  The competition of magnetic exchange interactions and tunneling underlies
many complex quantum phenomena observed in real materials. We study
non-equilibrium magnetization dynamics in an extended 2D system by loading
effective spin-1/2 bosons into a spin-dependent optical lattice, and we use the
lattice to separately control the resonance conditions for tunneling and
superexchange. After preparing a non-equilibrium anti-ferromagnetically ordered
state, we observe relaxation dynamics governed by two well-separated rates,
which scale with the underlying Hamiltonian parameters associated with
superexchange and tunneling. Remarkably, with tunneling off-resonantly
suppressed, we are able to observe superexchange dominated dynamics over two
orders of magnitude in magnetic coupling strength, despite the presence of
vacancies. In this regime, the measured timescales are in agreement with simple
theoretical estimates, but the detailed dynamics of this 2D, strongly
correlated, and far-from-equilibrium quantum system remain out of reach of
current computational techniques.
