Precise determination of ground-state hyperfine splitting and calculation of Zeeman coefficients for 171Yb+ microwave frequency standard

We report precise measurement of the hyperfine splitting and calculation of the Zeeman coefficients of the $^{171}$Yb$^+$ ground state. The absolute hyperfine splitting frequency is measured using high-resolution laser-microwave double-resonance spectroscopy at 0.1 mHz level, and evaluated using more accurate Zeeman coefficients. These Zeeman coefficients are derived using Land\'{e} $g_J$ factors calculated by two atomic-structure methods, multiconfiguration Dirac-Hartree-Fock, and multireference configuration interaction. The cross-check of the two calculations ensures an accuracy of the Zeeman coefficients at $10^{-2}$ Hz/G$^2$ level. The results provided in this paper improve the accuracy and reliability of the second-order Zeeman shift correction, thus further improving the accuracy of the microwave frequency standards based on $^{171}$Yb$^+$. The high-precision hyperfine splitting and Zeeman coefficients could also support could also support further experiments to improve the constraints of fundamental constants through clock frequency comparison of the Yb$^+$ system.