Evolution of competing magnetic order in the $J_{\mathrm{eff}}=1/2$ insulating state of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$

We investigate the magnetic properties of the series ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$ with neutron, resonant x-ray, and magnetization measurements. The results indicate an evolution and coexistence of magnetic structures via a spin-flop transition from $ab$-plane to $c$-axis collinear order as the $5d {\mathrm{Ir}}^{4+}$ ions are replaced with an increasing concentration of $4d {\mathrm{Ru}}^{4+}$ ions. The magnetic structures within the ordered regime of the phase diagram ($x<0.3$) are reported. Despite the changes in magnetic structure no alteration of the $J_{\mathrm{eff}}=1/2$ ground state is observed. The behavior of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$ is consistent with electronic phase separation and diverges from a standard scenario of hole doping. The role of lattice alterations with doping on the magnetic and insulating behavior is considered. The results presented here provide insight into the magnetic insulating states in strong spin-orbit coupled materials and the role perturbations play in altering the behavior.

Figure 1

XANES measurements at the Ir $L_3$ edge for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$, with $x=0$, 0.05, and 0.2, and a ${\mathrm{IrO}}_2$ standard. The white line absorption intensity and the derivative are both shown for each sample. The same absorption energy of 11.2175 keV is observed for all the samples measured indicating a valence of ${\mathrm{Ir}}^{4+}$.

Figure 2

Magnetization measurements on single crystals in the series ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$ for $x=0.05$, 0.1, 0.2, and 0.3. Field-cooled (FC) and zero-field-cooled (ZFC) results in an applied field of 100 Oe are shown. The ZFC curve is always lower than the FC for all concentrations measured.

Figure 3

(a) RMXS measurements on single crystals of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$ with $x=0.05$, 0.1, and 0.2. (b) Comparison of the intensity of $(1,0,2n+1)$ and $(1,0,2n)$ magnetic reflections in ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ measured with both neutrons and RMXS. The neutron and x-ray measurements involved different crystals from the same batch. The intensities have been normalized to their respective backgrounds intensities and scaled so all reflections are in a single plot. (c)–(l) Neutron-scattering rocking scan measurements on a single crystal of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ for several reflections. Scattering is observed at $(1,0,L)$ for both $L=\text{odd}$ and $L=\text{even}$.

Figure 4

By performing polarization analysis of (a) and (b) x-ray energy scans and (c) and (d) neutron rocking scans on ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ single crystals, the spin direction associated with the magnetic reflections is determined. Both measurements were performed at 5 K.

Figure 5

(a) Single-crystal synchrotron x-ray-diffraction measurements of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ indicated no splitting of diffraction peaks, consistent with a homogeneous sample. (b) Neutron diffraction additionally found no evidence for structural phase separation. (c)–(j) High-resolution $Z$-STEM analysis of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$ samples. (c),(d) $Z$-contrast images of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ at different magnifications with the beam parallel to $\left[201\right]$. Inset in (d) is a schematic model of the crystal with the Ir columns in green, the Sr columns in yellow, and the O columns (not imaged) in cyan. (e),(f) $Z$-contrast images of ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ with the same zone axis and the same magnification as in (c) and (d). (g) Line profile along the cyan segments in (c) and (e), showing the intensity (proportional to $Z^2$) of the Ir columns in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ and ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ samples. (h) Uniform thickness map and (i) Ir map of the region indicated with a green rectangle in (f). (j) Electron energy-loss spectrum from the region within the green rectangle in (f) showing the Ir edges used to generate the Ir map by plotting their combined integrated intensity. The red curve is a power-law background fitting function and the green curve shows the background-removed Ir edges.

Figure 6

(a) Experimental neutron-scattering intensities for the magnetic reflections in ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ are compared with calculated magnetic structures for the case of spins in the $ab$ plane and $c$ axis. (b) Corresponding magnetic structures within the nuclear unit cell.

Figure 7

(a) Intensity dependence of the (1 0 odd) magnetic reflection measured with neutrons at $\left(101\right)$ and RMXS at $(1,0,21)$ for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$. The RMXS results are fit to a power law and give a transition temperature at $T_{\mathrm{N}}=76.3\left(6\right)$. (b) Experimental intensities for magnetic reflections compared to the calculated intensities for $c$-axis aligned spins. (c) The magnetic structure for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$ with spins aligned along the $c$ axis.

Figure 8

(a),(b) Energy scans through the iridium $L_2$ and $L_3$ edges using RMXS on ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.9}{\mathrm{Ru}}_{0.1}{\mathrm{O}}_4$ and ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$ single crystals within the magnetically ordered phase ($T=5$ K). The red solid lines correspond to RMXS with polarization of $\sigma -\pi$. The grey line, a fluorescence measurement, is performed to indicate the energy of the resonant $L$ edges only and has been scaled to fit on the plot. (c),(d) XMCD and x-ray-absorption energy scans in a $\pm 3$ T field at 1.8 K for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.95}{\mathrm{Ru}}_{0.05}{\mathrm{O}}_4$ and ${\mathrm{Sr}}_2{\mathrm{Ir}}_{0.8}{\mathrm{Ru}}_{0.2}{\mathrm{O}}_4$. The variation of the XMCD signal above 12.84 keV (dotted line) is an artifact of the optics rather than from any XMCD signal from the sample.

Figure 9

Single-crystal neutron diffraction on ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$ for $x=0$, 0.05, 0.1, and 0.2 at 50 K. (a) The octahedral rotation in the $ab$ plane ($\alpha$). (b) Tetragonal distortion of the octahedra due to the difference between Ir-O bonds in the $ab$ plane and along the $c$ axis (${\mathrm{\Delta }}_{\mathrm{Ir}-\mathrm{O}}$).

Figure 10

Phase diagram for ${\mathrm{Sr}}_2{\mathrm{Ir}}_{1-x}{\mathrm{Ru}}_x{\mathrm{O}}_4$. The data points correspond to transition temperatures from single-crystal neutron diffraction and RMXS. M1 denotes $ab$-plane magnetic ordering and M2 indicates $c$-axis ordering. The insulating regions are based on results presented in Ref. [15].