Figure 1

(Color online) Crystal structure of ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$. Oxygen atoms are not shown for clarity. Gray dashed lines indicate chemical unit cells. (a) Polyhedral representation of structure. Light green and dark green polyhedra around Ba sites represent the two types of Ba coordination that alternate along the $c$ axis, 12-fold and 10-fold coordination, respectively. Red tetrahedra illustrate the ${\mathrm{Mn}}^{5+}$ coordination. (b) Simplified structure figure illustrating dominant exchange connectivity in ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ within and between the $S=1$ dimers. $J_1$ and $J_2$ exchanges correspond to distances of 4.569 and $5.711\mathrm{\AA }$, respectively.Reuse & Permissions

Figure 2

(Color online) Temperature dependent diffraction for ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ measured in the $\lambda =2.9\mathrm{\AA }$ configuration. Data are integrated between $-0.1$ and $0.1\mathrm{meV}$ energy transfer. Data have not been background subtracted or corrected for absorption. Higher temperature data are offset vertically from the $T=1.4\mathrm{K}$ data for presentation. Several characteristic Bragg peaks are indexed in the figure.Reuse & Permissions

Figure 3

(Color online) Temperature dependent lattice parameters of ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$. (a) $c$-axis lattice constant versus temperature. (b) $a$-axis lattice constant versus temperature. (c) $c∕a$ as a function of temperature. Solid points from Ref. 18 for $T=295\mathrm{K}$ are shown for comparison. Lattice constants were obtained from the weighted mean peak position of the (003), (006), (009), and (110) Bragg peaks for $\lambda =2.9$ and $4.4\mathrm{\AA }$. Error bars are the error in the mean. Solid lines in (a) and (b) are linear fits described in the text. The solid line in (c) is calculated based on the linear fits for the $a$- and $c$-axis lattice constants.Reuse & Permissions

Figure 4

(Color online) Measured and calculated INS intensity for ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ at $T=1.4\mathrm{K}$. (a) and (b) are data measured for incident wavelengths of $\lambda =4.4$ and $2.9\mathrm{\AA }$, respectively. (c) and (d) are the calculated scattering intensities corresponding to the coupled $S=1$ dimer model described in the text. (e) and (f) are the energy dependent integrated scattering intensity of the data and model calculations shown in (a)–(d) for wave vectors $0.65<Q<2{\mathrm{\AA }}^{-1}$ and $0.75<Q<3.25{\mathrm{\AA }}^{-1}$ for $\lambda =4.4$ and $2.9\mathrm{\AA }$, respectively. Model line shapes in (e) and (f) are fitted to the data including an elastic Gaussian line shape and a constant background as discussed in the text.Reuse & Permissions

Figure 5

(Color online) $T=1.4\mathrm{K}$ singlet-triplet single crystal dispersion relation determined for ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ based on powder average analysis. (a) Contour figure of dispersion in the hexagonal (HK0) plane. (b) Dispersion as a function of rlu along other primary directions of the hexagonal structure. Dispersion along the $\left(00L\right)$ and $\left(10L\right)$ directions is plotted using the top axis.Reuse & Permissions

Figure 6

(Color online) First moment of scattering intensity integrated between $\hslash \omega =0.75$ and $3\mathrm{meV}$ for the $T=1.4\mathrm{K}$ $\lambda =4.4$ and $2.9\mathrm{\AA }$ measurements shown in Figs. 4a, 4b. Solid lines correspond to fits described in the text with the fitted $\mid \mathbf{d}\mid$ value of $d=4.073\left(7\right)\mathrm{\AA }$.Reuse & Permissions

Figure 7

(Color online) Energy dependent scattering intensity for $0.9<Q<1.0{\mathrm{\AA }}^{-1}$ for a series of temperatures as measured in the $\lambda =2.9\mathrm{\AA }$ configuration. Data for different temperatures are vertically offset. Solid lines are fits to the Lorentzian functions described convolved with the energy dependent resolution of the instrument. The inset illustrates scattering intensity of the $T=12\mathrm{K}$ measurement plotted on a logarithmic intensity scale. The dotted red line corresponds to the spectral contribution of the lower energy mode, and the dashed blue line corresponds to the higher energy mode.Reuse & Permissions

Figure 8

(Color online) Temperature dependent integrated intensity and characteristic energy determined from fits to data shown in Fig. 7. (a) Total and neutron energy gain and loss portions of the integrated scattering intensity for both modes. The solid black line is a fit of the temperature dependent total scattering intensity of the isolated antiferromagnetic $S=1$ dimer including both singlet-triplet and thermally activated triplet-quintet excitations. The dashed line only includes singlet-triplet excitations. Solid blue and green curves are calculated from the singlet-triplet and triplet-quintet fitted scattering intensity. (b) Mode energy as a function of temperature. The $T=1.4\mathrm{K}$ spin-gap value determined from fitted exchange parameters is shown as a single red diamond. The solid line is a calculation of the RPA model temperature dependent spin gap using the determined values of exchange constants.Reuse & Permissions