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

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.

💡 Research Summary

This paper addresses the long‑standing discrepancy between short‑range and long‑range lithium‑ion transport measurements in Li₂MnO₃, a key component of Li‑excess layered cathodes. Experimental techniques such as muon‑spin relaxation (µ⁺SR) report a low activation energy (~0.15 eV) for local Li hops, while AC‑impedance spectroscopy on the same nominally stoichiometric powders yields a higher barrier (~0.45 eV) for macroscopic transport. Prior first‑principles studies, based on density‑functional theory with a Hubbard U correction (DFT+U) and static nudged‑elastic‑band (NEB) calculations, have explained the low barriers only by invoking highly clustered Li vacancies or divacancies, configurations that are unlikely in the nearly stoichiometric samples used experimentally. Moreover, these studies typically assume a fixed magnetic order (ferromagnetic, antiferromagnetic, or non‑magnetic), which does not reflect the paramagnetic state of Li₂MnO₃ at the temperatures relevant for diffusion (T ≫ T_N ≈ 36 K).

To resolve these issues, the authors combine three state‑of‑the‑art computational tools: (i) DFT+U for structural relaxation and initial NEB path generation, (ii) finite‑temperature dynamical mean‑field theory (DMFT) with a continuous‑time quantum Monte‑Carlo (CT‑QMC) impurity solver to capture dynamical electronic correlations, and (iii) a careful construction of a Mn‑d‑only Wannier basis that diagonalizes the Mn d‑block, thereby mitigating the large off‑diagonal Hamiltonian elements that arise from the low C2/m symmetry of Li₂MnO₃. The DMFT calculations are performed in a non‑charge‑self‑consistent manner on the relaxed structures, using a Slater‑Kanamori interaction with U = 4 eV and J = 0 eV (unless otherwise noted). The total energy within DMFT is evaluated via the standard DFT+DMFT expression, including the Migdal‑Galitskii contribution for the interaction energy.

Electronic‑structure analysis reveals a striking contrast between DFT+U and DMFT. While DFT+U shows almost identical projected densities of states (PDOS) on the Mn atom adjacent to the vacancy (Mn1) and a more distant Mn (Mn2), with only a modest change in d‑occupancy (Nd ≈ 4.88–4.89), DMFT produces a strongly site‑dependent redistribution: Mn1 retains an occupation of ≈3.0 electrons (in the d‑only subspace) whereas Mn2 drops to ≈2.0 electrons. This indicates that the vacancy‑induced hole is largely transferred to the Mn‑d‑like correlated subspace, a redistribution that is invisible in static DFT+U but crucial for the energetics of the transition state.

Six symmetry‑inequivalent Li‑migration pathways are examined: four intralayer hops and two interlayer hops, mirroring those studied previously. NEB calculations within DFT+U give activation energies ranging from 0.5 to 0.8 eV for all paths. When the same ionic configurations (initial, final, and saddle points) are re‑evaluated with DMFT, two low‑energy paths experience a dramatic reduction in barrier: the lowest‑energy interlayer hop (4h‑T‑Li‑4g‑4h) drops to 0.18 eV, and the next‑lowest intralayer hop (4h‑T‑Li‑2b‑4h) to 0.50 eV. The remaining four pathways retain barriers close to the DFT+U values. Energy‑decomposition analysis shows that the reduction originates primarily from a lower potential‑energy term (E_POT) in the DMFT total‑energy expression, reflecting the stabilization of the electronic structure at the saddle point due to dynamical correlations. The Fermi‑function correction term partially compensates this gain, but the net effect is a substantially lower migration barrier.

These two DMFT‑derived barriers quantitatively match the experimental activation energies: the 0.18 eV value reproduces the short‑range µ⁺SR result, while the 0.50 eV value aligns with the long‑range AC‑impedance measurement. Importantly, this agreement is achieved without invoking vacancy clustering, divacancies, or extrinsic disorder, consistent with the nearly stoichiometric powders used in the experiments. The study therefore provides a unified microscopic picture that reconciles local and macroscopic diffusion probes.

The broader significance of the work lies in demonstrating that finite‑temperature dynamical correlations, captured by DMFT, can fundamentally alter ion‑migration energetics in correlated oxides. For battery materials, this implies that static DFT‑based assessments may systematically overestimate diffusion barriers in systems where transition‑metal d electrons are strongly correlated and thermally fluctuating. The methodology presented—combining DFT+U NEB path generation with DMFT re‑evaluation—offers a practical route to incorporate strong electronic correlations into ion‑transport studies without the prohibitive cost of fully charge‑self‑consistent DFT+DMFT molecular dynamics. Future extensions could include charge‑self‑consistent DMFT, explicit treatment of oxygen p states, and application to other Li‑rich cathodes (e.g., Li₁₊ₓ(Ni,Co,Mn)O₂) where similar discrepancies between local and bulk transport measurements exist.

In summary, the paper convincingly shows that dynamical electronic correlations in the paramagnetic phase of Li₂MnO₃ lower the activation energies for specific Li‑hopping pathways, thereby reconciling divergent experimental observations and highlighting the necessity of incorporating finite‑temperature many‑body effects in the computational design of high‑performance, transition‑metal‑oxide battery cathodes.