  The Gutzwiller technique has long been known as a method to include
correlations in electronic structure calculations. Here we implement an
ab-initio Gutzwiller+LDA calculation, and apply it to a classic problem, the
ferromagnetism of bulk bcc Fe, whose nature has attracted recent interest. In
the conventional Stoner-Wohlfarth model, the ferromagnetic ordering of iron
sets in so that the electrons can reduce their mutual Coulomb repulsion at the
extra cost of some increase of electron kinetic energy. Density functional
theory within the spin polarized local density approximation (LDA) has long
supported that picture, showing that ferromagnetic alignment causes band
narrowing and a corresponding wavefunction localization, whence a kinetic
energy increase. However, because of its inadequate treatment of strong
intra-site correlations for localized d orbitals, LDA cannot be relied upon,
particularly when it comes to separately describing fine potential and kinetic
energy imbalances. With ab-initio Gutzwiller+LDA, we indeed find that the
effect of correlations is to dramatically reverse the balance, the
ferromagnetic ordering of Fe in fact causing a decrease of kinetic energy, at
the cost of some increase of potential energy. The underlying physical
mechanism, foreshadowed long ago by Goodenough and others, and more recently
supported by LDA+DMFT calculations, is that correlations cause eg and t2g 3d
orbitals to behave very differently. Weakly dispersive eg states are
spin-polarized and almost localized, while, more than half filled, the t2g are
broad band, fully delocalized states. Owing to intra-atomic Hund's rule
exchange which aligns eg and t2g spins, the propagation of itinerant t2g holes
is only allowed when different atomic spins are ferromagnetically aligned. We
thus conclude that double exchange is at work already in the most popular
ferromagnetic metal.
