  Magnon excitation in a spinor Bose-Einstein condensate by a driven magnetic
field is shown to have a close analogy with the dynamical Casimir effect. A
time-dependent external magnetic field amplifies quantum fluctuations in the
magnetic ground state of the condensate, leading to magnetization of the
system. The magnetization occurs in a direction perpendicular to the magnetic
field breaking the rotation symmetry. This phenomenon is numerically
demonstrated and the excited quantum field is shown to be squeezed.
