# Computational Prediction of Muon Stopping Sites in Silicon

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In a muon-spin relaxation experiment (μ+SR) spin-polarized positive muons are implanted in a sample to probe its local static and dynamic magnetic prop- erties. μ+SR is a sensitive probe of magnetism, but one of its limitations is not knowing the site of implantation of the muon, which prevents the use μ+SR for measuring magnetic moments or for comparing different magnetic structures.

There are, however, some experimental techniques that can determine the muon stopping sites, but these techniques are limited to certain specific cases. For instance, in some materials, the determination of the muon stopping site was possible by using accurate experimental studies of the muon frequency shift in an applied magnetic field. In particular, for semiconductor materials, the so-called channelling and blocking techniques have produced some experimental information on the location of the muon site. Nonetheless, the number of examples where the muon site can be determined by experimental means alone is limited.

In this work, we focus on the paramagnetic states formed by muons in semiconductors. In particular, we revisit the case of muons in pure Si, and use a combination of computational methods to estimate the muon stopping site and the temperature dependance of the muon’s hyperfine parameters. We use Ab Initio Random Structure Searching (AIRSS) to predict the muon stopping sites in Silicon. AIRSS is used to find the number of minima in the potential energy surface of a system. What you can do with this methodology is to find metastable minima as well as, potentially, the global minimum. Once the muon stopping sites have been identified, we estimate the effect of the zero point energy and the temperature on the muon’s hyperfine parameters. This is done with a methodology that treats the vibrations within the harmonic approximation and, at the harmonic level, uses a Monte Carlo method and a perturbative expansion to treat the coupling between vibrations. Our theoretical predictions are in reasonable agreement with well established experimental measurements.