The longitudinal and transverse nuclear magnetic relaxation rates 1/T-1 (T)
and 1/T-2 (T) are calculated for three-dimensional (3D) and two-dimensiona
l metallic ferromagnets (FM) and antiferromagnets (AFM) with localized magn
etic moments in the spin-wave temperature region. The contribution of the o
ne-magnon decay processes is strongly enhanced in comparison with the stand
ard T-linear Korringa term, especially for the FM case. For the 3D AFM case
this contribution diverges logarithmically,the divergence being cut at the
magnon gap omega(0) due to magnetic anisotropy, and for the 2D AFM case as
omega(0)(-1). The electron-magnon scattering processes yield T-2 ln(T/omeg
a(0)) and T-2/omega(0)(1/2) terms in 1/T-1 for the 3D AFM and 2D FM cases,
respectively. The tu ct-magnon ("Raman") contributions are investigated and
demonstrated to be large in the 2D FM case. [S0163-1829(99)09141-9].