Single Molecule Magnets (SMM) are clusters formed by a finite number of exchange-coupled transition-metal ions [1]. They exhibit many interesting properties, such as magnetic bistability and slow relaxation of the magnetisation. Macroscopic SMM samples are a collection of perfectly identical and weakly interacting clusters, allowing to observe quantum-mechanical effects through macroscopic measurements [2]. Moreover, these compounds are promising for several technological applications, such as quantum computing and high-density data storage.

A ring-shaped cluster consisting of eight CrIII ions (chemical formula: Cr₈F₈Piv₁₆, where Piv = pivalic acid) has been recently synthesised [3]. Susceptibility measurements suggested an antiferro-magnetic (AF) interaction between the CrIII ions, with an energy splitting of about 0.8 meV between the S = 0 ground state and the S = 1 first excited state.
We have prepared 4 grams of non-deuterated polycrystalline sample using the procedure reported in [3], and checked the sample integrity by X-ray diffraction at room temperature. The molecular structure of the cyclic cluster is shown in figure 1.

The system crystallises in the P42₁2 tetragonal space group. The Cr ions form an almost perfectly planar octagon, with a slightly distorted octahedral environment and an average intramolecular Cr-Cr distance of 3.388 Å. High-energy resolution inelastic neutron scattering experiments have been carried out on the time-focussing, time-of-flight spectrometer IN6 at ILL [4]. An energy-transfer range up to 4 meV in neutron-energy-loss has been explored, with different spectrometer configurations corresponding to energy resolution from 50 µeV to 170 µeV at the elastic peak. The instrument covers a wide range of scattering angles (from 10 to 114 degrees), corresponding to a maximum momentum transfer of Q = 2.6 Å^-1.

Figure 1: 3D view of the tetragonal Cr₈ unit cell (dotted line). Large blue spheres are Cr atoms, medium green and light-blue spheres are F and O atoms, respectively, and small red spheres are C atoms. H atoms, disordered solvent molecules and methyl groups are not shown for clarity.

Isotropic exchange is the dominant interaction in these systems. The magnetic energy spectrum consists of many spin multiplets split by anisotropic interactions, such as the local crystal field and dipolar interactions [5]. Neutron spectroscopy provides direct access to the energies and wavefunctions of the different spin states of the magnetic clusters. The lowest energy levels for Cr₈ are shown in figure 2.
The neutron spectra measured on IN6 with incident energies of 2.35, 3.86, and 4.86 meV are shown in figure 3. With the sample at T = 2 K, the excited states are not populated. In the energy range explored, the allowed transitions (with selection rule ΔS = 0,±1 and ΔM = 0,±1) are only those between the |S=0;M=0> ground state and the |S=1;M=0,±1> levels. The zero-field splitting of the first excited S=1 multiplet is well resolved. On increasing the temperature, the excited levels become progressively populated and transitions between them can be observed, offering the possibility of studying the details of the spin Hamiltonian and of determining the strength and topology of the exchange interactions. At T = 12 K and below 4 meV, transitions from the |S=1> first excited state to |S=2> and to other |S=1> multiplet levels are clearly visible, together with a |S=2>→|S=3> transition.

Figure 2: Lowest energy spin multiplets calculated for tetragonal Cr₈ assuming isotropic exchange interactions only, with parameters corresponding to the best fit of INS spectra.

TAt higher temperatures, transitions from the ground state almost vanish, due to the thermal population of many excited levels.

The experimental spectra have been reproduced using a microscopic spin Hamiltonian and the parameters describing the intra-cluster interactions have been determined by a best-fit procedure. The most important effects due to the mixing between different spin multiplets have been taken into account. These effects have proved important in determining the details of the neutron results, in particular they change the ratio between the intensities of the peaks at ~0.7 and ~0.9 meV by more than 20%. The spectra calculated using the best-fit parameters are shown by solid lines in figure 3. An interesting feature is the broadening of the transitions between excited multiplets, a signal that the lifetime of the excited states becomes shorter as the energy of the level increases.

To correctly reproduce the experimental data, a rhombic term [5] in the crystal-field Hamiltonian is necessary. In principle, this second-order in-plane anisotropy is not allowed by the C₄ symmetry exhibited by the cluster at room temperature, thus giving evidence that a low temperature distortion may take place. Preliminary neutron diffraction experiments confirm this assumption [6].

Figure 3: Inelastic neutron scattering results for Cr₈ at 2 K (red triangles) and 12 K (full circles), recorded on IN6 with an incident neutron energy of (upper panel) 2.35, (central panel) 3.86, and (lower panel) 4.86 meV. Intensities integrated over the whole scattering angle range are shown as a function of energy transfer. The empty sample-holder contribution (red line) has been subtracted after normalisation for absorption. Excitation peaks are labelled by indicating the total spin of the initial and final multiplet involved in the transition. The spectra calculated using the best-fit parameters are shown by solid lines.

The detailed knowledge of the microscopic interactions in molecular magnetic clusters is essential to make possible a rational design of these systems. Indeed, a large Ising-type anisotropy barrier for spin reversal, U, is essential for the realisation of a single-molecule magnet to be used in information storage devices. The system with the highest barrier discovered so far is Mn12-acetate, for which U = 61 K.

This value is far too small for practical applications, but the synthesis of magnetic clusters with sizeably higher anisotropy appears to be a difficult challenge. A deeper understanding of the origin of the magnetic anisotropy in SMM is necessary to achieve substantial progress and neutron scattering may prove to be an important tool to shed light in this matter