Structural and magnetic properties in the quantum $S=\frac{1}{2}$ dimer system Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$ with site disorder

We report a comprehensive study of dc susceptibility, specific-heat, neutron-diffraction, and inelastic neutron-scattering measurements on polycrystalline Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$ samples, where $x=0$, 0.06, 0.15, and 0.53. A Jahn-Teller structure transition occurs for $x=0$, 0.06, and 0.15 samples, and the transition temperature is reduced upon vanadium substitution from 70(2) K at $x=0$ to 60(2) K at $x=0.06$ and 0.15. The structure becomes less distorted as $x$ increases, and such transition disappears at $x=0.53$. The observed magnetic excitation spectrum indicates that the singlet ground state remains unaltered and spin-gap energy $\Delta =1.3\left(1\right)$ meV is identical within the instrument resolution for all $x$. In addition, the dispersion bandwidth $W$ decreases with increase of $x$. At $x=0.53$, $W$ is reduced to 1.4(1) meV from 2.0(1) meV at $x=0$.

Figure 1

Room-temperature hexagonal structure of Ba${}_3$Cr${}_2$O${}_8$ in a unit cell showing (a) the bilayers stacking along the crystallographic $c$ axis and (b) the interaction network where $J_0$ is the dominant nearest-neighbor intradimer coupling, and $J_1$, $J_2$, and $J_4$ are second, third, and fourth nearest-neighbor interdimer couplings. Color coding is as follows: blue, Cr; green, Ba; red, O.

Figure 2

Direct current susceptibility $\chi =M/H$ as a function of temperature in polycrystalline samples Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$, where $x=0$, 0.06, 0.15, and 0.53. The dashed lines are fits to Eq. (1) as described in the text. Inset: enlarged low-temperature part of susceptibility after background subtraction. The solid lines are fits to Eq. (3) as described in the text.

Figure 3

Neutron-diffraction pattern for Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$ ($x=0$, 0.06, 0.15, and 0.53) with Rietveld refinement at (a)–(d) $T=200$ K and (e)–(h) $T=4$ K, respectively. Left insets in (a), (e): the ${\left({\mathrm{CrO}}_4\right)}^{3-}$ tetrahedra in each phase. Right insets in (e)–(g): temperature dependence of the background subtracted intensity of a superlattice peak, which is indexed in terms of the hexagonal lattice parameters by convention. The red arrow indicates the position of the transition temperature.

Figure 4

Zero-field specific-heat measurements on Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$ at $x=0$, 0.06, and 0.53, where the data at $x=0$ are shifted up for 0.1 unit for the purpose of clarity.

Figure 5

Raw data of inelastic neutron-scattering intensity for Ba${}_3$Cr${}_2$O${}_8$ at (a) $T=1.5$ K and (b) $T=60$ K. (c) Inelastic magnetic neutron-scattering intensity after background subtraction from Ba${}_3$Cr${}_2$O${}_8$ at $T=1.5$ K. (d) A model in the single-mode approximation after being convolved with the instrumental resolution function as described in the text.

Figure 6

Inelastic magnetic neutron-scattering intensity measured at $T=1.5$ K after background subtraction from Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$ at (a) $x=0.06$, (b) $x=0.15$, and (c) $x=0.53$. The intensity at each $x$ is scaled by the number of Cr moles per chemical formula.

Figure 7

(a) Energy dependence of the magnetic scattering intensity for Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$ averaged over wave vectors from 0.5 to 1.5 ${\AA }^{-1}$ at $x=0$, 0.06, 0.15, and 0.53. Solid symbols are data. Black arrow indicates the spin-gap energy, and colored arrows indicate the upper boundary of the magnetic excitation spectrum for different $x$. (b) Wave-vector dependence of the magnetic scattering intensity for Ba${}_3$(Cr${}_{1-x}$V${}_x$)${}_2$O${}_8$ averaged over energy from 1.3 to 3.0 meV at $x=0$, 0.15, and 0.53. Solid lines are the fit to the first sum rule for the powder sample as described in the text. The inten-sity at each $x$ is scaled by the number of Cr moles in the sample.