Observation of Slow Relaxation and Single-Molecule Toroidal Behavior in a Family of Butterfly-Shaped Ln₄Complexes

A family of five isostructural butterfly complexes with a tetranuclear [Ln₄] core of the general formula [Ln₄(LH)₂(μ₂-η¹η¹Piv)(η²-Piv)(μ₃-OH)₂]⋅x H₂O⋅y MeOH⋅z CHCl₃(1: Ln=Dy^III, x=2, y=2, z=0; 2: Ln=Tb^III, x=0, y=0, z=6; 3: Ln=Er^III, x=2, y=2, z=0; 4: Ln=Ho^III, x=2, y=2, z=0; 5: Ln=Yb^III, x=2, y=2, z=0; LH₄=6-{[bis(2-hydroxyethyl)amino]methyl}-N′-(2-hydroxy-3-methoxybenzylidene)picolinohydrazide; PivH=pivalic acid) was isolated and characterized both structurally and magnetically. Complexes 1–5 were probed by direct and alternating current (dc and ac) magnetic susceptibility measurements and, except for 1, they did not display single-molecule magnetism (SMM) behavior. The ac magnetic susceptibility measurements show frequency-dependent out-of-phase signals with one relaxation process for complex 1 and the estimated effective energy barrier for the relaxation process was found to be 49 K. We have carried out extensive ab initio (CASSCF+RASSI-SO+SINGLE_ANISO+POLY_ANISO) calculations on all the five complexes to gain deeper insights into the nature of magnetic anisotropy and the presence and absence of slow relaxation in these complexes. Our calculations yield three different exchange coupling for these Ln₄complexes and all the extracted J values are found to be weakly ferro/antiferromagentic in nature (J₁=+2.35, J₂=−0.58, and J₃=−0.29 cm⁻¹for 1; J₁=+0.45, J₂=−0.68, and J₃=−0.29 cm⁻¹for 2; J₁=+0.03, J₂=−0.98, and J₃=−0.19 cm⁻¹for 3; J₁=+4.15, J₂=−0.23, and J₃=−0.54 cm⁻¹for 4 and J₁=+0.15, J₂=−0.28, and J₃=−1.18 cm⁻¹for 5). Our calculations reveal the presence of very large mixed toroidal moment in complex 1 and this is essentially due to the specific exchange topology present in this cluster. Our calculations also suggest presence of single-molecule toroics (SMTs) in complex 2. For complexes 3–5 on the other hand, the transverse anisotropy was computed to be large, leading to the absence of slow relaxation of magnetization. As the magnetic field produced by SMTs decays faster than the normal spin moments, the concept of SMTs can be exploited to build qubits in which less interference and dense packing are possible. Our systematic study on these series of Ln₄complexes suggest how the ligand design can help to bring forth such SMT characteristics in lanthanide complexes.