  To understand the collinear-magnetism-driven ferroelectricity in multiferroic
Ca3CoMnO6 compound, we have established an elastic diatomic Ising spin-chain
model with axial-next-nearest-neighbor interaction to describe its
magnetoelectric properties. By employing magneto-phonon decoupling and
transfer-matrix method, the possible ground-state configurations and
thermodynamic behaviors of the system have been exactly determined. From the
perspective of the ground-state configuration, we analyze the computational
results and make a detail comparison with experimental data. The parameter
relation for the appearance of electric polarization has been discussed. Our
data indicate that the magnetic coupling between nearest-neighbor spin pair is
antiferromagnetic rather than ferromagnetic. The system under the driven of
external magnetic field undergoes a different series of transitions from the
up-up-down-down spin configuration to the up-down-up state with peculiar 1/3
magnetization plateau, then to the up-up-up-down state, and finally saturated
at up-up-up-up state.
