  The spin and the chirality orderings of the three-dimensional Heisenberg spin
glass with the weak random anisotropy are studied under applied magnetic fields
by equilibrium Monte Carlo simulations. A replica symmetry breaking transition
occurs in the chiral sector accompanied by the simultaneous spin-glass order.
The ordering behavior differs significantly from that of the Ising SG, despite
the similarity in the global symmetry. Our observation is consistent with the
spin-chirality decoupling-recoupling scenario of a spin-glass transition.
