  We propose the use of periodic arrays of permanent magnetic films for
producing magnetic lattices of microtraps for confining, manipulating and
controlling small clouds of ultracold atoms and quantum degenerate gases. Using
analytical expressions and numerical calculations we show that periodic arrays
of magnetic films can produce one-dimensional (1D) and two-dimensional (2D)
magnetic lattices with non-zero potential minima, allowing ultracold atoms to
be trapped without losses due to spin flips. In particular, we show that two
crossed layers of periodic arrays of parallel rectangular magnets plus bias
fields, or a single layer of periodic arrays of square-shaped magnets with
three different thicknesses plus bias fields, can produce 2D magnetic lattices
of microtraps having non-zero potential minima and controllable trap depth. For
arrays with micron-scale periodicity, the magnetic microtraps can have very
large trap depths ($\sim$0.5 mK for the realistic parameters chosen for the 2D
lattice) and very tight confinement.
