Interrelationship between Li${}^{+}$ diffusion, charge, and magnetism in ${}^7\mathrm{Li}$Mn${}_2$O${}_4$ and ${}^7\mathrm{Li}$${}_{1.1}$Mn${}_{1.9}$O${}_4$ spinels: Elastic, inelastic, and quasielastic neutron scattering

Using quasielastic neutron scattering (QENS), we have investigated a self-diffusive behavior of Li${}^{+}$ ions for both ${}^7\mathrm{Li}$Mn${}_2$O${}_4$ and ${}^7\mathrm{Li}$${}_{1.1}$Mn${}_{1.9}$O${}_4$ spinels. In addition, we have carried out elastic and inelastic neutron scattering measurements using the same samples, to study the interrelationship between Li${}^{+}$ self-diffusion, magnetism, and charge distribution in the lattice. From the QENS results, the self-diffusion of Li${}^{+}$ was observable above 280 K, and a self-diffusion coefficient ($D_s^{\mathrm{Li}}$) for ${}^7\mathrm{Li}$Mn${}_2$O${}_4$ was estimated as $~{10}^{-8}$ cm${}^2$/s at 400 K. $D_s^{\mathrm{Li}}$ for ${}^7\mathrm{Li}$${}_{1.1}$Mn${}_{1.9}$O${}_4$ was comparable to that for ${}^7\mathrm{Li}$Mn${}_2$O${}_4$. Furthermore, combining with the results of elastic and inelastic measurements, it was found that ${}^7\mathrm{Li}$${}_{1.1}$Mn${}_{1.9}$O${}_4$ undergoes a transition from a low-temperature ($T$) short-range charge-ordered (SRCO) phase to a high-$T$ charge-disordered (CDO) phase at 280 K. The structure of the SRCO was determined as a hexagon, because the formation of hexagon spin clusters was deduced from a magnetic diffuse scattering at low $T$. Assuming the presence of the SRCO-CDO transition at 280 K, both the anomaly of the diffusive behavior at 280 K and the local lattice distortion below 280 K are reasonably explained, despite the absence of long-range CO for ${}^7\mathrm{Li}$${}_{1.1}$Mn${}_{1.9}$O${}_4$.

Figure 1

(a) $T$ dependence of the mean-square displacement for LiMn${}_2$O${}_4$ and Li${}_{1.1}$Mn${}_{1.9}$O${}_4$. (b) The $Q$ integrated energy spectra at 400 K of LiMn${}_2$O${}_4$ and Li${}_{1.1}$Mn${}_{1.9}$O${}_4$. Full width at the half maximum $\Gamma$ is estimated to be 12.0(0) $\mu$eV and 7.7(1) $\mu$eV, respectively. To gain better statistics, the energy increment is rebinned from the original data. The spectrum comprises the data of the integrated intensities over the $Q$ range between 0.25 and 1.75 Å${}^{-1}$. (c) A comparison of diffusion coefficient of the present neutron and the previous NMR data of Ref. 19, in logarithmic scale.

Figure 2

$T$ dependence of the elastic intensity [the mean-square displacement] for (a) [(c)] LiMn${}_2$O${}_4$ and (b) [(d)] Li${}_{1.1}$Mn${}_{1.9}$O${}_4$. Solid circles show the data obtained in the second heating run after 2-day interval. Such interval makes the data the same as those obtained in the initial heating run. Open squares show the data obtained in the third heating run immediately after the second heating run. The error bar for each data point is smaller than the size of the symbols.

Figure 3

Neutron scattering intensity as a function of energy transfer ($E$) and wave vector ($Q$) obtained at (a) 5 K, (b) 80 K, and (c) 330 K for LiMn${}_2$O${}_4$, (d) 5 K, (e) 50 K, and (f) 300 K for Li${}_{1.1}$Mn${}_{1.9}$O${}_4$.

Figure 4

Elastic and inelastic neutron scattering profiles as a function of wave vector $Q$ for LiMn${}_2$O${}_4$. The displayed $T$s were (a) and (d) 5 K, (b) and (e) 80 K, (c) and (f) 330 K. Here, to split the elastic and inelastic contribution, the elastic and the inelastic scattering intensity is integrated in the range $-0.02$ meV $<E<0.02$ meV and $-2$ meV$<E<-0.1$ meV, respectively. Due to an allowed kinematic region of the spectrometer of $E$ versus $Q$, the minus $E$ side was used in the inelastic scattering data. Numbers on the top of (a) represent the intensity of each magnetic peak. Minus values in the horizontal axis of the inset of (d) and (e) mean the energy gain from the incident neutron. The dashed line in (a) indicates the shape of the inelastic neutron scattering pattern of (d). The three peaks observed at $Q~1.6$, 1.65, and 1.7 Å${}^{-1}$ in the elastic profile (a), (b), and (c) are caused by contaminations from the cryostat or the other components (e.g., the sample holder, because we did not use a Cd mask due to its low melting point).

Figure 5

Elastic and inelastic neutron scattering profiles as a function of wave vector $Q$ for Li${}_{1.1}$Mn${}_{1.9}$O${}_4$. The displayed $T$s were (a) and (d) 5 K, (b) and (e) 80 K, (c) and (f) 330 K. The dashed line in (a) indicates the diffraction data of ${}^{110}\mathrm{Cd}$Fe${}_2$O${}_4$ powder,[36] which is explained by a hexagon cluster model using Eq. (5).

Figure 6

Schematic charge configuration for (a) Li${}_{1.1}$Mn${}_{1.9}$O${}_4$ and (b) LiMn${}_2$O${}_4$. Open spheres represent Mn${}^{3+}$ and solid spheres Mn.${}^{4+}$ In (a), bold hexagons indicate the arrangement of Mn ions; that is, gray (green) hexagons consist of Mn${}^{3+}$ ions, while black (red) hexagons show Mn${}^{4+}$ ions. The number ratio between the two hexagons corresponds to [Mn${}^{3+}$]/[Mn${}^{4+}$].