  We demonstrate, using dynamical mean-field theory with the hybridization
expansion continuous time quantum montecarlo impurity solver, a rich phase
diagram with {\em correlation driven metallic and half-metallic phases} in a
simple model of a correlated band insulator, namely, the half-filled ionic
Hubbard model (IHM) with first {\em and} second neighbor hopping ($t$ and
$t'$), an on-site repulsion $U$, and a staggered potential $\Delta$. Without
$t'$ the IHM has a direct transition from a paramagnetic band insulator (BI) to
an antiferromagnetic Mott insulator (AFI) phase as $U$ increases. For weak to
intermediate correlations, $t'$ frustrates the AF order, leading to a
paramagnetic metal (PM) phase, a ferrimagnetic metal (FM) phase and an
anti-ferromagnetic half-metal (AFHM) phase in which electrons with one spin
orientation, say up-spin, have gapless excitations while the down-spin
electrons are gapped. For $t'$ less than a threshold $ t_1$, there is a direct,
first-order, BI to AFI transition as $U$ increases, as for $t'=0$; for $t_4< t'
< \Delta/2$, the BI to AFI transition occurs via an intervening PM phase. For
$t' > \Delta/2$, there is no BI phase, and the system has a PM to AFI
transition as $U$ increases. In an intermediate-range $t_2 < t' < t_3$, as $U$
increases the system undergoes four transitions, in the sequence BI
$\rightarrow$ PM $\rightarrow$ FM $\rightarrow$ AFHM $\rightarrow$ AFI; the FM
phase is absent in the ranges of $t'$ on either side, implying three
transitions. The BI-PM, FM-AFHM and AFHM-AFI transitions, and a part of the
PM-FM transition are continuous, while the rest of the transitions are first
order in nature. The PM, FM and the AFHM phases have, respectively, spin
symmetric, partially polarized and fully polarized electron [hole] pockets
around the ($\pm\pi/2$, $\pm\pi/2$) [($\pm \pi, 0$), ($0. \pm \pi$)] points in
the Brillouin zone.
