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 ($\mu^+$SR). Based on the experiments in zero-field and weak longitudinal-fields at temperatures up to 400 K, we determined the fluctuation rate ($\nu$) 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 $\nu$ was in very good agreement with predictions from first-principles calculations, and we present the $\mu^+$SR technique as an % novel and optimal probe to detect $D_{\rm Li}$ for materials containing magnetic ions.