  Multiferroics, materials where spontaneous long-range magnetic and dipolar
orders coexist, represent an attractive class of compounds, which combine rich
and fascinating fundamental physics with a technologically appealing potential
for applications in the general area of spintronics. Ab-initio calculations
have significantly contributed to recent progress in this area, by elucidating
different mechanisms for multiferroicity and providing essential information on
various compounds where these effects are manifestly at play. In particular,
here we present examples of density-functional theory investigations for two
main classes of materials: a) proper multiferroics (where ferroelectricity is
driven by hybridization or purely structural effects), with BiFeO_3 as
prototype material, and b) improper multiferroics (where ferroelectricity is
driven by correlation effects and is strongly linked to electronic degrees of
freedom such as spin, charge, or orbital ordering), with rare-earth manganites
as prototypes.
