We introduce the effective Hamiltonian which describes
eg electrons in
doped bilayer La2−2xSr1+2xMn2O7
manganites and study magnetic and charge order using correlated wavefunctions.
The Hamiltonian includes: the kinetic energy, the crystal field splitting between
x2−y2 and
3z2−r2 orbitals, on-site
interactions—Coulomb U
and Hund’s exchange JH
between eg
electrons, antiferromagnetic superexchange interaction
J′>0 between
t2g core
S = 3/2 spins, and finally
the coupling between eg
electrons and Jahn–Teller local modes. The model reproduces reasonably
well the evolution of magnetic order with increasing hole doping
x in the experimentally
accessible range from x = 0.3
up to x = 0.9. Electron correlations are found to be of crucial importance for the
stability of the recently experimentally identified CE phase in a half-doped
(x = 0.5) bilayer (with zig-zag ferromagnetic chains in each plane coupled antiferromagnetically
with neighbouring chains in the same and in the other layer).