Role of Magnetic Exchange Interactions in the Magnetization Relaxation of {3d-4f} Single-Molecule Magnets: A Theoretical Perspective

Combined density functional and ab initio calculations are performed on two isomorphous tetranuclear {Ni₃^IIILn^III} star-type complexes [Ln=Gd (1), Dy (2)] to shed light on the mechanism of magnetic exchange in 1 and the origin of the slow magnetization relaxation in complex 2. DFT calculations correctly reproduce the sign and magnitude of the J values compared to the experiments for complex 1. Acute <Ni-O-Gd bond angles present in 1 instigate a significant interaction between the 4f_xyz orbital of the Gd^III ion and 3dx²-y² orbital of the Ni^II ions, leading to rare and strong antiferromagnetic Ni⋯Gd interactions. Calculations reveal the presence of a strong next-nearest-neighbour Ni⋯Ni antiferromagnetic interaction in complex 1 leading to spin frustration behavior. CASSCF+RASSI-SO calculations performed on complex 2 suggest that the octahedral environment around the Dy^III ion is neither strong enough to stabilize the m_J |±15/2a> as the ground state nor able to achieve a large ground-state-first-excited-state gap. The ground-state Kramers doublet for the Dy^III ion is found to be the m_J |±13/2a> state with a significant transverse anisotropy, leading to very strong quantum tunneling of magnetization (QTM). Using the POLY-ANISO program, we have extracted the J_NiDy interaction as -1.45 cm^-1. The strong Ni⋯Dy and next-nearest-neighbour Ni⋯Ni interactions are found to quench the QTM to a certain extent, resulting in zero-field SMM behavior for complex 2. The absence of any ac signals at zero field for the structurally similar [Dy(AlMe₄)₃] highlights the importance of both the Ni⋯Dy and the Ni⋯Ni interactions in the magnetization relaxation of complex 2. To the best of our knowledge, this is the first time that the roles of both the Ni⋯Dy and Ni⋯Ni interactions in magnetization relaxation of a {3d-4f} molecular magnet have been established.