Non-Fermi surface nesting driven commensurate magnetic ordering in Fe-doped $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$

$\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$, 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 ${\mathbf{q}}_{\mathrm{c}}=\left(0.250.250\right)$ in Fe-doped $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$, despite the magnetic fluctuations persisting at the incommensurate wave vectors ${\mathbf{q}}_{\mathrm{ic}}=\left(0.30.3L\right)$ 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, $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$ is also in proximity to a commensurate magnetic tendency that can be stabilized via Fe doping.

Figure 1

(a) Temperature dependence of out-of-plane dc susceptibility ${\chi }_{\mathrm{c}}$ of $\mathrm{S}{\mathrm{r}}_2\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{F}{\mathrm{e}}_x{\mathrm{O}}_4$ $\left(x=0.05\right)$. ZFC denotes zero-field-cooled data and FC represents field-cooled data with 1 T measurement field. Inset shows the isothermal magnetization as a function of field measured at 2 and 20 K after ZFC. (b) Temperature dependence of ac susceptibility measured with $h=10\mathrm{Oe}$. (c) Temperature dependence of specific heat measured at zero field. Inset shows the expanded view of the lower temperature region with the data measured at 9 T included for comparison. The solid red line is the linear fit for $16\mathrm{K}<T<30\mathrm{K}$. (d) In-plane and out-of-plane resistivity as a function of temperature.

Figure 2

(a) Neutron diffraction measurement across ${\mathbf{q}}_{\mathrm{c}}=\left(0.250.250\right)$ along [1 1 0] direction at $T=4$, 50, and 100 K measured on $\mathrm{S}{\mathrm{r}}_2\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{F}{\mathrm{e}}_x{\mathrm{O}}_4$ $\left(x=0.05\right)$. (b) Neutron diffraction measurement across ${\mathbf{q}}_{\mathrm{c}}=\left(0.250.250\right)$ along [0 0 1] direction at selected temperatures. (c) The intensity of magnetic Bragg peak ${\mathbf{q}}_{\mathrm{c}}=\left(0.250.250\right)$ as a function of temperature. Note that for (b) the sample measured is smaller than that for (a,c). (d) Contour map of elastic magnetic scattering intensity of $\mathrm{S}{\mathrm{r}}_2\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{F}{\mathrm{e}}_x{\mathrm{O}}_4$ $\left(x=0.03\right)$ at $T=1.6\mathrm{K}$ after subtracting the background measured at 80 K. Spurious peaks are denoted by red circles. The residue intensity near the nuclear peaks $(\pm 1\pm 10)$ is presumably due to the thermal shift in the lattice parameters.

Figure 3

(a,b) Schematic diagrams of the spin-density wave ordering of $\mathrm{S}{\mathrm{r}}_2\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{F}{\mathrm{e}}_x{\mathrm{O}}_4$ $\left(x=0.05\right)$. (c) X-ray absorption spectra of $\mathrm{S}{\mathrm{r}}_2\left(\mathrm{R}{\mathrm{u}}_{0.97}\mathrm{F}{\mathrm{e}}_{0.03}\right){\mathrm{O}}_4$ near the Fe $L$ edge in comparison with FeO and $\mathrm{F}{\mathrm{e}}_2{\mathrm{O}}_3$ indicating the $3+$ valence state of Fe dopants. (d) Lower panel: contour map of inelastic neutron scattering intensity as a function of $E$ and $K,H$ integrated from 0.2 to 0.4. Upper panel: the cut along [0 1 0] with the energy transfer $E$ integrated from 3 to 6 meV (black) and from −0.5 to 0.5 meV (red), respectively. $H$ is integrated from 0.2 to 0.4. Note that the intensities of these two curves are scaled. Data were measured on $\mathrm{S}{\mathrm{r}}_2\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{F}{\mathrm{e}}_x{\mathrm{O}}_4$ $\left(x=0.03\right)$.

Figure 4

Electronic structure for a $3\times 3\times 1$ supercell of $\mathrm{S}{\mathrm{r}}_2\mathrm{Ru}{\mathrm{O}}_4$ containing one Fe substitution. (a) Density of states and projections, showing majority spin as positive and minority spin as negative, implying that the Fe majority $d$ bands are filled corresponding to $\mathrm{F}{\mathrm{e}}^{3+}$. (b) Fat band plot of the band structure showing Ru character for the unsubstituted supercell (heavier symbols mean higher Ru character), in comparison with the Fe substituted cell, emphasized by heavier symbols. (c) Ru character from Ru neighboring Fe and (d) Ru not neighboring Fe.