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

To understand the ferroelectricity driven by collinear magnetism in a multiferroic spin-chain system, we have adopted an elastic diatomic Ising spin-chain model with axial next-nearest-neighbor interaction to describe its magnetoelectric properties. By employing magneto-phonon decoupling and the transfer-matrix method, the possible ground-state configurations and thermodynamic behaviors of the system have been determined exactly. The parameter relation for the appearance of electric polarization has been discussed from the perspective of the ground-state configuration. In the case of nearest-neighbor antiferromagnetic coupling, a novel series of zero-temperature transitions induced by magnetic field have been observed, from the up arrow up arrow down arrow down arrow spin configuration associated with ferroelectric order to the up arrow down arrow up arrow state with a peculiar 1/3 magnetization plateau, then to the up arrow up arrow up arrow down arrow state, and finally saturation in the up arrow up arrow up arrow up arrow state.