Surface reconstruction is a subtle phenomenon where small energy changes can give rise to very different surface structures. In this article we consider the possibility that the reconstruction of a heteroepitaxial system will depend on the presence of external electric or magnetic fields. First, we propose a theoretical framework based on an Ising-like extension of the Frenkel-Kontorova model, which is analysed in detail in 1D using the transfer matrix formalism, determining a complex phase diagram. Many-body spin configurations can be represented as a continuous matrix product state with interesting properties. The feasibility of our model is validated using simple ab initio calculations with density functional theory (DFT), which allow us to search actual materials where this complex phenomenon can be obtained in the laboratory.
II. THE ISING-FRENKEL-KONTOROVA MODELLet us consider a simple extension of the Frenkel-Kontorova model, that we have termed Ising-Frenkel-Kontorova (IFK), which consists of adding an Ising spin variable, + or −, to each film atom, representing its spin polarization along a certain easy axis. We will only con-