Solvents play important roles in our lives, they are also of interest in molecular materials, especially for molecular magnets. The solvatomagnetic effect is generally used for trigger and/or regulation of magnetic properties in molecule-based systems, however, molecular nanomagnets showing solvatomagnetic effects are very difficult to obtain. Here we report four 3d-4f heterometallic cluster complexes containing ROH lattice solvent molecules, [Cu3Tb2(H3L)2(OAc)2(hfac)4]∙2ROH {H6L = 1,3-Bis[tris(hydroxymethyl)methylamino]propane, hfac− = hexafluoroacetylacetonate; R = CH3, 1; R = C2H5, 2; R = C3H7, 3; R = H, 4}. Single-molecule magnet (SMM) properties of these four complexes were observed to be dependent on the ROH lattice solvent molecule. There is an interesting magneto-structural correlation: the larger the R group, the higher the energy barrier. For the first time, the solvatomagnetic effect is used for the continuous fine adjustment of the energy barrier of 0D molecular nanomagnets. Additionally, [Cu3Dy2(H3L)2(OAc)2(hfac)4]∙2MeOH (5), an analogue of [Cu3Tb2(H3L)2(OAc)2(hfac)4]∙2MeOH (1), is also reported for comparison.