  The down-going atmospheric \nu_{\mu} and {\bar{\nu_{\mu}}} fluxes can be
significantly altered due to the presence of eV^2-scale active-sterile
oscillations. We study the sensitivity of a large Liquid Argon detector and a
large magnetized iron detector (like the proposed ICAL at INO) to these
oscillations. Such oscillations are indicated by results from LSND, and more
recently, from MiniBooNE and from reanalyses of reactor experiments following
recent recalculations of reactor fluxes. There are other tentative indications
of the presence of sterile states in both the \nu and {\bar{\nu}} sectors as
well. Using the allowed sterile parameter ranges in a 3+1 mixing framework in
order to test these results, we perform a fit assuming active-sterile
oscillations in both the muon neutrino and antineutrino sectors, and compute
oscillation exclusion limits using atmospheric down-going muon neutrino and
anti-neutrino events. We find that (for both \nu_{\mu} and {\bar{\nu_{\mu}}}) a
Liquid Argon detector, an ICAL-like detector or a combined analysis of both
detectors with an exposure of 1 Mt yr provides significant sensitivity to
regions of parameter space in the range 0.1 < \Delta m^2 < 5 eV^2 for \sin^2
2\Theta_{\mu\mu}\geq 0.08. Thus atmospheric neutrino experiments can provide
complementary coverage in these regions, improving sensitivity limits in
combination with bounds from other experiments on these parameters. We also
analyse the bounds using muon antineutrino events only and compare them with
the results from MiniBooNE.
