  We numerically investigate the stationary and non-equilibrium critical
dynamics in three-dimensional isotropic Heisenberg antiferromagnets. Since the
non-conserved staggered magnetization couples dynamically to the conserved
magnetization density, we employ a hybrid simulation algorithm that combines
reversible spin precession with relaxational Kawasaki spin exchange processes.
We measure the dynamic critical exponent and identify a suitable intermediate
time window to obtain the aging scaling exponents. Our results support an
earlier renormalization group prediction: While the critical aging collapse
exponent assumes a universal value, the associated temporal decay exponent in
the two-time spin autocorrelation function depends on the initial distribution
of the conserved fields; here, specifically on the width of the initial spin
orientation distribution.
