Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Abstract

We revise the simple and yet powerful approach of the Double Adiabatic Approximation (DAA) to study positive muon embedding sites in condensed matter. This method introduces a tractable and reasonably accurate description of the quantum nature of the muon in Density Functional Theory (DFT) simulations aiming at identifying muon sites. Moreover, this approach overcomes the limitations of the harmonic approximation in terms of both computational efforts and accuracy. Notably, it also improves treatment of muon diffusion. We use the DAA and Nudged Elastic Band calculations to determine the muon sites and the activation energies between equivalent sites in MnSi and copper. In metallic Cu, the proposed phonon-assisted mechanism for the low-temperature muon diffusion in the lattice is confirmed. ■ INTRODUCTIONMuon spin rotation and relaxation (μSR) spectroscopy is an experimental technique that provides the time evolution of the muon spin polarization by exploiting the anisotropic emission of the decay positron.The main field of application of μSR is material science, but it is also adopted in chemistry for studying molecular dynamics and radical kinetics. 1−3 Both μ − SR and μ + SR exist, but, since μ − undergoes nuclear capture and the surviving μ − fall into atomic orbitals extremely close to the nuclei, μ + SR is more commonly used to investigate condensed matter.μSR experiments provide a measure of the microscopic field distribution at the interstitial site(s) where the μ + stop inside the sample. A seemingly embarrassing point is that these sites are usually unknown to the experimenter and the additional lack of knowledge on the perturbation generated locally by the positive muon probably represent the most common criticisms of the experimental technique. Even though in a large variety of cases ignoring the muon position does not represent a limitation, having access to information on interstitial sites and on muon-induced perturbations might be crucial to evaluate electronic properties such as long-range magnetic orders or localized magnetic moments.Predicting the position of interstitial muon sites is not a trivial task. During the final stages of thermalization in the sample the scattering between the muon and the atoms of the compound leads to a kinetic energy degradation from hundreds to tenths of electronvolts. Nonetheless, the identification of diamagnetic muon sites with approaches based on the Density Functional Theory (DFT) is emerging as a new and valuable strategy to routinely assist μSR experiments interpretation. After the pioneering work of Van de Walle et al., in recent years, this method, which provides information on the electronic and crystalline perturbations introduced by the muon, has been validated in many experimental cases with great success. 4−13 There are two main difficulties in the DFT approach. One is inherited from the mean-field description which cannot always correctly describe some classes of materials, like strongly correlated electrons systems or even some semiconductors mist...

Disentangling superconducting and magnetic orders in NaFe1−xNixAs using muon spin rotation

“…The five can-didate sites were grouped into two clusters based on relative calculated energies. Since the muon is treated as a classical particle within DFT, corrections due to its light mass can be included by taking into account the spread of the muon wavefunction in the Double Born-Oppenheimer (DBO) approximation method [43]. As described in Appendix A 2, we invoked the DBO approximation to examine the relative stability of the five candidate sites.…”

Toward the Computational Prediction of Muon Sites and Interaction Parameters

“…For MnSi the site identification by DFT, supporting accurate transverse field experiments and a careful data analysis, proved that the observed frequencies correspond to the latter case. 37,38 A similar instance is that of deconfined magnetic monopoles that are predicted by theory in spin ices, such as in some rare earth pyrochlores. A recent experiment claimed to have detected by µSR in Dy 2 Ti 2 O 7 a second Wien effect, also referred to as magnetricity, i.e.…”

“…44 The remarkable success of simple electrostatic potential predictions in simpler three dimensional metals may perhaps be justified by heuristic arguments on the screening of point charges. A recent confirmation is the case of MnSi where accurate supercell calculations 38 introduce only tiny improvements on the UEP predictions. However the accuracy of the UEP method in a layered material like LaFeAsO or LaCoPO is more surprising, and it should probably be considered just a fortunate case.…”

“…3 by the highly non ellipsoidal shape of the muon potential energy isosurface obtained by DAA in the case of MnSi. 38 The actual shape of the muon potential energy may be mapped within DAA, to avoid the harmonic approximation, but only inasmuch as the energy scales of the nuclei of the embedding system are well separated from those of the muon. Hence DAA may fail for systems with close-lying muon and hydrogen ions.…”

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

“…Earlier approaches towards a quantum-mechanical description of the muon zero-point vibration include calculations within the harmonic approximation [3,13]. However, the muon potential has been discussed and shown to be anharmonic, for instance by total energy calculations with site exploration algorithms [1,12,14,15]. Furthermore, a break down of the harmonic approximation takes place when within the range of the muon vibrations the potential is not dominated by the second-order term in its Taylor expansion.…”