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=DyIII, x=2, y=2, z=0; 2: Ln=TbIII, x=0, y=0, z=6; 3: Ln=ErIII, x=2, y=2, z=0; 4: Ln=HoIII, x=2, y=2, z=0; 5: Ln=YbIII, 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. © 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim