We discuss a cost-effective approach to understand magnetic relaxation in the new generation of rare-earth single-molecule magnets. It combines ab initio calculations of the crystal field parameters, of the magneto-elastic coupling with local modes, and of the phonon density of states with fitting of only three microscopic parameters. Although much less demanding than a fully ab initio approach, the method gives important physical insights into the origin of the observed relaxation. By applying it to high-anisotropy compounds with very different relaxation, we demonstrate the power of the approach and pinpoint ingredients for improving the performance of single-molecule magnets.

In positive muon spin rotation and relaxation spectroscopy it is becoming nowadays customary to take advantage of Density Functional Theory (DFT) based computational methods to aid the experimental data analysis. DFT aided muon site determination is especially useful for measurements performed in magnetic materials, where large contact hyperfine interactions may arise. Here we present a systematic analysis of the accuracy of the ab initio estimation of muon's hyperfine contact field on elemental transition metals, performing state of the art spin-polarized plane wave DFT and using the projector augmented pseudopotential approach, which allows to include the core state effects due to the spin ordering. We further validate this method in not-so-simple, noncentrosymmetric metallic compounds, presently of topical interest for their spiral magnetic structure giving rise to skyrmion phases, such as MnSi and MnGe. The calculated hyperfine fields agree with experimental values in all cases, provided the spontaneous spin magnetization of the metal is well reproduced within the approach. To overcome the known limits of the conventional mean field approximation of DFT on itinerant magnets, we adopt the so-called reduced Stoner theory [L. Ortenzi et al.,Phys. Rev. B 86, 064437 (2012)]. We establish the accuracy of the estimated muon contact field in metallic compounds with DFT and our results show improved agreement with experiments compared to those of earlier publications.

The estimation of the magnetic field generated at a given point by magnetic dipoles is an undergraduate exercise. However, under certain approximation, this is all that is needed to evaluate the local field at the muon site once the interstitial position of the muon in the unit cell is known. The development of an application to specifically solve this problem may therefore seem an excessive effort. At the same time, the lack of a general solution leads to the development of small ad hoc codes that are generally rewritten or re-adapted for different experiments and are poorly optimized. This and other motivations led to the development of MuESR, a python+C tool to perform dipolar field simulations. In this manuscript we will describe the tool, its features and its development strategies.

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. *

We present a systematic investigation of muon-stopping states in superconductors that reportedly exhibit spontaneous magnetic fields below their transition temperatures due to time-reversal symmetry breaking. These materials include elemental rhenium, several intermetallic systems and Sr2RuO4. We demonstrate that the presence of the muon leads to only a limited and relatively localized perturbation to the local crystal structure, while any small changes to the electronic structure occur several electron volts below the Fermi energy leading to only minimal changes in the charge density on ions close to the muon. Our results imply that the muon-induced perturbation alone is unlikely to lead to the observed spontaneous fields in these materials, whose origin is more likely intrinsic to the time-reversal symmetry broken superconducting state.