Approximate resolution convolution function for fitting a dispersion gap measured on a triple-axis spectrometer

TL;DR

This paper introduces an analytic convolution function for accurately fitting dispersion gaps in triple-axis spectrometer data, accounting for instrumental resolution effects, and demonstrates its superior performance over previous methods.

Contribution

The authors develop a new convolution function that improves the accuracy and reliability of fitting dispersion gaps in TAS measurements, considering typical instrumental resolution effects.

Findings

The new function outperforms previous fitting methods in accuracy.

It reliably reproduces known gap sizes from experimental data.

The function is simple to implement and converges reliably.

Abstract

We present an analytic convoluted-gap function, eq. 11 in the manuscript, for fitting dispersion gaps measured on triple-axis spectrometers (TAS). At the gap, the instrumental resolution skews the signal, producing a high-energy tail that complicates fitting. Our function assumes an instrumental $Q$-resolution with two equal wide and one narrow direction (typical of focused TAS instruments), and a parabolic dispersion at the gap, which is exact for quadratic and accurate for linear dispersions if the resolution is moderate. We demonstrate, that our function outperforms previous methods of fitting a gap, by giving a better fit and more accurate gap determination, seen in figure 4. Here, the anti-ferromagnetically gapped material; MnF$_2$ is simulated in a double-focusing TAS instrument. We also tested our function on experimental data on MnF$_2$ from a TAS-like instrument, where we reproduce the gap size from previous accurate experimentally determined measurements. The function is simple to implement, converges reliably, and we recommend its use for future gap fitting on TAS data.