### Syntax

spectra = sw_egrid(spectra,Name,Value)

### Description

spectra = sw_egrid(spectra,Name,Value) takes a calculated spectrum that contains $$S^{\alpha\beta}(Q,\omega)$$ and converts it into an intensity map I(i,j) via binning the energy values and selecting a given component of the $$9\times 9$$ spin-spin correlation matrix. For example by default (setting the component parameter to 'Sperp') it selects the neutron scattering cross section via calculating the following quantity:

$S_\perp(Q,\omega)=\sum_{\alpha\beta}(1-\hat{q}^\alpha\hat{q}^\beta)\cdot S^{\alpha\beta}(Q,\omega)$

### Examples

The line will create an energy bin, with steps of 0.1 and bins the spin-spin correlation function. Two different matrices will be calculated, first using the sum of the $$S^{xx}$$ and $$S^{yy}$$ components, second will contain the $$S^{zz}$$ component of the correlation function.

tri = sw_model('triAF',1)
spectra = tri.spinwave({[0 0 0] [1 1 0] 501})
E = linspace(0,5,501)
spectra = sw_egrid(spectra,'component',{'Sxx+Syy' 'Szz'},'Evect',E)
figure
sw_plotspec(spectra,'mode','color','axLim',[0 0.5],'dE',0.2)

### Input Arguments

spectra
Input structure, contains spin-spin correlation functions. Supported inputs are produced by spinw.spinwave, spinw.powspec and [spinw.scga].

### Name-Value Pair Arguments

'component'
A string that Selects a correlation function component that will be binned. The possible values are:
• 'Sperp' bins the magnetic neutron scattering intensity (the $$\langle S_\perp S_\perp\rangle$$ expectation value). Default.
• 'Sab' bins the selected components of the spin-spin correlation function. Letter a and b can be x, y or z. For example: 'Sxx' will convolute the $$S^{xx}(Q,\omega)$$ component of the correlation function with the dispersion. Here the $$xyz$$ is the standard coordinate system. *'Mab' bins the selected components of the spin-spin correlation function in the Blume-Maleev coordinate system. Letter a and b can be x, y or z. For example: 'Mxx' will convolute the xx component of the correlation function with the dispersion.
• 'Pab' bins the selected component of the polarisation matrix. Letter a and b can be x, y or z. For example: 'Pyy' will convolute the yy component of the polarisation matrix with the dispersion. The coordinates used are in the Blume-Maleev coordinate system, see below.
• 'Pa' bins the intensity of the calculated polarised neutron scattering, with inciden polarisation of Pa where letter a can be x, y or z. For example: 'Py' will convolute the scattering intensity simulated for incident polarisation $$P_i\|y$$. The used coordinates are in the Blume-Maleev coordinate system.
• 'fName' where fName is one of the field names of the input structure spectra. This field should contain a matrix with dimensions of $$[n_{mode}\times n_{hkl}]$$.

Any linear combination of the above are allowed, for example: 'Sxx+2*Syy' will bin the linear combination of the xx component of the spin-spin correlation function with the yy component. Several cross section can be convoluted and stored independently, if component is a cell array containing strings each containing any linear combination of cross sections as above, the cell array needs to have size $$[1\times n_{cell}]$$, for example {'Sxx' 'Syy' 'Szz'}.

'Evect'
Row vector that defines the center/edge of the energy bins of the calculated output, number of elements is $$n_E$$. The energy units are defined by the spinw.unit property. Default value is an edge bin: linspace(0,1.1*maxOmega,501).
'binType'
String, determines the type of bin give, possible options:
• 'cbin' Center bin, the center of each energy bin is given.
• 'ebin' Edge bin, the edges of each bin is given. Default value is 'ebin'.
'T'
Temperature, used to calculate the Bose factor in units depending on the Boltzmann constant stored in spinw.unit. Default temperature is taken from obj.single_ion.T. The Bose factor is included in swConv field of the output.
'sumtwin'
If true, the spectra of the different twins will be summed together weighted with the normalized volume fractions, see spinw.twin. Default value is true.
'modeIdx'
Select certain spin wave modes from the $$2*n_{magatom}$$ number of modes to include in the output. Default value is 1:2*nMagAtom to include all modes.
'epsilon'
Error limit, used to determine whether a given energy bin is uniform or not. Default value is $$10^{-5}$$.
'autoEmin'
Due to the finite numerical precision, the spin wave energies can contain small imaginary values. These can ruin the convoluted spectrum at low energies. To improve the spectrum, the lowest energy bin should start above the imaginary part of the spin wave energy. If 'autoEmin' is set to true, it calculates the bottom of the first energy bin automatically and overwrites the given value. Only works if the input energy bin starts with zero. Default value is false.
'imagChk'
Checks whether the imaginary part of the spin wave dispersion is smaller than the energy bin size. Default value is true.

### Output Arguments

spectra same as the input spectra plus additions fields:

swConv
Stores the selected cross section binned in energy in a matrix with dimensions of $$[n_E\times n_{hkl}]$$. Includes the Bose factor.
swInt
Stores the selected cross sections for every mode in a matrix with dimensions of $$[n_{mode}\times n_{hkl}]$$.
T
Input temperature.
component
Cell that contains the input component selector strings.
Evect
Input energy bin vector, defines the energy bin edge positions (converted from the given bin centers if necessary).
param
All the input parameters.

If 'component' parameter is a cell array or the spectra of multiple twins are convoluted separately, swConv and swInt will be a cell that packages the matrices corresponding to each component/twin. The dimensions of the cell are $$[n_{conv}\times n_{twin}]$$.