Electronic structure of cubic Li(Fe0.1Mn1.9)O4 studied with Mössbauer spectroscopy and first-principles calculation

Abstract

Mössbauer spectrum was collected in ${\mathrm{Fe}}^{\text{3+}}$ doped cubic ${\mathrm{LiMn}}_2{\mathrm{O}}_4\mathrm{ (}{\mathrm{LiFe}}_{\text{0.1}}{\mathrm{Mn}}_{\text{1.9}}{\mathrm{O}}_4)$ by using ${}^{57}\mathrm{Fe}$ as the radiation source. In the model of the crystal-field theory, the energy gaps between different $d$ orbitals, ${\mathrm{\Delta E(b}}_{\text{1g}}{\mathrm{-a}}_{\text{1g}})$ and ${\mathrm{\Delta E(b}}_{\text{2g}}{\mathrm{-e}}_g\mathrm{),}$ characterize the strength of the Jahn–Teller effect in the crystal. A relationship between the Mössbauer quardrupole splitting and the energy gaps was established, based on which both ${\mathrm{\Delta E(b}}_{\text{1g}}{\mathrm{-a}}_{\text{1g}})$ and ${\mathrm{\Delta E(b}}_{\text{2g}}{\mathrm{-e}}_g)$ of the $[{\mathrm{MnO}}_6]$ octahedron in ${\mathrm{LiFe}}_{\text{0.1}}{\mathrm{Mn}}_{\text{1.9}}{\mathrm{O}}_4$ are estimated to be about 0.41 and 0.30 eV, respectively. Electronic structure of ${\mathrm{LiMn}}_2{\mathrm{O}}_4$ was studied theoretically via ab initio calculation based on the density-functional theory. Calculation shows that a gap about 0.28 eV between the filled $\mathrm{Mn}\mathrm{ d}$ bands is equivalent to ${\mathrm{\Delta E(b}}_{\text{2g}}{\mathrm{-e}}_g\mathrm{).}$ It also shows that the first unoccupied states are dominated by $\mathrm{Mn}\text{\hspace{0.05em}3d}$ contribution essentially from both $a_{\text{1g}}$ and $b_{\text{1g}}$ of $\mathrm{Mn}\mathrm{ d}$ states. Distance between the two peaks in the first unoccupied band was used to calculate ${\mathrm{\Delta E(b}}_{\text{1g}}{\mathrm{-a}}_{\text{1g}}\mathrm{),}$ which is about 0.36 eV. The Mössbauer quardrupole splitting characterizes Jahn–Teller distortion and its effect on the fine structure of $\mathrm{Mn}\text{\hspace{0.05em}3d}$ bands.