  Electron- and hole-doped La$_2$CoMnO$_6$(LCMO) are investigated using first
principles DFT calculations. Hole and electron doping are achieved respectively
by introducing Sr$^{2+}$ at La$^{3+}$ sites and by inducing O-site vacancies in
LCMO. Electronic structure calculations suggest that hole doping alters the
charge and valence state of Co ions, whereas electron doping influences the Mn
ions. Introduction of defects is found to enhance antisite disorder(ASD) at
Co/Mn site, which is expected to influence the magnetodielectric properties of
the system. Our calculations suggest that while ASD and/or hole doping induces
half-metallicity in LCMO, electron doping restores its insulating state.
Mean-field calculations performed using exchange constants obtained by mapping
DFT total energies of different collinear spin configurations onto the Ising
Hamiltonian find that defects tend to reduce the Curie temperature ($T_C$).
Interestingly, the calculated linear optical properties of the system suggest
that the material becomes optically active with high values of birefringence in
the presence of defects, a property that is highly sought-after in the optical
communications and laser industry.
