Introduction 

The resolution function of a triple-axis neutron spectrometer is determined by beam divergence, wavelength spread, mosaicity of the sample, etc.

The resolution function has an elliptic shape on the horizontal scattering plane at the elastic condition. Specifically, the width along the longitudinal direction (Wl) tends to be wider than that along transverse direction (Wt). 

When evaluating widths of magnetic peaks, it is necessary to take into account that the shape of the resolution function and the scan directions. For instance, the figure below is showing the scattering profiles of a magnetic peak in the isosceles triangular lattice antiferromagnet CoNb2O6. These profiles were measured along four different directions, and thus have different shapes. [TN et al. Phys. Rev. B 90, 064431 (2014)]

Longitudinal width : Wl

Wl is determined by a θ-2θ scan, in which the resolution ellipse is moving along the radial direction from the origin of the reciprocal space. 

The data is normally measured as a function of 2θ. By using the wavenumber of the neutron, ki, the 2theta angle can be converted to the momentum transfer of the neutron Q (= 2ki sin(2θ/2)). The data is plotted as a function of Q. By fitting a Gaussian function to the data, we obtain the Q value for the nuclear reflection and the width, that is Wl. 

Transverse width : Wt

Wt is determined by a ω scan, in which the resolution ellipse is moving perpendicular to the radial direction. 

The data is normally measured as a function of ω, while the 2theta angle is fixed. The Q value of the nuclear reflection is obtained by the relation Q = 2ki sin(2θ/2). The data is plotted as a function of ω. By fitting a Gaussian function to the data, we obtain the width of the peak dω in radian unit. The transverse width Wt is given by Qdω. 

Q-dependence of the resolution function

Wl and Wt are Q dependent. Normally, dω does not change with Q, and thus Q can be approximated as Wt=Qdω. Wl is minimized when the 2θ angle for the sample is close to the 2θ angle for the monochromator. We often use a quadratic function to interpolate the data. 

Reciprocal lattice scans

The estimation of the resolution function is particularly important when measuring reciprocal lattice scans which is not parallel/perpendicular to the radial direction. 

The figure below shows the resolution function for a (H,H,3/2) line scan in a triangular lattice magnet. [TN et al. PRB 79,214423 (2009)] The angle between the long axis of the ellipse and the scan direction is varying with H. Therefore, the resolution width along the scan direction also changes with H.