  We present a general scheme for synthesizing a spatially periodic magnetic
field, or a magnetic lattice (ML), for ultracold atoms using pulsed gradient
magnetic fields. Both the period and the depth of the artificial ML can be
tuned, immune to atomic spontaneous emission often encountered in optical
lattices. The effective Hamiltonian for our 2-dimensional ML has not been
discussed previously in condensed matter physics. Its band structures show
interesting features which can support topologically nontrivial phases. The
technical requirements for implementing our protocol are readily available in
today's cold atom experiments. Realization of our proposal will significantly
expand the repertoire for quantum simulation with ultracold atoms.
