Great interest is being shown in investigating magnetic interactions that efficiently influence lanthanide single-molecule magnet behavior. A series of heterometallic complexes {M(2)Ln(2)(Hhms)(2)(CH3COO)(6)(CH3OH)(2)(H2O)(2)]center dot(NO3)(2) (M = Ni-II, Ln = Dy-III (1), Gd-III (2), and Y-III (3); M = Co-II, Ln = Dy-III (4), Ge-III (5), and Yu(III) (6)) have been prepared with a compartmental Schiff-base ligand, 1-(2-hydroxy-3-methoxybenzylidene)-semicarbazide (H(2)hms), featuring a zigzag-shaped Mu(II)-Ln(III)-Ln(III)-M-II metallic core arrangement. In complexes 1-6, a unique monophenoxo/diacetate asymmetric bridging connects M-II ion with Ln(III) ion, and four acetates bridge two Ln(III) ions where acetates play essential roles as coligand in generating the tetranuclear units. Magnetic studies reveal the presence of predominant ferromagnetic coupling in Dy-III and Gd-III derivatives, and slow relaxation of magnetization is observed for {(Ni2Dy2III)-Dy-II} and {(Co2Dy2III)-Dy-II} with an energy barrier of 16.0 K for {(Ni2Dy2III)-Dy-II} and 6.7 K for {(Co2Dy2III)-Dy-II} under zero static field. Compared with the analogue {(Co2Dy2III)-Dy-II}, the {(Ni2Dy2III)-Dy-II} shows longer relaxation time and an absence of the quantum tunnelling of the magnetization (QTM) at low temperatures. Ab initio calculations suggest that the zero-field QTM of {(Ni2Dy2III)-Dy-II} is effectively interrupted thanks to the ferromagnetic exchange coupling generated between Ni-II and Dy-III ions. The presence of ferromagnetic exchange between Ni-II and Dy-III ions is more conducive to zero-field single-molecule magnet behaviors than in isomorphic {(Co2Dy2III)-Dy-II} where the exchange is antiferromagnetic.