  Nuclear-spin entangling gates with divalent atoms can be executed by one
global laser pulse when $\Delta_{\text{Z}}<\Omega$, where $\Delta_{\text{Z}}$
is the Zeeman-splitting-dominated frequency difference for the clock-Rydberg
transitions of the two nuclear-spin qubit states and $\Omega$ is the maximal
Rabi frequency. Concerning the sensitivity of Rydberg-state energy to magnetic
fluctuation, the gate is compatible with large-scale atomic arrays for weaker
magnetic field is suitable for ensuring uniform field in a large qubit array.
The gate can have a high fidelity because the relaxation and dephasing of
Rydberg states, which limit the fidelity and grow with $1/\Omega$, can be
mitigated with easily attainable large $\Omega$.
