Non-Fermi surface nesting driven commensurate magnetic ordering in Fe-doped Sr${}_2$RuO${}_4$

Sr${}_2$RuO${}_4$, an unconventional superconductor, is known to possess an incommensurate spin density wave instability driven by Fermi surface nesting. Here we report a static spin density wave ordering with a commensurate propagation vector $q_c$ = (0.25 0.25 0) in Fe-doped Sr${}_2$RuO${}_4$, despite the magnetic fluctuations persisting at the incommensurate wave vectors $q_{ic}$ = (0.3 0.3 L) as in the parent compound. The latter feature is corroborated by the first principles calculations, which show that Fe substitution barely changes the nesting vector of the Fermi surface. These results suggest that in addition to the known incommensurate magnetic instability, Sr${}_2$RuO${}_4$ is also in proximity to a commensurate magnetic tendency that can be stabilized via Fe doping.