Superexchange

Abstract: We argue that the newly discovered superconductivity in a nearly magnetic, Fe-based layered compound is unconventional and mediated by antiferromagnetic spin fluctuations, though different from the usual superexchange and specific to this compound. This resulting state is an example of extended s-wave pairing with a sign reversal of the order parameter between different Fermi surface sheets. The main role of doping in this scenario is to lower the density of states and suppress the pair-breaking ferromagnetic fluctuations.

Abstract: The theory of indirect exchange in poor conductors is examined from a new viewpoint in which the $d$ (or $f$) shell electrons are placed in wave functions assumed to be exact solutions of the problem of a single $d$-electron in the presence of the full diamagnetic lattice. Inclusion of $d$-electron interactions leads to three spin-dependent effects which, in the usual order of their sizes, we call: superexchange per se, which is always antiferromagnetic; direct exchange, always ferromagnetic; and an indirect polarization effect analogous to nuclear indirect exchange. Superexchange itself is shown to be closely related to the poor conductivity, in agreement with experiment. By means of crystal field theory the parameters determining superexchange can be estimated, and in favorable cases (NiO, LaFe${\mathrm{O}}_{3}$) the exchange integrals can be evaluated with accuracy of several tens of percent. Qualitative understanding of the whole picture of exchange in iron group oxides and fluorides follows from these ideas.

Abstract: In this paper the general formalism of Kramers indicating the existence of superexchange interaction has been reduced, under simplifying assumptions, to the point where actual formulas for the interaction can be written down directly in terms of spin operators, with certain exchange and transition integrals as parameters. Two results of physical interest are the following: (a) superexchange must be expected to show the directional properties (as far as directional relations of interacting magnetic ions are concerned) of the orbitals in the outer shell of the non-magnetic connecting ions; and (b) the sign of the effective exchange integral depends upon the sign of the internal exchange coupling of an added electron on the magnetic ion.

Abstract: With the perovskite multiferroic $R\mathrm{Mn}{\mathrm{O}}_{3}$ $(R=\mathrm{Gd},\mathrm{Tb},\mathrm{Dy})$ as guidance, we argue that the Dzyaloshinskii-Moriya interaction (DMI) provides the microscopic mechanism for the coexistence and strong coupling between ferroelectricity and incommensurate magnetism. We use Monte Carlo simulations and zero-temperature exact calculations to study a model incorporating the double-exchange, superexchange, Jahn-Teller, and DMI terms. The phase diagram contains a multiferroic phase between $A$ and $E$ antiferromagnetic phases, in excellent agreement with experiments.