Lithium diffusion in spinel ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ films detected with ${}^8\mathrm{Li}\beta$-NMR

Diffusion of ${\mathrm{Li}}^{+}$ in (111) oriented thin films of the spinels ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ has been studied with ${}^8\mathrm{Li}\beta$-detected NMR in the temperature range between 5 and 310 K. In ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$, the spin-lattice relaxation rate ($1/T_1$) versus temperature shows a clear maximum around 100 K ($=T_{\max }$) which we attribute to magnetic freezing of dilute ${\mathrm{Ti}}^{3+}$ local magnetic moments, consistent with the results of magnetization and muon spin relaxation (${\mu }^{+}\mathrm{SR}$) measurements. The decrease in $1/T_1$ with temperature above $T_{\max }$ indicates that ${\mathrm{Li}}^{+}$ starts to diffuse with a thermal activation energy ($E_a$) of 0.11(1) eV. In ${\mathrm{LiTi}}_2{\mathrm{O}}_4$, on the contrary, as temperature increases from 200 K, $1/T_1$ increases monotonically up to 310 K. This suggests that Li also starts to diffuse above 200 K with $E_a=0.16\left(2\right)\mathrm{eV}$ in ${\mathrm{LiTi}}_2{\mathrm{O}}_4$. Comparison with conventional Li-NMR on ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ implies that both $\beta$-NMR and ${\mu }^{+}\mathrm{SR}$ sense short-range Li motion, i.e., a jump diffusion of ${\mathrm{Li}}^{+}$ to the nearest neighboring sites.

Figure 1

The crystal structure of spinel ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$. The tetrahedral $A$ site is occupied by ${\mathrm{Li}}^{+}$, while the octahedral $B$ site is occupied by 1/6 ${\mathrm{Li}}^{+}$ and 5/6 ${\mathrm{Ti}}^{4+}$. On the other hand, for ${\mathrm{LiTi}}_2{\mathrm{O}}_4$, the $B$ site is occupied by ${\mathrm{Ti}}^{3.5+}$.

Figure 2

The asymmetry time spectrum of ${}^8\mathrm{Li}$ in the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ film measured at 5, 100, and 300 K with $H=1.9\mathrm{T}$. Solid lines represent the best fit of Eq. (3) with $\beta =1/3$.

Figure 3

The temperature dependences of (a) the spin-lattice relaxation rate ($1/T_1$) of ${}^8\mathrm{Li}\beta$-NMR with $H=1.9\mathrm{T}$, (b) the exponential relaxation rate ($\lambda$) and the hopping rate ($\nu$) of ${\mu }^{+}\mathrm{SR}$ [27], and (c) magnetic susceptibility ($M/H$) with $H=1\mathrm{T}$ [27] for ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$. Both $\beta$-NMR and ${\mu }^{+}\mathrm{SR}$ spectra were measured for the film sample, while $M$ was measured for a powder sample. The $\beta$-NMR data was obtained by fitting the time spectrum with Eq. (3) and $\beta =1/3$. The ${\mu }^{+}\mathrm{SR}$ data was obtained by fitting the zero field and weak longitudinal spectra with the exponentially relaxing dynamic Kubo-Toyabe function [27]. The vertical broken line represents the temperature below which the $M/H$ curve deviates from a Curie-Weiss behavior at high temperatures.

Figure 4

(a) The spin-lattice relaxation rate ($1/T_1$) and (b) the exponential relaxation rate ($\lambda$) and the hopping rate ($\nu$) as a function of inverse temperature for the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ film. In (a), blue solid lines represent the fit results using a thermal activation process, $1/T_1=Aexp(-E_a/k_{\mathrm{B}}T)$, with $E_a=0.108\left(7\right)\mathrm{eV}$ [0.106(4) eV] for the $\beta$-NMR data measured with $H=1.9\mathrm{T}$ [6.55 T]. Green broken lines represent a possible BPP relationship, although it is eventually impossible to fit the $1/T_1$ vs $T^{-1}$ curve with BPP due to the absence of a clear maximum. In (b), a green line shows the fit result using a relationship, $\nu ={\nu }_0+Aexp(-E_a/k_{\mathrm{B}}T)$, with $E_a=0.12\left(2\right)\mathrm{eV}$ for the $\mu \mathrm{SR}$ data.

Figure 5

The nuclear resonance spectra of ${}^8\mathrm{Li}$ for the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ film measured at 5, 100, and 200 K. Solid lines represent the fit using a Lorentz function.

Figure 6

The temperature dependence of (a) the full width at half maximum (FWHM) of the resonance line and the field distribution width ($\mathrm{\Delta }$) and (b) the frequency shift ($K$) and the exponential relaxation rate ($\lambda$) for the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ film. The data of FWHM and $F$ were obtained by fitting the resonance spectrum with a Lorentz function. $\mathrm{\Delta }$ and $\lambda$ were obtained from the ${\mu }^{+}\mathrm{SR}$ measurements. For FWHM, 10 Oe corresponds to 6.3 kHz.

Figure 7

The temperature dependences of (a) the spin-lattice relaxation rate ($1/T_1$) of ${}^8\mathrm{Li}\beta$-NMR measured with $H=1.0$, 1.9, and 6.55 T and (b) the exponential relaxation rate ($\lambda$) and the hopping rate ($\nu$) of ${\mu }^{+}\mathrm{SR}$ [27] for the ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ film. The data were obtained by fitting the $\beta$-NMR time spectrum with Eq. (3) with $\beta =1$. The range of each axis in (a) and (b) is the same as that for Fig. 3 for comparison.

Figure 8

(a) The spin-lattice relaxation rate ($1/T_1$) of ${}^8\mathrm{Li}\beta$-NMR measured with $H=1.0$ and 1.9 T and (b) the exponential relaxation rate ($\lambda$) and the hopping rate ($\nu$) of ${\mu }^{+}\mathrm{SR}$ [27] as a function of inverse temperature for the ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ film. A solid line in (a) represents the fit result using a thermal activation process for the data with $H=1.9\mathrm{T}$; namely, $1/T_1=1/T_{1,0}+Aexp(-E_a/k_{\mathrm{B}}T)$, where $E_a=0.16\left(2\right)\mathrm{eV}$. In (b), $E_a=0.17\left(6\right)\mathrm{eV}$ [27].

Figure 9

(a) The nuclear resonance spectra of ${}^8\mathrm{Li}$ for the ${\mathrm{LiTi}}_2{\mathrm{O}}_4$ film measured at 5, 12, and 250 K, and the temperature dependences of (b) FWHM and (c) $K$. The data in (b) and (c) were obtained by fitting the resonance spectrum with a Voigt function. Such fit results are plotted in (a) as a green solid line. $\mathrm{\Delta }$ and $\lambda$ obtained from the ${\mu }^{+}\mathrm{SR}$ measurements [27] are also plotted for comparison.

Figure 10

The charge and discharge curves for (a) the ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ and (b) ${\mathrm{Li}}_4{\mathrm{Ti}}_5{\mathrm{O}}_{12}$ films.