Quantum effects in muon spin spectroscopy within the stochastic self-consistent harmonic approximation

Muon spin rotation experiments involve muons that experience zero-point vibration at their implantation sites. Quantum-mechanical calculations of the host material usually treat the muon as a point impurity, ignoring its zero-point vibrational energy that, however, plays a role in determining the stability of calculated implantation sites and estimating physical observables. As a first-order correction, the muon zero-point motion is usually described within the harmonic approximation, despite the anharmonicity of the crystal potential. Here we apply the stochastic self-consistent harmonic approximation, a quantum variational method devised to include anharmonic effects in total energy and vibrational frequency calculations, in order to overcome these limitations and provide an accurate ab initio description of the quantum nature of the muon. We applied this full quantum treatment to the calculation of the muon contact hyperfine field in textbook-case metallic systems, such as Fe, Ni, Co including MnSi and MnGe, improving agreement with experiments. Our results show that there are anharmonic contributions to the muon vibrational frequencies with the muon zero-point energies above 0.5 eV. Finally, in contrast to the harmonic approximation, we show that including quantum anharmonic fluctuations, the muon stabilizes at the octahedral site in bcc Fe.
RDR acknowledges grants from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 654000. RDR, PB and IJO also acknowledge computing resources provided by, the Swiss National Supercomputing Centre (CSCS) under Project ID sm16, CINECA under Project ID IsC58, the STFC Scientific Computing Departments SCARF cluster and the HPC resources at the University of Parma, Italy. IE acknowledges funding from the Spanish Ministry of Economy and Competitiveness (FIS2016-76617-P). This work is part of the PhD thesis of IJO at the University of Parma, Italy