High-pressure synthesis of ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$, a rhodate analog of the layered perovskite Sr-ruthenate

A layered perovskite-type oxide ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ was synthesized by a high-pressure technique with the support of convex-hull calculations. The crystal and electronic structure were studied by both experimental and computational tools. Structural refinements for powder x-ray diffraction data showed that ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ crystallizes in a ${\mathrm{K}}_2{\mathrm{NiF}}_4$-type structure, isostructural to ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and ${\mathrm{Ba}}_2{\mathrm{IrO}}_4$. Magnetic, resistivity, and specific-heat measurements for polycrystalline samples of ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ indicate that the system can be characterized as a correlated metal. Despite the close similarity to its ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ counterpart in the electronic specific-heat coefficient and the Wilson ratio, ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ shows no signature of superconductivity down to 0.16 K. Whereas the Fermi surface topology has reminiscent pieces of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$, an electronlike $e_{\mathrm{g}}-\left(d_{x^2-y^2}\right)$ band descends below the Fermi level, making this compound unique also as a metallic counterpart of the spin-orbit coupled Mott insulator ${\mathrm{Ba}}_2{\mathrm{IrO}}_4$.

Figure 1

Bottom panel: convex hull of enthalpy formation calculated for stoichiometries between BaO and ${\mathrm{RhO}}_2$ at selected pressures up to 20 GPa. For readability, the abscissa in the top shows composition range and in the bottom it shows composition ratio. Solid-black points represent stable compositions, and empty colored circles represent unstable ones. The crystal structure of stable and unstable phases is shown in the top and presented as the Ruddlesden-Popper sequence (${\mathrm{Ba}}_{n+1}{\mathrm{Rh}}_n{\mathrm{O}}_{3n+1}$). Lower formation enthalpy means the structure and composition are thermodynamically accessible to synthesis. For each pressure, the line of stability is indicated. We can rule out the synthesis of $n=1$ and 2 at the studied pressures. The prediction that the 2-1-4 phase is stabilized upon pressure is confirmed in our experiments.

Figure 2

(a) Crystal structure of ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ and (b) a schematic representation of the local structure with bond lengths around the Rh and Ba atoms. (c) Observed (red crosses), calculated (green line), and differential (blue line) synchrotron x-ray diffraction patterns. The green tick marks indicate the calculated peak positions.

Figure 3

The temperature dependence of (a) electrical resistivity and (b) magnetic susceptibility for ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$. The green dashed line shows the fitting of the experimental data with $\rho ={\rho }_0+A{T}^{\alpha }$ and $\chi ={\chi }_0+C/(T+\theta )$ below 50 K. The inset of (a) shows no superconducting signals down to 0.16 K.

Figure 4

(a) Temperature dependence of the specific heat for ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ (blue dots), and the reported specific heat of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ (red dots) and ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$ (green dots). (b) $T^2$ dependence of specific heat divided by temperature for ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ (blue dots). The blue dashed line shows the fitting of the experimental data with $T/C=\gamma +\beta T^2$ between 2.0 and 7.5 K.

Figure 5

Full-potential DFT-LSDA band structure including spin-orbit coupling along selected high-symmetry points at zero pressure. For comparison with the band structure of ${\mathrm{Sr}}_2{\mathrm{RhO}}_4$, see Fig. S6 [25].

Figure 6

DFT-LSDA Fermi surfaces including spin-orbit coupling for ${\mathrm{Ba}}_2{\mathrm{RhO}}_4$ and ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$. Two-dimensional projections are along the $k_z$ vector. The first Brillouin zone and selected high-symmetry points for the structure with $I4/mmm$ are shown.