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The roles of the fine-structure intramanifold resonances to the Zeeman shiftscaused by the blackbody radiation (BBRz shifts) in the optical clocktransitions are analyzed. The clock frequency measurement in the $^1S_0-^3P_0$clock transition of the singly charged aluminium ion (Al$^+$) has already beenreached the $10^{-19}$ level at which the BBRz effect can be significant indetermining the uncertainty. In view of this, we probe first the BBRz shift inthis transition rigorously and demonstrate the importance of the contributionsfrom the intramanifold resonances explicitly. To carry out the analysis, wedetermine the dynamic magnetic dipole (M1) polarizabilities of the clock statesover a wide range of angular frequencies by employing two variants ofrelativistic many-body methods. This showed the BBRz shift is highly suppresseddue to blue-detuning of the BBR spectrum to the $^3P_0-^3P_1$ fine-structureintramanifold resonance in Al$^+$ and it fails to follow the usually assumedstatic M1 polarizability limit in the estimation of the BBRz shift. Theresonance also leads to a reversal behavior of the temperature dependence and acancellation in the shift. After learning this behavior, we extended ouranalyses to other optical clocks and found that these shifts are of the orderof micro-hertz leading to fractional shifts in the clock transitions at the$10^{-20}$ level or below.

Suppression of Black-body Radiation Induced Zeeman Shifts in the Optical Clocks due to the Fine-structure Intramanifold Resonances