The Role of DFT Calculations in μ⁺SR Studies of Battery Materials

Internal nuclear magnetic fields in various battery materials have been predicted using density functional theory (DFT) calculations to interpret the μ+SR results, particularly for identifying the diffusing species responsible for the dynamic behavior observed. In materials where Li+ and Na+ ions are mobile, these cations readily change positions to minimize electrostatic repulsion with the implanted μ+. As a result, the μ+ sits at the bottom of a deep potential well, stabilizing itself through a "self-trapping″ effect, making it a stable observer for detecting ion diffusion in battery materials. In contrast, in many metals and oxides, the implanted μ+ diffuses even at low temperatures. In these materials, the local lattice distortion caused by the implanted μ+ is relatively small compared to that in battery materials. To assess the stability of the implanted μ+, we propose a ratio between the measured nuclear magnetic field distribution width (Δexp) and the DFT-predicted value without lattice relaxation (Δmin), namely, Δexp/Δmin, as an indicator of whether cations or μ+ are diffusing. This indicator provides a comprehensive understanding of the diffusive behavior detected with μ+SR in various materials, including battery materials, metals, and other oxides.