  With the development of microwave atomic clocks, the Zeeman shifts for the
spectral lines of black-body radiation need to be investigated carefully. In
this Letter, the frequency shifts of hyperfine splittings of atomic ground
states due to the magnetic field of black-body radiation are reported. The
relative frequency shifts of different alkali atoms and alkali-like ions, which
could be candidates of microwave atomic clocks, were calculated. The results
vary from $-0.977\times10^{-17}[T(K)/300]^{2}$ to
$-1.947\times10^{-17}[T(K)/300]^{2}$ for different atoms considered. These
results are consistent with previous work but with greater precision, detailed
derivations, and a clear physical picture.
