  It is by now established that neutrinos mix, have (different) non-zero
masses, and therefore oscillate. The oscillation parameters themselves,
however, are not all well-known. An open problem is that of the neutrino mass
hierarchy. We study the possibility of determining the neutrino mass hierarchy
with atmospheric neutrinos using an iron calorimeter detector capable of charge
identification such as the proposed MONOLITH and ICAL/INO detectors. We find
that such detectors are sensitive to the sign of the mass-squared difference,
\delta_{32} = m_3^2 - m_2^2, provided the as-yet unknown mixing angle between
the first and third generations, \theta_{13}, is greater than 6 degrees (\sin^2
2\theta_{13} > 0.04). A result with a significance greater than 90% CL requires
large exposures (more than 500 kton-years) as well as good energy and angular
resolution of the detected muons (better than 15%), especially for small
\theta_{13}. Hence obtaining definitive results with such a detector is
difficult, unless \theta_{13} turns out to be large. In contrast, such
detectors can establish a clear oscillation pattern in atmospheric neutrinos in
about 150 kton-years, therefore determining the absolute value of \delta_{32}
and \sin^2 2 \theta_{23} to within 10%.
