Ferroelectricity induced by interatomic magnetic exchange interaction

Multiferroics, where two or more ferroic order parameters coexist, is one of the hottest fields in condensed matter physics and materials science[1-9]. However, the coexistence of magnetism and conventional ferroelectricity is physically unfavoured[10]. Recently several remedies have been proposed, e.g., improper ferroelectricity induced by specific magnetic[6] or charge orders[2]. Guiding by these theories, currently most research is focused on frustrated magnets, which usually have complicated magnetic structure and low magnetic ordering temperature, consequently far from the practical application. Simple collinear magnets, which can have high magnetic transition temperature, have never been considered seriously as the candidates for multiferroics. Here, we argue that actually simple interatomic magnetic exchange interaction already contains a driving force for ferroelectricity, thus providing a new microscopic mechanism for the coexistence and strong coupling between ferroelectricity and magnetism. We demonstrate this mechanism by showing that even the simplest antiferromagnetic (AFM) insulator MnO, can display a magnetically induced ferroelectricity under a biaxial strain

Two-Particle-Self-Consistent Approach for the Hubbard Model

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.Comment: Chapter in "Theoretical methods for Strongly Correlated Systems", Edited by A. Avella and F. Mancini, Springer Verlag, (2011) 55 pages. Misprint in Eq.(23) corrected (thanks D. Bergeron