  The direct measurement of gravitational waves is a powerful tool for
surveying the population of black holes across the universe. The first
gravitational wave catalog from LIGO has detected black holes as heavy as
$\sim50~M_\odot$, colliding when our Universe was about half its current age.
However, there is yet no unambiguous evidence of black holes in the
intermediate-mass range of $10^{2-5}~M_\odot$. Recent electromagnetic
observations have hinted at the existence of IMBHs in the local universe;
however, their masses are poorly constrained. The likely formation mechanisms
of IMBHs are also not understood. Here we make the case that multiband
gravitational wave astronomy --specifically, joint observations by space- and
ground-based gravitational wave detectors-- will be able to survey a broad
population of IMBHs at cosmological distances. By utilizing general
relativistic simulations of merging black holes and state-of-the-art
gravitational waveform models, we classify three distinct population of
binaries with IMBHs in the multiband era and discuss what can be observed about
each. Our studies show that multiband observations involving the upgraded LIGO
detector and the proposed space-mission LISA would detect the inspiral, merger
and ringdown of IMBH binaries out to redshift ~2. Assuming that next-generation
detectors, Einstein Telescope, and Cosmic Explorer, are operational during
LISA's mission lifetime, we should have multiband detections of IMBH binaries
out to redshift ~5. To facilitate studies on multiband IMBH sources, here we
investigate the multiband detectability of IMBH binaries. We provide analytic
relations for the maximum redshift of multiband detectability, as a function of
black hole mass, for various detector combinations. Our study paves the way for
future work on what can be learned from IMBH observations in the era of
multiband gravitational wave astronomy.
