  Density functional band calculations have been performed to study
LaNiO$_3$/LaAlO$_3$ superlattices. Motivated by recent experiments reporting
the magnetic and metal-insulator phase transition as a function of LaNiO$_3$
layer thickness, we examined the electronic structure, magnetic properties, and
orbital occupation depending on the number of LaNiO$_3$ layers. Calculations
show that the magnetic phase is stabler than the nonmagnetic for finite and
positive $U$ values. The orbital polarization is significantly reduced by $U$
even in the magnetic regions. The implications of the results are discussed in
comparison to recent experimental and theoretical studies within the
limitations of the LDA$+U$ method.
