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 (III) Ln(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 4fxyz orbital of the Gd(III) ion and 3d${{_{x{^{2}}- y{^{2}}}}}$ 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 mJ |±15/2〉 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 mJ |±13/2〉 state with a significant transverse anisotropy, leading to very strong quantum tunneling of magnetization (QTM). Using the POLY_ANISO program, we have extracted the JNiDy 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.

Role of Single-Ion Anisotropy and Magnetic Exchange Interactions in Suppressing Zero-Field Tunnelling in {3d-4f} Single Molecule Magnets.

Extensive ab initio CASSCF/RASSI-SO/SINGLE_ANISO/POLY_ANISO calculations have been undertaken on eight structurally similar previously synthesized [CuII(L)(C3H6O)LnIII(NO3)3] (Ln = Dy (1), Tb (3), Ho (5), and Er (7)) and [VIVO(L)(C3H6O)LnIII(NO3)3] (Ln = Dy (2), Tb (4), Ho (6), and Er (8)) (here H2L = N,N'-bis(3-methoxysalicylidene)-1,3-diamino-2,2-dimethylpropane) complexes (crystal structures reported earlier). Our estimated exchange interactions (J) using the Lines model for complexes 1-8 (1.55 cm-1, 0.15 cm-1, 5.30 cm-1, 0.06 cm-1, 1.05 cm-1, -0.18 cm-1, 0.24 cm-1, and -0.02 cm-1 for complexes 1-8 respectively) match well with the experimental values (HE-EPR and pulse magnetization technique) reported earlier and offer confidence in the methodology employed. We have established the mechanism of magnetic coupling for this series to rationalize the observation that LnCu complexes are strongly coupled compared to LnV complexes. Besides, the results procured based on the BS-DFT method imply a crucial role of overlap between the 3d and 4f orbitals, the formally empty 5d/6s/6p orbitals of LnIII ion in the exchange coupling mechanism. To probe the origin/absence of magnetization relaxation observed in these complexes 1-8, both the single-ion and the exchange anisotropy are analyzed. Our calculations reveal that stronger exchange interaction quenches the quantum tunnelling of magnetization behavior in these complexes; however, for LnV complexes the exchange interaction was too small to offer a large blockade barrier. In the quest to obtain a stronger exchange interaction, we have assessed several models and have developed a magneto-structural correlation. An antagonizing behavior between the JCuDy and Ucal values are noted for the Dy-O-O-Cu dihedral angle correlation developed on complex 1. This highlights the subtle nature of the magnetic anisotropy in this class of complexes and postulates that both the single-ion anisotropy and the exchange interaction are needed to be targeted simultaneously to achieve a new generation {3d-4f} single molecule magnets (SMM).