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This page illustrates the results of the NMI3 JRA 8 project on muon site determination by ab-initio techniques. The project was funded by European Project 226507 – NMI3.

The strategy was demonstrated, within the project, in two papers, dealing respectively with the muon interstitial site in fluorides [1] and in iron pnictides under pressure [2]. Further illustrations are contained in a review paper [3].

The strategy is summarised as follows.

The material under investigation is simulated by DFT, e.g. by Quantum Espresso (QE).

Muon sites in a metal

In a first category of materials, notably metals, the candidate site is the minimum of the bare Coulomb potential, {$V(\mathbf{r})$}, that is straightforward to obtained from the DFT calculations.
The site is stable if the quantum muon wave function has a localised state in this potential. This can be determined by a harmonic approximations of {$V$} and a comparison of the corresponding Zero Point Energy with the energy barriers to neighboring minima. Or, better, by solving the Schroedinger equation for the muon, with the Hamiltonian {${\cal H}=-\frac{\hbar^2\nabla^2}{2m_\mu}+V(\mathbf{r})$}

muon sites in Insulators

In other materials, typically insulators, one must simulate by DFT a supercell with a muon (hydrogen) included, and relax the lattice.
The site is, again, stable if the muon Schroedinger equation finds a bound ground state.

The code for solving the muon Schroedinger equantion by importing QE Coulomb potential on a grid, FSCHR, is provided below. The code runs on linux and it requires FEAST

Download source and instructions FSCHR.tar.gz

The code performing the Double Adiabatic Approximation is available as a Git repository here:

https://gitorious.org/double-adiabatic-approximation https://bitbucket.org/bonfus/dbo

Please carefully test your results before using it in production!

[1] F. Bernardini et al Phys. Rev. B 87, 115148 (2013)

[2] R. De Renzi et al Supercond. Sci. Technol. 25, 084009 (2012)

[3] J.S. Möller et al 88, Phys. Scr. (2013)

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