  The large-scale dynamics of plasmas is well described within the framework of
magnetohydrodynamics (MHD). However, whenever the ion density of the plasma
becomes sufficiently low, the Hall effect is likely to become important. The
role of the Hall effect has been studied in several astrophysical plasma
processes, such as magnetic reconnection, magnetic dynamo, MHD turbulence or
MHD instabilities. In particular, the development of small-scale instabilities
is essential to understand the transport properties in a number of
astrophysical plasmas. The magneto-rotational instability, which takes place in
differentially rotating accretion disks embedded in relatively weak magnetic
fields, is just one example. The influence of the large-scale velocity flows on
small-scale instabilities is often approximated by a linear shear flow. In this
paper we quantitatively study the role of the Hall effect on plasmas embedded
in large-scale shear flows. More precisely, we show that a new instability
develops as long as the Hall effect is present, which we therefore term as the
Hall magneto-shear instability. As a particular case, we recover the so-called
magneto-rotational instability and quantitatively assess the role of the Hall
effect on its development and evolution.
