Persistence of antiferromagnetic order upon La substitution in the $4d^4$ Mott insulator ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$

The chemical and magnetic structures of the series of compounds ${\mathrm{Ca}}_{2-x}{\mathrm{La}}_x{\mathrm{RuO}}_4$ $[x=0$, 0.05(1), 0.07(1), 0.12(1)] have been investigated using neutron diffraction and resonant elastic x-ray scattering. Upon La doping, the low-temperature S-$Pbca$ space group of the parent compound is retained in all insulating samples $[x\le 0.07(1\left)\right]$, but with significant changes to the atomic positions within the unit cell. These changes can be characterized in terms of the local ${\mathrm{RuO}}_6$ octahedral coordination: with increasing doping, the structure, crudely speaking, evolves from an orthorhombic unit cell with compressed octahedra to a quasitetragonal unit cell with elongated ones. The magnetic structure on the other hand, is found to be robust, with the basic $\mathbf{k}=(0,0,0)$, $\mathbf{b}$-axis antiferromagnetic order of the parent compound preserved below the critical La doping concentration of $x\approx 0.11$. The only effects of La doping on the magnetic structure are to suppress the A-centred mode, favoring the B mode instead, and to reduce the Néel temperature somewhat. Our results are discussed with reference to previous experimental reports on the effects of cation substitution on the $d^4$ Mott insulator ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$, as well as with regard to theoretical studies on the evolution of its electronic and magnetic structure. In particular, our results rule out the presence of a proposed ferromagnetic phase, and suggest that the structural effects associated with La substitution play an important role in the physics of the system.

Figure 1

(a) ${\mathrm{Ca}}_2{\mathrm{RuO}}_4$ crystal structure ($Pbca$ space group, No. 61) highlighting the ${\mathrm{RuO}}_6$ octahedra tilt and rotation discussed in the text. $r_z$ and $r_{x,y}$ correspond to the apical and in-plane Ru-O bond lengths, respectively. (b) Magnetic ordering of neighboring ${\mathrm{RuO}}_2$ layers for the A- and B-centred magnetic modes [19]. The black arrows represent the ${\mathrm{Ru}}^{4+}$ ordered moments, while the white horizontal arrows correspond to the direction of the net magnetization induced by the moment canting.

Figure 2

${\mathrm{Ca}}_{2-x}{\mathrm{La}}_x{\mathrm{RuO}}_4$ temperature-doping phase diagram. The filled squares represent the temperatures (from Ref. [27]) at which the transition between the high-temperature quasitetragonal metallic phase (L-$Pbca$) and the low-temperature orthorhombic one (S-$Pbca$) occurs. The small and large filled circles are the Néel temperatures taken from Ref. [27] and derived from our bulk magnetization measurements [30], respectively. The error bars reflect the uncertainty in the doping level measured by means of EDX.

Figure 3

Structural changes of ${\mathrm{Ca}}_{2-x}{\mathrm{La}}_x{\mathrm{RuO}}_4$ as a function of doping at $T=10$ K. (a) Phase diagram as a function of the ${\mathrm{RuO}}_6$ octahedra distortion $1-\frac{r_x+r_y}{2r_z}$ (with $r_{x,y}$ and $r_z$ in-plane and apical Ru-O bond length, respectively) and unit cell distortion $1-\frac{a}{b}$ ($a,b$ in-plane lattice parameters of the Pbca unit cell). The horizontal line separates the regions corresponding to octahedral compression ($1-\frac{r_x+r_y}{2r_z}<0$) and elongation ($1-\frac{r_x+r_y}{2r_z}>0$). (b) Ru-O-Ru bond angle (circles) and ${\mathrm{RuO}}_6$ octahedra tilt angle away from the $\mathbf{c}$ axis (squares) as a function of the La content. The horizontal error bars reflect the uncertainty in the doping level measured by means of EDX.

Figure 4

Ru $L_3$ and $L_2$ energy resonances of magnetic diffraction peaks at different temperatures across the Néel transition in the (a) undoped, (b) $x=0.05$ and (c) 0.07 sample. The filled symbols refer to the total scattered intensity corrected for self-absorption and normalized to the $L_3$ peak intensity for each sample. The solid lines represent a quadratic interpolation to the data points and are meant just as a guide to the eye. The data were measured at $\psi =0^{\circ }$ for $x=0$ and 0.05 at $T=100,120$ K, while the low-temperature $x=0.05$ and 0.07 data sets correspond to an average of the spectra collected in the range $\psi =0^{\circ }–{60}^{\circ }$ and at $\psi =0^{\circ }\text{and}{30}^{\circ }$, respectively [30]. The normalized XANES used for the self-absorption correction is also shown.

Figure 5

Temperature dependence of the (013) (dark blue circles) and (014) magnetic diffraction peaks in the undoped and $x=0.05$ (light blue squares) and $x=0.07$ (red triangles) samples, respectively. The data points correspond to the total diffracted intensity integrated over a rocking curve at $E=2.838$ keV and $\psi =0^{\circ }$ and normalized to the low-temperature value.

Figure 6

Polarization dependence of magnetic diffraction peaks in the (a) undoped, (b) $x=0.05$ and (c) 0.07 sample at $\mathrm{T}=7-8$ K. The filled symbols refer to the scattered intensity measured over a rocking scan in the $\sigma -{\pi }^{\prime }$ (blue circles) and $\sigma -{\sigma }^{\prime }$ (red squares) channels of the polarization analyser crystal normalized to the $\sigma -{\pi }^{\prime }$ peak intensity, while the solid lines represent a fit to Voigt profile. The data were collected at $E=2.838$ keV and $\psi ={110}^{\circ },{50}^{\circ }{30}^{\circ }$ for $x=0,0.05,0.07$, respectively.

Figure 7

Azimuthal dependence [azimuthal reference (010)] of the (013) and (014) magnetic diffraction peaks in the (a) undoped and (b) doped ($x=0.05,0.07$) samples at $T=7–8$ K, respectively. The filled symbols refer to the scattered intensity integrated over a rocking curve at $E=2.838$ keV corrected for the geometry-dependent self-absorption factor [30]. The solid lines represent the calculated azimuthal dependence (except for an arbitrary scale factor) assuming the C-AFM structure with $\mathbf{b}$-axis moments reported by Braden et al. [19]. The intensity is normalized to the calculated value at $\psi =0^{\circ }$.

Figure 8

Comparison between the (013) (blue circles) and (014) (red squares) Ru $L_3$ resonances in the (a) undoped and (b) $x=0.05$ sample. The filled symbols refer to the total scattered intensity at $T=7–8$ K corrected for self-absorption and normalized to the peak intensity of the dominant mode. The solid lines represent a quadratic interpolation to the data points and are meant just as a guide to the eye. The data were measured at $\psi =0^{\circ }$, apart from the (014) in the undoped sample, for which $\psi ={80}^{\circ }$.

Figure 9

Intensity maps of the (004) Bragg peak and (014) magnetic reflection ($T=8$ K, $\psi =0^{\circ }$) in the $x=0.05$ sample as a function of the incident x-ray beam position on the crystal (beam size $0.1\times 0.1{\mathrm{mm}}^2$). The color scale represents the integrated intensity over a rocking scan measured in each position normalized to the (004) peak value (the dark regions are off the sample).