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Li diffusion in Li$_x$CoO$_2$ probed by muon-spin spectroscopy

The diffusion coefficient of Li$^+$ ions ($D_{\rm Li}$) in the battery material Li$_x$CoO$_2$ has been investigated by muon-spin relaxation ($μ^+$SR). Based on the experiments in zero-field and weak longitudinal-fields at temperatures up to 400 K, we determined the fluctuation rate ($ν$) of the fields on the muons due to their interaction with the nuclear moments. Combined with susceptibility data and electrostatic potential calculations, clear Li$^+$ ion diffusion was detected above $\sim150$K. The $D_{\rm Li}$ estimated from $ν$ was in very good agreement with predictions from first-principles calculations, and we present the $μ^+$SR technique as an % novel and optimal probe to detect $D_{\rm Li}$ for materials containing magnetic ions.