  We study the ground state properties of the one-dimensional quarter-filled
strongly correlated electronic chain coupled by $J$ to another chain of
antiferromagnetic Ising moments. We focus on the case where the large Coulomb
interactions localize the charges on every other site. Both the electronic
spins and the Ising moments interact antiferromagnetically within each chain by
$J_{\rm eff}$ and $J'$, respectively. Since the number of electrons is half as
that of the Ising moments the period of magnetic correlation of these two
chains are incommensurate. In the presence of $J$, the frustration of $J_{\rm
eff}$ and $J'$ arises, which may lead the system to the intriguing
magneto-electric effect.
