  In a wide variety of materials, such as copper oxides, heavy fermions,
organic salts, and the recently discovered iron pnictides, superconductivity is
found in close proximity to a magnetically ordered state. The character of the
proximate magnetic phase is thus believed to be crucial for understanding the
differences between the various families of unconventional superconductors and
the mechanism of superconductivity. Unlike the AFM order in cuprates, the
nature of the magnetism and of the underlying electronic state in the iron
pnictide superconductors is not well understood. Neither density functional
theory nor models based on atomic physics and superexchange, account for the
small size of the magnetic moment. Many low energy probes such as transport,
STM and ARPES measured strong anisotropy of the electronic states akin to the
nematic order in a liquid crystal, but there is no consensus on its physical
origin, and a three dimensional picture of electronic states and its relations
to the optical conductivity in the magnetic state is lacking. Using a first
principles approach, we obtained the experimentally observed magnetic moment,
optical conductivity, and the anisotropy of the electronic states. The theory
connects ARPES, which measures one particle electronic states, optical
spectroscopy, probing the particle hole excitations of the solid and neutron
scattering which measures the magnetic moment. We predict a manifestation of
the anisotropy in the optical conductivity, and we show that the magnetic phase
arises from the paramagnetic phase by a large gain of the Hund's rule coupling
energy and a smaller loss of kinetic energy, indicating that iron pnictides
represent a new class of compounds where the nature of magnetism is
intermediate between the spin density wave of almost independent particles, and
the antiferromagnetic state of local moments.
