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 ↑↑↓↓ spin configuration associated with ferroelectric order to the ↑↓↑ state with a peculiar 1/3 magnetization plateau, then to the ↑↑↑↓ state, and finally saturation in the ↑↑↑↑ state.