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Using ab initio dynamical mean-field theory we explore the electronic andmagnetic states of layered Li$_x$MnO$_2$ as a function of $x$, the state ofcharge. Constructing real-space Wannier projections of Kohn-Sham orbitals basedon the low-energy subspace of Mn $3d$ states and solving a multi-impurityproblem, our approach focuses on local correlations at Mn sites. Theantiferromagnetic insulating state in LiMnO$_2$ has a moderate N\'{e}eltemperature of $T_N=296\,K$ in agreement with experimental studies. Upondelithiation the system proceeds through a number of states: ferrimagneticcorrelated metals at $x$=0.92, 0.83; multiple charge disproportionatedferromagnetic correlated metals with large quasiparticle weights at $x$=0.67,0.50, 0.33; ferromagnetic metals with small quasiparticle weights at $x$=0.17,0.08 and an antiferromagnetic insulator for the fully delithiated state,$x=0.0$. At moderate states of charge, $x=0.67-0.33$, a mix of +3/+4 formaloxidation states of Mn is observed, while the overall nominal oxidation of Mnstate changes from +3 in LiMnO$_2$ to +4 in MnO$_2$. In all these cases thehigh-spin state emerges as the most likely state in our calculationsconsidering the full $d$~manifold of Mn based on the proximity of $e_g$ levelsin energy to $t_{2g}$. The quasiparticle peaks in the correlated metallicstates were attributed to polaronic states based on previous literature forsimilar isoelectronic JT driven materials, arising due to non-Fermi liquid typebehaviour of the strongly correlated system.

The importance of electronic correlations in exploring the exotic phase diagram of layered Li$_x$MnO$_2$