Noncommutative Dirac oscillator in an external magnetic field

We show that (2+1)$(2+1)$-dimensional noncommutative Dirac oscillator in an external magnetic field is mapped onto the same but with reduced angular frequency in absence of magnetic field. We construct the relativistic Landau levels by solving corresponding Dirac equation in (2+1)$(2+1)$-dimensional noncommutative phase space. All the Landau levels become independent of noncommutative parameter for a critical value of the magnetic field. Several other interesting features along with the relevance of such models in the study of atomic transitions in a radiation field have been discussed.