  We show that by displacing two optical lattices with respect to each other,
we may produce interactions similar to the ones describing ferro-magnetism in
condensed matter physics. We also show that particularly simple choices of the
interaction lead to spin-squeezing, which may be used to improve the
sensitivity of atomic clocks. Spin-squeezing is generated even with partially,
and randomly, filled lattices, and our proposal may be implemented with current
technology.
