  We propose a method to reach the antiferromagnetic state of two-dimensional
Fermi gases trapped in optical lattices: Independent subsystems are prepared in
suitable initial states and then connected by a sudden or slow quench of the
tunneling between the subsystems. Examples of suitable low-entropy subsystems
are double wells or plaquettes, which can be experimentally realised in Mott
insulating shells using optical super-lattices. We estimate the effective
temperature T* of the system after the quench by calculating the distribution
of excitations created using the spin wave approximation in a Heisenberg model.
We investigate the effect of an initial staggered magnetic field and find that
for an optimal polarisation of the initial state the effective temperature can
be significantly reduced from T*$\approx$1.7 Tc at zero polarisation to
T*<0.65Tc, where Tc is the crossover temperature to the antiferromagnetic
state. The temperature can be further reduced using a finite quench time. We
also show that T* decreases logarithmically with the linear size of the
subsystem.
