Figure 1

Measured inelastic neutron scattering data for powder HgCr${}_2$O${}_4$. (a),(b) Scattering intensity distributions in $(Q,E)$ space above and below $T_N$, respectively. The vertical tone indicates the scattering intensity in arbitrary units. (c) $Q$ dependence of $E$-integrated intensity. The integration ranges are given in each panel. The solid lines are a guide to the eye. (d) $E$ dependence of intensity integrated from $Q=0.5$ to 2.0 Å${}^{-1}$ measured at several temperatures. In the data for 10, 7, and 5 K, the vertical origins are shifted to the height shown by horizontal solid lines on the right side, and the solid curves are a guide to the eye. The solid curve for the 3 K data is obtained by a multi-Gaussian fitting, indicated by the dotted and broken lines. The errors are smaller than the symbols used.Reuse & Permissions

Figure 2

Dynamical structure modeling of spin-excitation modes in HgCr${}_2$O${}_4$. (a) Experimental $Q$ dependence (symbols) and calculated $Q$ dependence (curves). The experimental data are obtained by subtracting a low-$Q$ background component fitted with a Lorentzian from the raw data [top panel in Fig. 1c]. The latter curves are obtained from a kagome-star dodecamer model consisting of hexa-I and hexa-II (b), and show the common results calculated independently using Eqs. (1) and (4) (see the text). The broken and dotted curves broaden approximately with reciprocals of the hexa-I and hexa-II spatial sizes around the main peaks at $Q\simeq 1.5$ and 0.9 Å${}^{-1}$, respectively. (b) Kagome-star dodecamer model. The subunits hexa-I and hexa-II are depicted by bold lines. The closed and open circles indicate up and down spins, respectively, fluctuating dynamically in arbitrary directions. Exchange interactions $J_1$ and $J_2$ are also defined. (c) Energy schemes of hexa-I and hexa-II obtained by exact diagonalization of Eqs. (2) and (3). The hexa-I part in HgCr${}_2$O${}_4$ is converted into hexa-I in the other chromates by tuning the energy scale.[20]Reuse & Permissions