  A new method to implement an asymmetrical two-dimensional magnetic lattice is
proposed. The asymmetrical two-dimensional magnetic lattice can be created by
periodically distributing magnetic minima across the surface of magnetic thin
film where the periodicity can be achieved by milling $n\times n$ square holes
on the surface of the film. The quantum device is proposed for trapping and
confining ultracold atoms and quantum degenerate gases prepared in the low
magnetic field seeking-state at low temperature, such as the Bose-Einstein
Condensate (BEC) and ultracold fermions. We present detailed analysis of the
analytical expressions and the numerical simulation procedure used to calculate
the external magnetic field. We also, describe the magnetic band gap structure
exhibited by the asymmetric effect of the magnetic minima and show some of the
possible application. We analyze the effect of changing the characteristic
parameters of the magnetic lattice, such as the separating periodicity length
and the hole size along with the applications of the external magnetic bias
fields to maintain and allocate a suitable non-zero magnetic local minima at
effective $z$-distance above the thin film surface. Suitable values are shown
which keep the trapped ultracold atoms away from the thermal Majorana spin-flip
and the surface Casimir-Polder effect.
