Muon spin rotation and relaxation study for energy materials

A muon spin rotation and relaxation ($\mu^{+}$SR) technique is very popular for studying microscopic internal magnetic fields in condensed matters. Recently, $\mu^+$SR measurements are also used to investigate the intrinsic nature of battery materials and hydrogen storage materials. Here, I wish to review the recent progress of the $\mu^+$SR research on such materials. In 2009, it was found that Li$^+$-ion diffusion in solids is detectable with $\mu^+$SR even in the materials containing magnetic ions [JS ${\it et~al.}$, PRL ${\bf103}$, 147601], while NMR is unable to do so due to the effect of localized magnetic moments on a spin-lattice relaxation rate. Such finding looks to open the door for the $\mu^+$SR research on energy materials. Since then, many battery materials have been investigated with $\mu^+$SR in order to determine their intrinsic diffusion coefficient ($D$) of Li$^+$ and Na$^+$ ions [M. Mansson $\&$ JS, Phys. Scr. ${\bf88}$, 068509]. Furthermore, using such intrinsic $D$, the other important parameters are successfully derived, such as, the reactive surface area [JS ${\it et~al.}$, Phys. Chem. Chem. Phys. B ${\bf15}$, 10402], diffusion pathway [JS ${\it et~al.}$, PRB ${\bf87}$, 024409], and density of mobile ions [H. Nozaki ${\it et~al.}$, Solid State Ionics ${\bf262}$, 585]. In 2008, the internal magnetic field in a complex hydrogen storage material, NaAlH$_4$, was studied with $\mu^+$SR [R. Kadono ${\it et~al.}$, PRL ${\bf100}$, 026401]. Despite the absence of magnetic ions, $\mu^+$SR spectrum exhibited a clear oscillation, indicating the formation of a H-$\mu^+$-H system in NaAlH$_4$. Moreover, it was proposed that the yield of the H-$\mu^+$-H system depends on the hydrogen desorption temperature ($T_{\rm d}$) through the diffusion of H in NaAlH$_4$. More systematic $\mu^+$SR work on $M$BH$_4 (M=$Li, Na, K, Mg, Ca, Sc) provided a clear relationship between the yield of the H-$\mu^+$-H system and $T_{\rm d}$ [JS ${\it et~al.}$, PRB ${\bf81}$, 092103]. In addition, very recent {\it in-situ} $\mu^+$SR measurements on MgH$_2$ during hydrogen desorption reaction revealed the importance of H-diffusion in solids for determining $T_{\rm d}$ [JS, J. Phys. Soc. Jpn, ${\bf85}$, 091012].