Origin of the Unusual Ground-State Spin S = 9 in a Cr₁₀ Single-Molecule Magnet

The molecular wheel [Cr₁₀(OMe)₂₀(O₂CCMe₃)₁₀], abbreviated {Cr₁₀}, with an unusual intermediate total spin S = 9 and non-negligible cluster anisotropy, D/k_B = -0.045(2) K, is a rare case among wheels based on an even number of 3d-metals, which usually present an antiferromagnetic (AF) ground state (S = 0). Herein, we unveil the origin of such a behavior. Angular magnetometry measurements performed on a single crystal confirmed the axial anisotropic behavior of {Cr₁₀}. For powder samples, the temperature dependence of the susceptibility plotted as χT(T) showed an overall ferromagnetic (FM) behavior down to 1.8 K, whereas the magnetization curve M(H) did not saturate at the expected 30 μ_B/fu for 10 FM coupled 3/2 spin Cr³⁺ ions, but to a much lower value, corresponding to S = 9. In addition, the X-ray magnetic circular dichroism (XMCD) measured at high magnetic field (170 kOe) and 7.5 K showed the polarization of the cluster moment up to 23 μ_B/fu. The magnetic results can be rationalized within a model, including the cluster anisotropy, in which the {Cr₁₀} wheel is formed by two semiwheels, each with four Cr³⁺ spins FM coupled (J_FM/k_B = 2.0 K), separated by two Cr³⁺ ions AF coupled asymmetrically (J₂₃/k_B = J₇₈/k_B = -2.0 K; J₃₄/k_B = J₈₉/k_B = -0.25 K). Inelastic neutron scattering and heat capacity allowed us to confirm this model leading to the S = 9 ground state and first excited S = 8. Single-molecule magnet behavior with an activation energy of U/k_B = 4.0(5) K in the absence of applied field was observed through ac susceptibility measurements down to 0.1 K. The intriguing magnetic behavior of {Cr₁₀} arises from the detailed asymmetry in the molecule interactions produced by small-angle distortions in the angles of the Cr-O-Cr alkoxy bridges coupling the Cr³⁺ ions, as demonstrated by ab initio and density functional theory calculations, while the cluster anisotropy can be correlated to the single-ion anisotropies calculated for each Cr³⁺ ion in the wheel.