  Quantum criticality in iron pnictides involves both the nematic and
antiferromagnetic degrees of freedom, but the relationship between the two
types of fluctuations has yet to be clarified. Here we study this problem in
the presence of a small external uniaxial potential, which breaks the
$C_4$-symmetry in the B$_{1g}$ sector. We establish an identity that connects
the spin excitation anisotropy, which is the difference of the dynamical spin
susceptibilities at $\vec{Q}_1=\left(\pi,0\right)$ and
$\vec{Q}_2=\left(0,\pi\right)$, with the dynamical magnetic susceptibility and
static nematic susceptibility. Using this identity, we introduce a scaling
procedure to determine the dynamical nematic susceptibility in the quantum
critical regime, and illustrate the procedure for the case of the optimally
Ni-doped BaFe$_2$As$_2$[Y. Song \textit{et al.}, Phys. Rev. B 92, 180504
(2015)]. The implications of our results for the overall physics of the
iron-based superconductors are discussed.
