# Quantifying uncertainties in crystal electric field Hamiltonian fits to neutron data

### Submission summary

 As Contributors: Allen Scheie Arxiv Link: https://arxiv.org/abs/2107.14164v4 (pdf) Code repository: https://github.com/asche1/PyCrystalField/tree/master/Publications/UncertaintySimulations Date accepted: 2022-03-22 Date submitted: 2022-03-01 17:04 Submitted by: Scheie, Allen Submitted to: SciPost Physics Core Academic field: Physics Specialties: Condensed Matter Physics - Experiment Condensed Matter Physics - Computational Approaches: Experimental, Computational

### Abstract

We systematically examine uncertainties from fitting rare earth single-ion crystal electric field (CEF) Hamiltonians to inelastic neutron scattering data. Using pyrochlore and delafossite structures as test cases, we find that uncertainty in CEF parameters can be large despite visually excellent fits. These results show Yb$^{3+}$ compounds have particularly large $g$-tensor uncertainty because of the few available peaks. In such cases, additional constraints are necessary for meaningful fits.

Published as SciPost Phys. Core 5, 018 (2022)

### Author comments upon resubmission

We thank the referee for the recommendation to clarify the Q-dependent scattering in the neutron cross section equation. Although the simulations we perform neglect such terms and thus are irrelevant to our results, it is best to avoid confusion for readers.

Sincerely,
Allen Scheie

### List of changes

We have updated the text following Eq. 2 clarifying (i) that the cross section is based on the inner product of the magnetic moment with the eigenstates, (ii) that the equation generally has Q-dependent terms because of the magnetic form factor and potentially anisotropic g-tensors, and (iii) common experimental practice is to fit to a constant Q slice of data, such that all Q-dependent terms can be neglected.