Herein we report heteroleptic Co(II) diimine complexes [Co(H(2)bip)(2)Cl-2] (1), [Co(H(2)bip)(2)Br-2] (2), [Co (H(2)bip)(3)]Br-2 center dot 1MeOH (3) and [Co(H(2)bip)(2)(Me(2)bpy)]Br-2 center dot(MeCN)(0.5)center dot(H2O)(0.25) (4) (H(2)bip = 2,2'-bi-1,4,5,6-tetra-hydropyrimidine, bpy = 2,2'-dipyridyl, Me(2)bpy = 4,4'-Me-2,2'-dipyridyl), purposefully prepared to enable a systematic study of magnetic property changes arising from the increase of overall ligand field from s/p-donor chlorido (1) to p-acceptor 4,4'Me-2,2'bpy (4). The presence of axial and rhombic anisotropy (D and E) of these compounds is sufficient to allow 1-4 to show field-induced slow relaxation of magnetization. Interestingly, we found as the effective ligand field is increased in the series, rhombicity (E/D) decreases, and the magnetic relaxation profile changes significantly, where relaxation of magnetization at a specific temperature becomes gradually faster. We performed mechanistic analyses of the temperature dependence of magnetic relaxation times considering Orbach relaxation processes, Raman-like relaxation and quantum tunnelling of magnetization (QTM). The effective energy barrier of the Orbach relaxation process (U-eff) is largest in compound 1 (19.2 cm(-1)) and gradually decreases in the order 1 > 2 > 3 > 4 giving a minimum value in compound 4 (8.3 cm(-1)), where the Raman-like mechanism showed the possibility of different types of phonon activity below and above similar to 2.5 K. As a precursor of 1, the tetrahedral complex [Co(H(2)bip)Cl-2] (1a) was also synthesized and structurally and magnetically characterized: this compound exhibits slow relaxation of magnetization under an applied dc field (1800 Oe) with a record slow relaxation time of 3.39 s at 1.8 K.