Figure 1

Ball-and-stick representation of the magnetic cores of (a) Mn${}_7$Na-11 and (b) Mn${}_7$Na-16, which are analogous to the disks Mn${}_7$-11 and Mn${}_7$-16, respectively (Mn${}^{\mathrm{II}}$: green, Mn${}^{\mathrm{III}}$: yellow, O: red, N: blue; C and H atoms are omitted). Additionally, the classical spin configuration in the respective $S=11$ and 16 ground states is depicted by green and red arrows. (c) Exchange-coupling constants used in the magnetic modeling.Reuse & Permissions

Figure 2

(a) Integrated INS spectra recorded on Mn${}_7$-11 at an incoming wavelength of $\lambda =5.0$ Å at the indicated temperatures. (b) $S(Q,\omega )$ plot of the 1.5-K data. The intensity is color coded from blue (low intensity) to red (high intensity). (c) Experimental $Q$ dependence of the INS intensity of peaks I, II, and III at $T=1.5$ K (solid symbols) and simulated curves (solid lines). In addition, the intensity as function of $Q$ at an energy of 0.75 meV is shown (open circles), which indicates the nonmagnetic INS contribution. The labels indicate observed peaks.Reuse & Permissions

Figure 3

Integrated INS spectra recorded on Mn${}_7$-16 at an incoming wavelength of (a) $\lambda =6.5$ Å and (b) 5.0 Å at the indicated temperatures. (c) Experimental $Q$ dependence of the INS intensity of peaks I, II, and III at $T=1.5$ K (solid symbols) and simulated curves (solid lines). A constant was added to the simulations (dashed lines) accounting for nonmagnetic scattering contributions. The $Q$ dependence for peak I was determined from the 6.5-Å data, and those of peaks II and III from the 5.0-Å data.Reuse & Permissions

Figure 4

(a) Comparison of simulated and experimental INS spectra on Mn${}_7$-11 ($\lambda =5.0$ Å). The dashed and dotted lines correspond to species 1 and 2, respectively. The solid line corresponds to a mixture of the two species in a ratio of 1:1.4. (b) Energy spectrum (in zero field and with anisotropy neglected) as a function of total spin $S$ for the two species. Red long bars correspond to species 1 and black short bars to species 2. The three experimental transitions are indicated by the arrows.Reuse & Permissions

Figure 5

Magnetic susceptibility, plotted as $\chi T$ vs $T$, for Mn${}_7$-11 (red open circles) and Mn${}_7$-16 (blue open squares). The solid lines represent the simulated curves; the dotted and dashed lines represent the two species introduced in the modeling for each compound (see text).Reuse & Permissions

Figure 6

(a) Comparison between simulation and background corrected INS spectrum of Mn${}_7$-16 ($\lambda =5.0$ Å, $T=1.5$ K). The dashed and dotted lines correspond to species 1 and 2, respectively. The solid line corresponds to a mixture of the two species in a ratio of 1:1. The inset shows the estimated background. (b) Energy spectrum (in zero field and with anisotropy neglected) as function of total spin $S$ for the two species. Red long bars correspond to species 1 and black short bars to species 2. The three experimental transitions are indicated by the arrows. The multiplets in the $S=15,16$ sectors are labeled by the irreducible representations of the $D_3$ symmetry group (for clarity, only the states of one species are labeled).Reuse & Permissions

Figure 7

$Q$ dependence of low-temperature INS transitions, normalized to the maximum for each transition. (a) Mn${}_7$-16. Transitions are labeled by the irreducible representation ($D_3$ symmetry group) of the involved excited state. (b) Homogeneous six-membered ferromagnetic Heisenberg ring with $a=3.31$ Å, the average Mn-Mn distance in the considered Mn${}_7$ disks. The magnetic form factor of the ions was set to $F\left(Q\right)=1$. Transitions are labeled by $q$. The delta-function-like peaks represent the INS intensities for the infinite chain at the excitation energies corresponding to $k=\pm q\pi /3$. (c) Six-membered ferromagnetic Heisenberg ring with alternating spins as in Mn${}_7$-11, but uniform exchange coupling. The ion positions of Mn${}_7$Na-11 were used in the simulation. Transitions are labeled by the irreducible representation ($D_3$ symmetry group) of the involved excited state. In all panels, the $Q$ dependence of a transition within the ground-state multiplet is also shown for comparison, which belongs to $A_1$ in panels (a) and (c) and $q=0$ in panel (b).Reuse & Permissions