Tuning the orbital-lattice fluctuations in the mixed spin-dimer system ${\mathrm{Ba}}_{3-\mathrm{x}}{\mathrm{Sr}}_{\mathrm{x}}{\mathrm{Cr}}_2{\mathrm{O}}_8$

In $A_3{\mathrm{Cr}}_2{\mathrm{O}}_8$, where $A$ = Sr or Ba, the ${\mathrm{Cr}}^{5+}$ ions surrounded by oxygen ions in a tetrahedral coordination are Jahn-Teller active. The Jahn-Teller distortion leads to a structural transition and a related emergence of three twinned monoclinic domains below the structural phase transition. This transition is highly dynamic over an extended temperature range for $A$ = Sr. We have investigated mixed compounds ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Cr}}_2{\mathrm{O}}_8$ with $x=2.9$ and $x=2.8$ by means of x-ray and neutron diffraction, Raman scattering, and calorimetry. Based on the obtained evolution of the phonon frequencies, we find a distinct suppression of the orbital-lattice fluctuation regime with increasing Ba content. This stands in contrast to the linear behavior exhibited by unit cell volumes, atomic positions, and intradimer spin-spin exchange interactions.

Figure 1

(a) Hexagonal and (b) monoclinic unit cells in $A_3{\mathrm{Cr}}_2{\mathrm{O}}_8$. ${\mathrm{Cr}}^{5+}$ ions, represented in blue, are located in oxygen tetrahedra, ${\mathrm{O}}^{2-}$ ions are represented by red spheres, and $A$ = Sr/Ba by green spheres. Dimer bonds are represented in orange.

Figure 2

(a) Two ${\mathrm{CrO}}_4$ tetrahedra forming a dimer unit in the hexagonal and the monoclinic phases (top). Corresponding occupation of electronic levels in each phase (bottom). (b) Heat capacity-temperature dependences for both samples: $x=2.9$ (black curve) and $x=2.8$ (red curve) showing $\lambda$-like Jahn-Teller transitions at 260 K and 242 K, respectively.

Figure 3

(a) Color contour plot of the temperature dependence of the x-ray diffraction pattern for $x=2.9$ powder. The centered reflection (3, 0, 0)${}_h$ splits into $({-6,0,2)}_m$ and $({-3,3,1)}_m$ at lower temperatures. (b) Temperature dependence of the integrated intensity of (1,1,${-3)}_h$, (1,1,${-1.5)}_h$, and (0, 0, 6)${}_h$ reflections of a $x=2.9$ single crystal. Dotted lines show $T_{JT}=260$ K and $T^{*}=150$ K. (c) The unit cell volume and monoclinic angle $\beta$ in the monoclinic symmetry $C2/c$ as a function of temperature (red and blue data points, respectively). The lines are guides to the eye.

Figure 4

(a) Raman spectra collected at $T=320$ K (red curve) and at 10 K (blue curve) for $x=2.9$. Color plot spectra in the temperature range from 5 K to 340 K for (b) $x=2.9$ and (c) $x=2.8$. Temperature evolution of the phonon frequencies for (d) $x=2.9$ and (e) $x=2.8$. The red line is a fit of the mode around $70{\mathrm{cm}}^{-1}$.

Figure 5

(a) Scattering intensity of Raman spectra collected at $T=5$ K for $x=2.9$ (blue curve) and $x=2.8$ (red curve). Puncture green box shows the range of Raman shift from 110 ${\mathrm{cm}}^{-1}$ to 150 ${\mathrm{cm}}^{-1}$. (b) Temperature evolution of the entropy $S$ calculated from the heat capacity data [Fig. 2] for $x=2.9$ (blue curve) and $x=2.8$ (red curve). The green puncture line is the entropy limit $S=R$ log4.

Figure 6

Temperature range of the fluctuation regime $|T_{JT}\text{−}{T}^{*}|$ (filled black spheres) and intradimer interaction $J_0$ (open red squares, Ref. [19]) versus Sr content $x$ in ${\mathrm{Ba}}_{3-x}{\mathrm{Sr}}_x{\mathrm{Cr}}_2{\mathrm{O}}_8$. Lines in the respective color indicate a linear dependence of these quantities on the Sr content $x$ for comparison.