With the development of microwave atomic clocks, black-body radiation Zeemanshifts need to be considered carefully. In this Letter, the frequency shifts ofhyperfine splittings of ground state due to black-body magnetic field areinvestigated. The relative frequency shifts of different alkali atoms andalkali-like ions which could be candidates of microwave atomic clocks arecalculated, and results are from -0.977*10^(-17) [T(K)/300]^2 to-1.947*10^(-17) [T(K)/300]^2 for different atoms. These results are consistentwith previous works but with more precision, detailed derivations and clearphysical pictures.
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