Multiferroics seen from theoretic derivation of a tight binding model

One presented some lattice models, while the theoretic derivation has not been found, and the importance of correlation effects has to be emphasized. On the basis of the non-relativistic Hamiltonian from the Dirac equation, we derive in detail a tight binding model. We find that both ferromagnetism and ferroelectricity are from the correlation effect between electrons, and magnetic and electric orders are strongly coupled due to the spin-orbit interaction.