  Integrable spin systems possess interesting geometrical and gauge invariance
properties and have important applications in applied magnetism and
nanophysics. They are also intimately connected to the nonlinear Schr\"odinger
family of equations. In this paper, we identify three different integrable spin
systems in (2 + 1) dimensions by introducing the interaction of the spin field
with more than one scalar potential, or vector potential, or both. We also
obtain the associated Lax pairs. We discuss various interesting reductions in
(2 + 1) and (1 + 1) dimensions. We also deduce the equivalent nonlinear
Schr\"odinger family of equations, including the (2 + 1)-dimensional version of
nonlinear Schr\"odinger--Hirota--Maxwell--Bloch equations, along with their Lax
pairs.
