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A new family of tetranuclear Mn complexes [Mn4X4L4] (H2L = salicylidene-2-ethanolamine; X = Cl (1) or Br (2)) and [Mn4Cl4(L')4] (H2L' = 4-tert-butyl-salicylidene-2-ethanolamine, (3)) has been synthesized and studied. Complexes 1-3 possess a square-shaped core with ferromagnetic exchange interactions between the four Mn(III) centers resulting in an S = 8 spin ground state. Magnetochemical studies and high-frequency EPR spectroscopy reveal an axial magnetoanisotropy with D values in the range -0.10 to -0.20 cm(-1) for complexes 2 and 3 and for differently solvated forms of 1. As a result, these species possess an anisotropy-induced energy barrier to magnetization reversal and display slow relaxation of the magnetization, which is observed as hysteresis for 1 and 3 and frequency-dependent peaks in out-of-phase AC susceptibility measurements for 3. The effective energy barrier was determined to be 7.7 and 7.9 K for 1 and 3, respectively, and evidence for quantum tunneling of the magnetization was observed. Detailed magnetochemical studies, including measurements at ultralow temperatures, have revealed that complexes 1 and 2 possess solvation-dependent antiferromagnetic intermolecular interactions. Complex 3 displays ferromagnetic intermolecular interactions and approaches a ferromagnetic phase transition with a critical temperature of approximately 1 K, which is coincident with the onset of slow relaxation of the magnetization due to the molecular anisotropy barrier to magnetization reversal. It was found that the intermolecular interactions have a significant effect on the manifestation of slow relaxation of the magnetization, and thereby, these complexes represent a new family of "exchange-biased single-molecule magnets", where the exchange bias is controlled by chemical and structural modifications.