Weakly Coupled $s=1/2$ Quantum Spin Singlets in ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathbf{O}}_8$

Using single crystal inelastic neutron scattering with and without the application of an external magnetic field and powder neutron diffraction, we have characterized magnetic interactions in ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$. Even without a field, we found that there exist three singlet-to-triplet excitation modes in the ($h$, $h$, $l$) scattering plane. Our complete analysis shows that the three modes are due to spatially anisotropic interdimer interactions that are induced by lattice distortions of the tetrahedron of oxygens surrounding the Jahn-Teller active ${\mathrm{Cr}}^{5+}(3d^1)$. The strong intradimer coupling of $J_0=2.38(2)\mathrm{meV}$ and weak interdimer interactions ($|J_{\mathrm{inter}}|\le 0.52(2)\mathrm{meV}$) makes ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$ a good model system for weakly coupled $s=1/2$ quantum spin dimers.

Figure 1

Schematic diagram of the crystal structure of ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$ that shows (a) the triangular network of ${\mathrm{Cr}}^{5+}$ dimers in the $ab$ plane and their relative stacking along the $c$ axis in an $ABCABC$ arrangement. (b) Two oriented ${\mathrm{Cr}}^{5+}$ tetrahedra bound with four oxygen (${\mathrm{O}}^{2-}$) ions to afford the ${\mathrm{Cr}}^{5+}$ dimer arrangement with magnetic exchange, $J_0$, which is at a distance of $d_0=3.97\AA$. (c) The $ab$-plane projection of the ${\mathrm{Cr}}^{5+}$ ions, showing the alternative exchange pathways.

Figure 2

Contour maps of dispersion relations along (a) ($0,0,l$), (b) ($h$, $h$, 3), and (c) ($h$, $h$, $3h$) directions. The data were taken by performing constant $\mathit{Q}$ scans of ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$ single crystals at 1.7 K. The point symbols represent the peak positions obtained by fitting the data with simple Gaussians. (d), (e) Calculated dispersions and intensities based on a model of spatially anisotropic interdimer interactions, which is described in the text.

Figure 3

Constant $\mathit{Q}$ scan with several different magnetic fields ($H$) (a) at $\mathit{Q}=(0,0,4.5)$ and (b) at $\mathit{Q}=(0.5,0.5,3)$ scan, and $H$ dependence of the peak positions in $\hslash \omega$ (c) at $\mathit{Q}=(0,0,4.5)$ and (d) at $\mathit{Q}=(0.5,0.5,3)$. The lines represent the Zeeman splitting.

Figure 4

Elastic neutron scattering data obtained from a single crystal of ${\mathrm{Ba}}_3{\mathrm{Cr}}_2{\mathrm{O}}_8$, (a) as a function of the wave vector at 140 K (blue, or dark, circles) and 6 K (red, or light, circles) and (b) as a function of temperature that shows the (1, 0, 2.5) superlattice peak appears below 70 K. (c), (d) Neutron diffraction data obtained from a powder sample at two different temperatures, 100 K and 4 K. The line in (a) is fit to a Gaussian, while the lines in (c) and (d) are the results of the crystal refinements using Rietveld analysis based on $R\overline{3}m$ and $C2/c$ symmetry, respectively. The nuclear Bragg peaks are indexed in terms of the hexagonal lattice parameters for convenience. Insets in (c) and (d) show the local oxygen environment in each phase.