Spin-orbit entangled $j=\frac{1}{2}$ moments in ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$: A frustrated fcc quantum magnet

We establish the double perovskite ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$ as a nearly ideal model system for $j=1/2$ moments, with resonant inelastic x-ray scattering indicating that the ideal $j=1/2$ state contributes by more than 99% to the ground-state wave function. The local $j=1/2$ moments form an fcc lattice and are found to order antiferromagnetically at $T_N=14\mathrm{K}$, more than an order of magnitude below the Curie-Weiss temperature. Model calculations show that the geometric frustration of the fcc Heisenberg antiferromagnet is further enhanced by a next-nearest neighbor exchange, and a significant size of the latter is indicated by ab initio theory. Our theoretical analysis shows that magnetic order is driven by a bond-directional Kitaev exchange and by local distortions via a strong magnetoelastic effect. Both, the suppression of frustration by Kitaev exchange and the strong magnetoelastic effect are typically not expected for $j=1/2$ compounds making ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$ a riveting example for the rich physics of spin-orbit entangled Mott insulators.

Figure 1

(a) Cubic double-perovskite structure as observed in x-ray diffraction. Small green (large blue) octahedra are centered around the ${\mathrm{Ir}}^{4+}$ (${\mathrm{Ce}}^{4+}$) sites. Light gray (red) spheres depict ${\mathrm{Ba}}^{2+}$ (${\mathrm{O}}^{2-}$) ions. Each Ir moment is coupled to 12 nearest neighbors [orange and black lines in (c)] and to six next-nearest neighbors [along the edges of the cube in (c)], enhancing the frustration. Our RIXS data reveal local distortions from cubic symmetry. Assuming that the distortion is tetragonal, as schematically illustrated in (b), we find a massive bond-dependent variation of the nearest-neighbor exchange constants between Ir moments as depicted in (c), where couplings indicated in orange and black have different strength, reducing the frustration.

Figure 2

Magnetic susceptibility of ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$, measured on an assembly of 20 single crystals with 21mg total mass in a field of 1T. The red curve denotes a Curie-Weiss fit which yields ${\chi }_0=1.2\times {10}^{-4}$ emu/mol, while the blue curve corresponds to a fit restricted to ${\chi }_0=0$. The upper inset shows the same data plotted as $1/(\chi -{\chi }_0)$. The lower inset displays the linear field dependence of the magnetization, using $T=20$ K as a representative example.

Figure 3

RIXS data of ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$. (a) RIXS peaks at 0.61 eV and 0.71 eV correspond to excitations to $j=3/2$ states which are split by a noncubic crystal field. Data at 300 K show a slightly enhanced peak width but the same splitting as at 10 K. (b)–(d) Dispersion along high-symmetry directions at 10 K. The dashed line denotes the peak energy at the $\mathrm{\Gamma }$ point, 0.61 eV. The largest dispersion is observed from $\mathrm{\Gamma }$ to $L$, i.e., along ($hhh$). All RIXS spectra were measured in the Brillouin zone around (0 0 10) to achieve a scattering angle $2\theta$ close to ${90}^{\circ }$ which suppresses the contribution of the elastic line at zero energy loss.

Figure 4

(a) Phase diagram for the $J_1-J_2-K$ model. We find ordered phases with ordering wave vectors (100) (red), $\left(\frac{1}{2}\frac{1}{2}\frac{1}{2}\right)$ (green), and $\left(1\frac{1}{2}0\right)$ (blue), an incommensurate spiral phase (yellow) whose ordering wave vector continuously varies within the phase, and a spin liquid regime (gray). The lines indicate the phase boundaries of the classical model for comparison. White and black circles mark high-degeneracy points of the classical model (see text), their corresponding sets of $\mathbf{q}$ vectors are shown in (b) and (c), respectively. The star indicates the parameter set obtained for ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$. (d) The frustration parameter $f=|{\mathrm{\Theta }}_{\mathrm{CW}}|/T_N$ shows the suppression of ordering tendencies caused by the interplay of geometric and exchange frustration. Gray: spin liquid regime.

Figure 5

Frustration parameter as a function of the tetragonal distortion ${\mathrm{\Delta }}_{\mathrm{CF}}$. Colors indicate different types of magnetic order, with respective structure factors, calculated using the pf-FRG scheme, shown to the right. The abbreviation ICS denotes the incommensurate spiral phase.

Figure 6

Results of single-crystal x-ray diffraction. Histogram of the intensities of peaks forbidden in $Fm\overline{3}m$ divided by their respective error bars. Left: $T$ = 100 K. Right: room temperature. Blue lines: Gaussian fits. Note that negative values of the intensities arise due to the subtraction of a small overall background. The data do not yield any significant evidence for reflections of a noncubic structure.

Figure 7

Optical conductivity of ${\mathrm{Ba}}_2{\mathrm{CeIrO}}_6$, showing the onset of excitations across the Mott gap.