Dzyaloshinsky-Moriya interaction and long lifetime of the spin state in the Cu${}_3$ triangular spin cluster by inelastic neutron scattering measurements

Inelastic neutron scattering (INS) experiments have been performed on the Cu${}_3$ triangular molecular nanomagnet using powder samples. In the medium resolution INS experiment, two peaks were observed at $\hslash \omega =0.5$ and 0.6 meV, whereas an additional excitation peak was detected at very low energy $\hslash \omega =0.1$ meV in the higher resolution experiment. A model Hamiltonian and its optimum interaction parameters were determined from the observed peak position, width, and intensity. A key ingredient of the model Hamiltonian is Dzyaloshinsky-Moriya interactions as suggested in the earlier reports, which is now directly evidenced by the observation of the 0.1-meV peak, corresponding indeed to a splitting of ground-state quartet into two doublets. Temperature dependences of integrated intensity of the 0.5- and 0.6-meV peaks are well reproduced by the Boltzmann distribution function up to 10 K, above which a small deviation was detected. Nevertheless, the inelastic peaks were visible even at very high temperatures as 50 K, indicating extraordinary weak coupling between spins and lattice vibrations (or any other perturbations) compared to the other known molecular nanomagnets.

Figure 1

(a) A structure of the Cu${}_3$ spin cluster, where each circle represents the Cu${}^{2+}$ ion. The distances between Cu${}^{2+}$ ions $d_{1,2}$, $d_{2,3}$, and $d_{3,1}$ are written in the text. (b) Schematic view of the energy levels of the model Hamiltonian obtained by the optimum parameters given in Eq. (2). $\hslash {\omega }_0$ represents the splitting between the two low-lying $S_{\mathrm{total}}=1/2$ spin doublets by the DM interaction, whereas $\hslash {\omega }_1$ and $\hslash {\omega }_2$ correspond to the inelastic neutron scattering (INS) peaks at 0.5 and 0.6 meV in the INS spectra measured at HER as shown in Fig. 2.

Figure 2

The INS spectra of $Q=0.95$ Å${}^{-1}$ at (a) $T=0.71$, (b) 1.40, (c) 2.62, (d) 4.03, (e) 6.05, (f) 10.17, (g) 30.78, and (h) 51.55 K measured at HER and the fitting results (details are written in text). The error bars here and in all subsequent figures represent one standard deviation. The background subtracted INS spectra measured at HER and the calculated intensities using Eq. (2) in Ref.18 of $Q=0.95$ Å${}^{-1}$ at (i) $T=0.71$, (j) 1.40, (k) 2.62, (l) 4.03, (m) 6.05, (n) 10.17, (o) 30.78, and (p) 51.55 K are illustrated.

Figure 3

The integrated and expected intensities of the peaks at (a) $\hslash \omega =0.5$ and (b) 0.6 meV, and the widths of the INS peaks and the resolution-limited widths at (c) $\hslash \omega =0.5$ and (d) 0.6 meV.

Figure 4

(Color online) The INS spectra of $0.1\le Q\le 1.3$ Å${}^{-1}$ at $T=1.5$ and 30 K measured at DCS using deuterated powder Cu${}_3$. We use a log scale for the vertical axis. Both spectra are fitted by a similar procedure as in Figs. 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h.

Figure 5

The experimental and calculated $1/\chi$ in $B=0.1$ T.