arguments#

res struct type with the following fields:

ft contains the Fourier transform in a matrix with dimensions \([3\times 3\times n_{magExt}\times n_{magExt}\times n_{hkl}]\) or \([1\times 1\times n_{magExt}\times n_{magExt}\times n_{hkl}]\) for Heisenberg and non-Heisenberg Hamiltonians respectively (if isomode is 'auto'). Here \(n_{magExt}\) is the number of magnetic atoms in the magnetic cell and \(n_{hkl}\) is the number of reciprocal space points.
hkl Matrix with the given reciprocal space points stored in a matrix with dimensions \([3\times n_{hkl}]\).
isiso True is the output is in Heisenberg mode, when the ft matrix has dimensions of \([1\times 1\times n_{magExt}\times n_{magExt}\times n_{hkl}]\), otherwise it is false.