  We theoretically investigate finite-temperature thermodynamics and
demagnetization cooling of two-component Bose-Bose mixtures in a cubic optical
lattice, by using bosonic dynamical mean field theory (BDMFT). We calculate the
finite-temperature phase diagram, and remarkably find that the system can be
heated from the superfluid into the Mott insulator at low temperature,
analogous to the Pomeranchuk effect in 3He. This provides a promising many-body
cooling technique. We examine the entropy distribution in the trapped system
and discuss its dependence on temperature and an applied magnetic field
gradient. Our numerical simulations quantitatively validate the spin-gradient
demagnetization cooling scheme proposed in recent experiments.
