In order to study the diffusive nature of lithium transition-metal phospho-olivines, we measured muon-spin relaxation (${\mu }^{+}$SR) spectra for the polycrystalline Li$M$PO${}_4$ samples with $M=\text{Mn}$, Fe, Co, or Ni in the temperature range between 50 and 500 K. The ${\mu }^{+}$SR spectra under zero applied field are strongly affected by the magnetic moments of the 3$d$ electrons in the $M^{2+}$ ions so that, for LiMnPO${}_4$, it was difficult to detect the relaxation change caused by the diffusion due to the large Mn${}^{2+}(S=5/2)$ moments. However, diffusive behavior was clearly observed via the relaxation due to nuclear dipolar fields above $\sim$150 K for LiFePO${}_4$, LiCoPO${}_4$, and LiNiPO${}_4$ as $S$ decreased from 2 to 1. From the temperature dependence of the nuclear field fluctuation rate, self-diffusion coefficients of Li${}^{+}$ ions ($D_{\mathrm{Li}}$) at 300 K and its activation energy ($E_a$) were estimated, respectively, as $\sim$$3.6\left(2\right)\times {10}^{-10}$ cm${}^2$/s and $E_a=0.10\left(2\right)$ eV for LiFePO${}_4$, $\sim$$1.6\left(1\right)\times {10}^{-10}$ cm${}^2$/s and $E_a=0.10\left(1\right)$ eV for LiCoPO${}_4$, and $\sim$$2.7\left(4\right)\times {10}^{-10}$ cm${}^2$/s and $E_a=0.17\left(2\right)$ eV for LiNiPO${}_4$, assuming that the diffusing Li${}^{+}$ ions jump between the regular site and interstitial sites.

• Received 23 December 2011

DOI:https://doi.org/10.1103/PhysRevB.85.054111