  A spin version of dynamical mean-field theory is extended for magnetically
ordered states in the Heisenberg model. The self-consistency equations are
solved with high numerical accuracy by means of the continuous-time quantum
Monte Carlo with bosonic baths coupled to the spin. The resultant solution is
critically tested by known physical properties. In contrast with the mean-field
theory, soft paramagnons appear near the transition temperature. Moreover, the
Nambu-Goldstone mode (magnon) in the ferromagnetic phase is reproduced
reasonably well. However, antiferromagnetic magnons have an energy gap in
contradiction to the Nambu-Goldstone theorem. The origin of this failure is
discussed in connection with an artificial first-order nature of the
transition.
