Supplementary Material Containing DFT Structure Files and Convergence Tests for our μSR study on Fe2O3

Supplemental material for Local Electronic Structure and Dynamics of Muon-Polaron Complexes in Fe2O3

M. H. Dehn,1,2,3 J. K. Shenton,4,* D. J. Arseneau,3 W. A. MacFarlane,2,3,5 G. D. Morris,3 A. Maigné,2 N. A. Spaldin4 and R. F. Kiefl1,2,3

1Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
2Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC V6T 1Z4, Canada
3Triumf, Vancouver, BC V6T 2A3, Canada
4Department of Materials, ETH Zurich, CH-8093 Zürich, Switzerland
5Department of Chemistry, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada
* For queries about the supplemental material in this repository contact J. Kane Shenton.

In these notebooks we provide supplemental material for our work on understanding the behaviour of muon-polaron complexes in Fe2O3.

We provide VASP input and output files for each of the candidate muon stopping sites and states identified in the paper (also labelled as in the paper). We summarise the muon stopping sites and provide the code for analysing hyperfine tensors in the jupyter notebook: Muon-site-summary.ipynb. There one can also find a summary of the computational details for the paper.

We further provide vasprun.xml files for some of the tests of convergence with respect to plane-wave cutoff energy and k-point sampling density. These tests are summarised in the jupyter notebook: Convergence_tests-ENCUT-KPOINTS.ipynb.

A major source of uncertainty stems from the choice of Hubbard Ueff correction. We varied Ueff in the range 3 − 6 eV to gauge the impact of this parameter on the predicted energies and precession frequencies of the four charge-neutral muon-polaron complex states. This analysis is available in the notebook:  muons_wrt_U.ipynb. Although the numerical values do vary as a function of Ueff, the qualitative behaviour as well as the ordering of frequencies and energy differences presented in the paper (corresponding to Ueff  = 4 eV) remain robust throughout the range: 3 − 5 eV which is the range typically employed for Fe d states.

Finally, in the notebook: Separating_the_muon-polaron_complex.ipynb, we analyse the separation of muon from the polaron in different configurations. Here again we provide the VASP input and output files as well as the code used to analyse these results.

These jupyter notebooks may be previewed on github or via the jupyter notebook viewer. The latter does a better job of rendering the inline LaTeX and is therefore preferred.

Note that all of files are currently compressed to save space. These must be uncompressed before the notebooks will run. In each notebook there is a cell one can run to decompress the files needed for that particular notebook.