We study the dynamical entanglement between the spin and the spatial degrees of freedom for a spin- 1/2 charged particle in a square billiard, subject to a nonhomogeneous magnetic field, a system which is classically nonintegrable. This system has three degrees of freedom, one of them being strictly quantum, and we consider initial states which are coherent states with spin in the x direction. The center of the coherent state can be chosen to lie on classically chaotic or regular initial conditions. We show that for chaotic initial conditions the entanglement is rather fast and increases monotonically, while for the regular ones it may present strong recoherences, whose period is related to the classical motion. We also show that this system exhibits special initial conditions which entangle even faster than a typical chaotic one.70045201