  We use ultracold spin--1/2 atomic fermions ($^6$Li) to realize the Hubbard
model on a three-dimensional (3D) optical lattice. At relatively high
temperatures and at densities near half-filling, we show that the gas forms a
Mott insulator with unordered spins. To observe antiferromagnetic order that is
predicted to occur at lower temperatures, we developed the compensated optical
lattice method to evaporatively cool atoms in the lattice. This cooling has
enabled the detection of short-range magnetic order by spin-sensitive Bragg
scattering of light.
