Dilute magnetism and spin-orbital percolation effects in ${\mathrm{Sr}}_2$${\mathrm{Ir}}_{1-x}$${\mathrm{Rh}}_x$${\mathrm{O}}_4$

We have used a combination of resonant magnetic x-ray scattering and x-ray absorption spectroscopy to investigate the properties of the doped spin-orbital Mott insulator ${\mathrm{Sr}}_2$${\mathrm{Ir}}_{1-x}$${\mathrm{Rh}}_x$O${}_4$ ($0.07\le x\le 0.70$). We show that Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$ represents a unique model system for the study of dilute magnetism in the presence of strong spin-orbit coupling, and provide evidence of a doping-induced change in magnetic structure and a suppression of magnetic order at $x_c\sim 0.17$. We demonstrate that Rh-doping introduces Rh${}^{3+}$/Ir${}^{5+}$ ions which effectively hole-dope this material. We propose that the magnetic phase diagram for this material can be understood in terms of a novel spin-orbital percolation picture.

Figure 1

(a) Potential effects of Rh doping on the electronic band structure of Sr${}_2$IrO${}_4$. Isoelectronic substitution of Rh${}^{4+}$ for Ir${}^{4+}$ is expected to tune the strength of the SOC, while substitution of Rh${}^{3+}$ is expected to reduce SOC and effectively hole-dope the system. (b) X-ray absorption spectra collected at the Rh $L_3$ edge ($2p_{3/2}\to 4d$) for a series of Rh-based reference samples. The position of the white-line peak in Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$ is consistent with a Rh${}^{3+}$ oxidation state. (c) Doping dependence of Rh $L_3$-edge absorption spectra for Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$. The position of the white-line feature remains unchanged for $0.07\le x\le 0.70$. (d) X-ray absorption spectra collected at the Ir $L_3$ edge ($2p_{3/2}\to 5d$) for samples with $x=0$ and $x=0.42$. The positive chemical shift and the broadening of the white-line feature are consistent with a mixed population of Ir${}^{4+}$ and Ir${}^{5+}$ ions introduced by doping.

Figure 2

(a) Canted antiferromagnetic ground states of Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$. The AF-I spin configuration is observed for $x=0$, while the AF-II configuration is observed for $0.07\le x\le 0.15$. The net ferromagnetic moment in each Ir-O layer is denoted by a green arrow. (b) Observed magnetic Bragg peaks in Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$ for $x=0.07$ and $x=0.11$. (c) Theoretical modeling of the magnetic structure factor is consistent with a canted antiferromagnetic structure (AF-II) which has a magnetic easy axis in the $ab$ plane. (d) The azimuthal dependence of the (0,1,21) magnetic peak intensity confirms that the orientation of the moments is along the $a$ and $b$ axes. The data in panels (b)–(d) were collected at $T=7$ K and $E_i=11.217$ keV, using $\sigma$-$\pi$ polarization analysis.

Figure 3

Temperature dependence of the (0,1,21) magnetic Bragg peak measured at the Ir $L_3$ edge. The magnetic peak intensity is significantly reduced above $T_{N2}$, but remains finite up to $T_{N1}$ (as shown in the inset). Magnetic peak intensities from the $x=0.07$ and $x=0.11$ samples have been normalized with respect to each other, using the intensities of nearby structural Bragg peaks for reference. Data in this panel were collected at $E_i=11.217$ keV, using $\sigma$-$\pi$ polarization analysis.

Figure 4

(a) The magnetic phase diagram of Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$, as constructed from RMXS and previously reported magnetization results [9]. The disappearance of magnetic order at $x_c\sim 0.17$ can be understood in terms of a spin-orbital percolation picture. (b) If Ir${}^{4+}$ is substituted for Rh${}^{4+}$, then each dopant ion introduces one magnetic/orbital defect (replacing a $J_{\mathrm{eff}}=1/2$ Ir moment with a $S=1/2$ Rh moment). In this scenario, a doping of $x=0.21$ falls well below the spin-only percolation threshold of $x_p=0.407$. (c) Alternatively, if Ir${}^{4+}$ is substituted for Rh${}^{3+}$, then each dopant ion introduces two magnetic/orbital defects (one from the Rh${}^{3+}$ [$S=0$], and one from its Ir${}^{5+}$ [$J_{\mathrm{eff}}=0$] ionic counterpart). In this scenario, the same doping ($x=0.21$) is now sufficient to exceed the percolation threshold and destroy magnetic order. The discrepancy between $2x_c$ and $x_p$ reflects the importance of orbital percolation effects, which arise due to the strong SOC of this system.

Figure 5

Magnetic correlation lengths in Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$. (a) Reciprocal space scans through the (0,1,21) magnetic Bragg peak in Sr${}_2$Ir${}_{0.93}$Rh${}_{0.07}$O${}_4$ at temperatures below ($T=20$ K) and above ($T=90$, 105 K) the magnetic transition at $T_{N2}$. (b) Temperature dependence of the magnetic peak width along [0,0,L] for samples with $x=0.07$ and $x=0.11$. The FWHM in this panel represents the intrinsic peak width, determined from resolution-convoluted fits. The broadening of the magnetic peak widths above $T_{N2}$ indicates the presence of finite magnetic correlation lengths between $T_{N1}$ and $T_{N2}$. The correlation lengths within this phase range from 800 to 1000 Å.

Figure 6

Energy dependence of the (0,1,21) magnetic Bragg peak measured at the Ir $L_3$ ($E=11.215$ keV) and $L_2$ ($E=12.824$ keV) absorption edges. The large $L_3/L_2$ intensity ratio associated with the $J_{\mathrm{eff}}=1/2$ ground state remains unaffected by Rh concentrations up to $x=0.11$. All data presented in this figure were collected at $T=7$ K.

Figure 7

High-resolution x-ray diffraction measurements on Sr${}_2$Ir${}_{1-x}$Rh${}_x$O${}_4$. This figure presents a collection of longitudinal ($\theta$-2$\theta$) scans through the (0,0,24) structural Bragg peak and (1,2,21) superlattice Bragg peak for samples with $x=0$, 0.11, 0.15, 0.24, and 0.42. For illustrative purposes, scans through the (0,0,24) peak (2$\theta$ $\sim$ 61.8${}^{\circ }$) have been horizontally translated and centered. The (1,2,21) superlattice peak arises due to correlated rotations of the IrO${}_6$/RhO${}_6$ octahedra. The width of the superlattice peak is approximately equal to that of the Bragg peak for $0\le x\le 0.24$, indicating that the IrO${}_6$/RhO${}_6$ rotations are well correlated at low dopings. By $x=0.42$ the superlattice peak is considerably broader, indicating significant rotational disorder at higher dopings. All data presented in this figure were collected at $T=300$ K.