  The Z-vector method in the relativistic coupled-cluster framework is used to
calculate magnetic hyperfine structure constant ($A_J$) of alkali metals and
singly charged alkaline earth metals in their ground state electronic
configuration. The Z-vector results are in very good agreement with the
experiment. The $A_J$ values of Li, Na, K, Rb, Cs, Be$^{+}$, Mg$^{+}$,
Ca$^{+}$, and Sr$^{+}$ obtained in the Z-vector method are compared with the
extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The
same basis and cutoff are used for the comparison purpose. The comparison shows
that Z-vector method with the singles and double approximation can produce more
precise wavefunction in the nuclear region than the ECC method.
