  Motivated by growing indications for a distinct form of nematic correlations
in the extremely hole doped iron pnictide compounds $A$Fe$_2$As$_2$
($A$=K,Rb,Cs), we consider spin-driven nematic order in the general case of
incommensurate magnetic fluctuations. We classify the nematic order parameters
by broken mirror symmetries of the tetragonal $D_{4h}$ point group, and use
this scheme to construct a general Ginzburg-Landau theory that links the
nematic order to spatial pattern of magnetic fluctuations. Our analysis points
to incommensurate magnetic fluctuations of wavevector $(q,q)$ as underlying a
$B_{2g}$ nematic order in $A$Fe$_2$As$_2$. We substantiate this idea by
microscopic calculations of the nematic order based on 3-sublattice
$(2\pi/3,2\pi/3)$ spin correlations in an extended bilinear-biquadratic
Heisenberg model. We summarize the existing evidence in support of the proposed
mechanism, suggest ways to further test it in future experiments, and discuss
the implications of our results for iron-based high temperature
superconductivity.
