Revealing Short- and Long-range Li-ion diffusion in Li$_2$MnO$_3$ from finite-temperature dynamical mean field theory

Abstract: Li$_2$MnO$_3$ remains a crucial component of the Li-excess layered cathode family, $(1-x)\,\mathrm{LiMO_2} + x\,\mathrm{Li_2MnO_3}$ ($M$ = Mn, Ni, Co, \dots), but its role in limiting Li-ion mobility remains under debate. Here we combine DFT+$U$, finite-temperature DMFT with a continuous-time quantum Monte Carlo impurity solver, and nudged-elastic-band (NEB) calculations to investigate Li$^+$ migration for a single Li vacancy in paramagnetic Li$_2$MnO$_3$. Dynamical electronic correlations within DMFT substantially reduce the activation energies of the lowest-barrier pathways, yielding $E_a = 0.18$ eV for the shortest-range Li jump and $E_a = 0.50$ eV for the next-lowest pathway. The 0.18 eV barrier quantitatively reproduces the short-range activation energy extracted from $μ^+$SR measurements, whereas the 0.50 eV barrier is consistent with the long-range transport activation energy obtained from ac-impedance measurements. This single-vacancy, paramagnetic DMFT description therefore provides a coherent explanation of both local and macroscopic probes without requiring highly clustered vacancy configurations or strong extrinsic disorder, an assumption compatible with nearly stoichiometric Li$_2$MnO$_3$ powders. Our results highlight the importance of finite-temperature dynamical correlations for Li-ion migration in correlated oxides and provide a framework for incorporating strong Coulomb interactions in future studies of transition-metal oxide battery materials.