Singlet Orbital Ordering in Bilayer ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$

We perform an extensive study of ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$, the $n=2$ member of the Ruddlesden-Popper ${\mathrm{Sr}}_{n+1}{\mathrm{Cr}}_n{\mathrm{O}}_{3n+1}$ system. An antiferromagnetic ordering is clearly visible in the magnetization and the specific heat, which yields a huge transition entropy, $R\ln (6)$. By neutron diffraction as a function of temperature we have determined the antiferromagnetic structure that coincides with the one obtained from density functional theory calculations. It is accompanied by anomalous asymmetric distortions of the ${\mathrm{CrO}}_6$ octahedra. Strong coupling and Lanczos calculations on a derived Kugel-Khomskii Hamiltonian yield a simultaneous orbital and moment ordering. Our results favor an exotic ordered phase of orbital singlets not originated by frustration.

Figure 1

Specific heat of ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$ (red line) and measured specific heat of ${\mathrm{Sr}}_3{\mathrm{Ti}}_2{\mathrm{O}}_7$ baseline (blue squares) (see Supplemental Material [13]). Left inset: low temperature specific heat showing that $\gamma =0$, i.e. no free carriers at $T=0$, confirming the nonmetallic electrical resistivity behavior (see Supplemental Material [13]). Right inset: excess specific heat (red line) and entropy of transition (blue line) as a function of temperature.

Figure 2

Upper panel: variation of the lattice parameters as a function of temperature of ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$ (orange circles: XRD; green squares: neutrons). Upper inset: variation of the Cr-apical O distances as a function of temperature. Middle inset: schematic deformation of the structure, with a clear separation of the twin ${\mathrm{CrO}}_2$ layers. Lower panel: neutron diffraction spectra for ${\mathrm{Sr}}_3{\mathrm{Cr}}_2{\mathrm{O}}_7$ at different temperatures, showing the appearing of the numbered magnetic peaks at 300 K. The calculated magnetic structure at 2 K is shown in the Supplemental Material [13] and coincides with the second one in Fig. 3.

Figure 3

Upper panel: band structure and DOS for the nonmagnetic structure. Lower panel: energies for the different magnetic configurations we have considered. Different colors, different moment orientations. Values are referred to the completely ferromagnetic solution.

Figure 4

(a) Scheme of the dominant fourth-order perturbation term in the $z$ direction. The arrows indicate the spin of the occupied Cr orbitals after the first hop from an O atom (middle) to a Cr atom (right). (b) Scheme of the contribution of $xy$ orbitals to the Heisenberg interaction in the $xy$ plane. (c)–(e): Three different phases with a spin structure compatible (arrows) observed experimentally: antiferromagnetic in the planes and ferromagnetic between the layers. The color of the arrow distinguishes the orbital. The orbital pseudospins (c) are paired as singlets (gray ovals) along the outplane bonds, (d) have the same antiferro-orbital correlations in and out of the planes, and (e) are ferro-orbital in the planes and antiferro-orbital out of the planes. (f)–(h): evolution of the energy for each of these phases as a function of the parameter $\delta$ that describes the crystal field.