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The diffusion coefficient of Li$^+$ ions ($D_{\rm Li}$) in the batterymaterial Li$_x$CoO$_2$ has been investigated by muon-spin relaxation($\mu^+$SR). Based on the experiments in zero-field and weaklongitudinal-fields at temperatures up to 400 K, we determined the fluctuationrate ($\nu$) of the fields on the muons due to their interaction with thenuclear moments. Combined with susceptibility data and electrostatic potentialcalculations, clear Li$^+$ ion diffusion was detected above $\sim150$K. The$D_{\rm Li}$ estimated from $\nu$ was in very good agreement with predictionsfrom first-principles calculations, and we present the $\mu^+$SR technique asan % novel and optimal probe to detect $D_{\rm Li}$ for materials containingmagnetic ions.

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