Computational prediction of muon stopping sites using ab initio random structure searching (AIRSS)

Abstract

The stopping site of the muon in a muon-spin relaxation experiment is in general unknown. There are some techniques that can be used to guess the muon stopping site, but they often rely on approximations and are not generally applicable to all cases. In this work, we propose a purely theoretical method to predict muon stopping sites in crystalline materials from first principles. The method is based on a combination of ab initio calculations, random structure searching, and machine learning, and it has successfully predicted the Mu and Mu stopping sites of muonium in Si, diamond, and Ge, as well as the muonium stopping site in LiF, without any recourse to experimental results. The method makes use of Soprano, a Python library developed to aid ab initio computational crystallography, that was publicly released and contains all the software tools necessary to reproduce our analysis.

Computational prediction of muon stopping sites: A novel take on the unperturbed electrostatic potential method

“…24 The stopping sites are (a) located within a planar region that is perpendicular to the ⟨111⟩ direction and (b) situated within ≈1.5 Å of one of the oxygen atoms defining the planar region. Figures (4) and (5) show the O ⟨111⟩ site predicted by the UEP method. An example of a planar region perpendicular to the ⟨111⟩ direction is indicated in yellow.…”

“…(7), which corresponds to the planar region in Fe 3 O 4 that is perpendicular to the ⟨111⟩ direction and and is indicated in yellow in Fig. (5).…”

“…However, since we know that H (symm) is both symmetric and traceless, it only has five independent components we care about, and four of the equations are just linear combinations of the other. We can then write this as a system of five equations in five variables in the matrix form, (W (5) − I)H (5)…”

“…where H (5) is a column vector containing the five independent components in any order we like, and the precise form of W (5) depends on the convention we chose. One can then check for each special Wyckoff position whether there is any vector that satisfies all these conditions.…”

“…[1][2][3][4] In our previous work, we presented a set of computational approaches for finding the muon stopping site that could be applied to the case of finding the stopping site of muonium, the pseudo-atom formed by a positive muon when it captures an electron. This set of approaches requires the use of many randomly initialized calculations, based on either the Density Functional Theory (DFT) approximation 5 or the much faster, lower level approximation of Density Functional Tight Binding (DFTB). 6 The DFTB approach is by far the faster of the two, but it depends on parameterizations fitted on more fundamental theory calculations that are not available for all elements of the periodic table.…”