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Recent experiments reported an unusual nematic behavior of heavily hole-dopedpnictides $A$Fe$_{2}$As$_{2}$, with alkali $A$ = Rb, Cs. In contrast to the$B_{2g}$ nematic order of the parent $Ae$Fe$_{2}$As$_{2}$ compounds (withalkaline earth $Ae$ = Sr, Ba), characterized by unequal nearest-neighbor Fe-Febonds, in the hole-doped systems nematic order is observed in the $B_{1g}$channel, characterized by unequal next-nearest-neighbor Fe-Fe (diagonalFe-As-Fe) bonds. In this work, using density functional theory, we attributethis behavior to the evolution of the magnetic ground state along the series$Ae_{1-x}A_{x}$Fe$_{2}$As$_{2}$, from single stripes for small $x$ to doublestripes for large $x$. Our simulations using the reduced Stoner theory showthat fluctuations of Fe moments are essential for the stability of thedouble-stripe configuration. We propose that the change in the nature of themagnetic ground state is responsible for the change in the symmetry of thevestigial nematic order that it supports.

Evolution from $B_{2g}$ nematics to $B_{1g}$ nematics in heavily hole-doped iron-based superconductors