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To understand the collinear-magnetism-driven ferroelectricity in multiferroicCa3CoMnO6 compound, we have established an elastic diatomic Ising spin-chainmodel with axial-next-nearest-neighbor interaction to describe itsmagnetoelectric properties. By employing magneto-phonon decoupling andtransfer-matrix method, the possible ground-state configurations andthermodynamic behaviors of the system have been exactly determined. From theperspective of the ground-state configuration, we analyze the computationalresults and make a detail comparison with experimental data. The parameterrelation for the appearance of electric polarization has been discussed. Ourdata indicate that the magnetic coupling between nearest-neighbor spin pair isantiferromagnetic rather than ferromagnetic. The system under the driven ofexternal magnetic field undergoes a different series of transitions from theup-up-down-down spin configuration to the up-down-up state with peculiar 1/3magnetization plateau, then to the up-up-up-down state, and finally saturatedat up-up-up-up state.

Rigorous determination of the ground-state phases and thermodynamics in an Ising-type multiferroic Ca3CoMnO6 chain