  The spectral function of transverse spin fluctuations, including the
contributions from both the single-particle and the collective (magnon)
excitations in an antiferromagnet, is evaluated for the Hubbard model with NN
and NNN hoppings in the full U-range from weak coupling to strong coupling. For
the NN hopping model, the magnon excitations are dominant for U > 2.5 (d=2), so
that an effective spin description of the AF state holds down to a surprisingly
low U value. In the weak coupling limit the spectral function is suppressed at
low energies, as if due to an effective gap. NNN hopping t' leads to magnon
softening and also a significant increase in the low-energy spectral function
due to single-particle excitations. Evolution of the magnon spectrum with t' is
studied in the strong coupling limit, and the quantum spin- fluctuation
correction to sublattice magnetization in d=2 and the Neel temperature in d=3
are also evaluated.
