  We numerically investigate the non-equilibrium critical dynamics in
three-dimensional anisotropic antiferromagnets in the presence of an external
magnetic field. The phase diagram of this system exhibits two critical lines
that meet at a bicritical point. The non-conserved components of the staggered
magnetization order parameter couple dynamically to the conserved component of
the magnetization density along the direction of the external field. Employing
a hybrid computational algorithm that combines reversible spin precession with
relaxational Monte Carlo updates, we study the aging scaling dynamics for the
model C critical line, identifying the critical initial slip, autocorrelation,
and aging exponents for both the order parameter and conserved field, thus also
verifying the dynamic critical exponent. We further probe the model F critical
line by investigating the system size dependence of the characteristic spin
wave frequencies near criticality, and measure the dynamic critical exponents
for the order parameter including its aging scaling at the bicritical point.
