  Using ab initio dynamical mean-field theory we explore the electronic and
magnetic states of layered Li$_x$MnO$_2$ as a function of $x$, the state of
charge. Constructing real-space Wannier projections of Kohn-Sham orbitals based
on the low-energy subspace of Mn $3d$ states and solving a multi-impurity
problem, our approach focuses on local correlations at Mn sites. The
antiferromagnetic insulating state in LiMnO$_2$ has a moderate N\'{e}el
temperature of $T_N=296\,K$ in agreement with experimental studies. Upon
delithiation the system proceeds through a number of states: ferrimagnetic
correlated metals at $x$=0.92, 0.83; multiple charge disproportionated
ferromagnetic 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 formal
oxidation states of Mn is observed, while the overall nominal oxidation of Mn
state changes from +3 in LiMnO$_2$ to +4 in MnO$_2$. In all these cases the
high-spin state emerges as the most likely state in our calculations
considering the full $d$~manifold of Mn based on the proximity of $e_g$ levels
in energy to $t_{2g}$. The quasiparticle peaks in the correlated metallic
states were attributed to polaronic states based on previous literature for
similar isoelectronic JT driven materials, arising due to non-Fermi liquid type
behaviour of the strongly correlated system.
