Interesting spin Hamiltonians can be realized with ultracold atoms in a
two-component Mott insulator (2CMI). It was recently demonstrated that the
application of a magnetic field gradient to the 2CMI enables new techniques of
thermometry and adiabatic cooling. Here we present a theoretical description
which provides quantitative analysis of these two new techniques. We show that
adiabatic reduction of the field gradient is capable of cooling below the Curie
or N\'eel temperature of certain spin ordered phases.Comment: 5 pages, 5 figures (v4): Added journal referenc
