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Dzyaloshinsky-Moriya interaction and long life time 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 spectrum measured, there are two peaks at $\hbarω=0.5$ and 0.6 meV. Comparing the observed $Q$ dependences of these peaks with calculations, these two INS peaks originate from the Cu$_3$ cluster. From the observed peak position, width, and intensity, we have determined the optimum parameters of the spin Hamiltonian consisted of the antiferromagnetic exchange and the Dzyaloshinsky-Moriya interactions, which can also reproduce the magnetic susceptibility measurement. In addition, we have directly observed that the ground state quartet is split into two doublets with the energy separation of 0.103 meV using high-resolution neutron spectroscopy, which exactly corresponds to that expected from the optimum parameters obtained from the medium resolution xperiment. The temperature dependences of the integrated intensities of the 0.5 and 0.6 meV peaks are well reproduced by the Boltzmann distribution of the energy levels of the model Hamiltonian below 10 K. Furthermore, the inelastic peaks were visible even at very high temperatures as 50 K. This indicates extraordinary weak coupling between phonons (or any other perturbations) and spin states in the Cu$_3$ cluster, compared to the other known molecular nanomagnets.