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Magnetic spectra in the tridiminished-icosahedron \{Fe$_9$\} nano-cluster by inelastic neutron scattering

Inelastic neutron scattering (INS) experiments under applied magnetic field at low temperatures show detailed low lying magnetic excitations in the so called tridiminshed iron icosahedron magnetic molecule. The magnetic molecule consists of nine iron Fe$^{3+}$ ($s = 5/2$) and three phosphorous atoms that are situated on the twelve vertices of a nearly perfect icosahedron. The three phosphorous atoms form a plane that separates the iron cluster into two weakly coupled three- and six-ion fragments, \{Fe$_3$\} and \{Fe$_6$\}, respectively. The magnetic field INS results exhibit an $S=1/2$ ground state expected from a perfect equilateral triangle of the \{Fe$_3$\} triad with a powder averaged $g$-value $=2.00$. Two sets of triplet excitations whose temperature and magnetic field dependence indicate an $S=0$ ground state with two non-degenerate $S=1$ states are attributed to the \{Fe$_6$\} fragment. The splitting may result from a finite coupling between the two fragments, single-ion anisotropy, antisymmetric exchange couplings, or from magnetic frustration of its triangular building blocks.