Non-Fermi surface nesting driven commensurate magnetic ordering in Fe-doped Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$.

Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$, an unconventional superconductor, is known to possess an incommensurate spin density wave instability driven by Fermi surface nesting. Here we report a new static spin density wave ordering with a commensurate propagation vector \textbf{q}$_{\mathrm{c}}$ $=$ (0.25 0.25 0) in Fe-doped Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$, despite that the magnetic fluctuations still persist at the incommensurate wave vectors \textbf{q}$_{\mathrm{ic}} \quad =$ (0.3 0.3 $L)$. First principles calculations show that Fe substitution barely changes the nesting vector of the Fermi surface, but leads to antiferromagnetic polarization in the nearest-neighbor Ru magnetic moments. Our results imply that in addition to the known incommensurate magnetic instability, Sr$_{\mathrm{2}}$RuO$_{\mathrm{4}}$ is also in proximity to a commensurate magnetic tendency that can be stabilized via tuning the local exchange interaction between Ru and dilute magnetic impurities.