The longitudinal and transverse nuclear magnetic relaxation rates 1/T-1(T)
and 1/T-2(T) are calculated for three- and two-dimensional (3D and 2D) meta
llic ferro- and antiferromagnets (FM and AFM) with localized magnetic momen
ts in the spin-wave temperature region. The contribution of the one-magnon
decay processes is strongly enhanced in comparison with the standard T-line
ar Korringa term, especially for the FM case. For the 3D AFM case this cont
ribution diverges logarithmically, the divergence being cut at the magnon g
ap omega (0) due to magnetic anisotropy, and for the 2D AFM case as omega (
-1)(0) The electron-magnon scattering processes yield T(2)ln(T/omega (0)) a
nd T-2/omega (1)(0)/(2)-terms in 1/T-1 for the 3D AFM and 2D FM cases, resp
ectively. The two-magnon ("Raman") contributions are investigated and demon
strated to be large in the 2D FM case. Peculiarities of the isotropic 2D li
mit (where the correlation length is very large) are analyzed.