Two-dimensional (2D) coordination polymers consisting of Mn-III Schiff-base complexes and dicarboxylic acids, [{Mn(salen)}4(L1)](PF6)2.(CH3OH)2 (C4; H(2)L1 = adipid acid) and [{Mn(salen)}(4)(L2)](PF6)(2)center dot(CH3OH)(4) (C4'; H(2)L2 = E,E-1,3-butadiene-1,4-dicarboxylic acid) (salen(2-) = N,N'-(ethylene)bis(salicylideneiminato), were synthesized by using a one-pot reaction and characterized by using single-crystal X-ray crystallographic analysis. One-dimensional (1D) chains composed of Mn(salen) dimers, [Mn-2], bridged by carboxylato ligands (-[Mn-2]-OCO-[Mn-2]-), were linked by dicarboxylato ligands with n-butyl (-C4H8-) (C4) and butadienyl aliphatic groups (-C4H4-) (C4'). From static magnetic measurements on both C4 and C4', there were ferromagnetic interactions between the Mn-III ions through the phenoxo oxygen atoms of the salen2-, and antiferromagnetic interactions between the Mn-III ions through carboxylato ligands (-OCO-). As a result, weak ferromagnetism occurred because of the zigzag-shaped chain structure of C4 and C4', and magnetic anisotropy for Mn(salen). In the magnetization curves for C4', weak interchain interactions (j(linker)) occurred through the pi-conjugated butadienyl linkers in C4', which C4 did not have. In other words, changing from saturated to unsaturated aliphatic groups in the dicarboxylic acid linkers resulted in weak interactions between 1D-magnetic chain moieties. Therefore, in the case of only C4', antiferromagnetic phase transition appeared at 2.3 K. Both coordination polymers exhibited slow relaxation of the magnetizations, which originated from SCM moieties, because C4 and C4' showed magnetic correlations. It is noteworthy that alternating current (ac) susceptibilities for C4' are frequency-dependent around the Neel temperature. From analysis of the ac susceptibilities for C4, alpha (dispersion coefficient of the relaxation of magnetization) varied linearly with 1/T. This signifies that C4 behaved as an SCM with a single relaxation process. On the other hand, in alpha versus 1/T plots for C4', an inflection point was observed at the Neel temperature, indicating that J(linkers) had an effect on the distribution of the relaxation times. Moreover, the inflection point for C4' disappeared when a dc magnetic field was applied. This is the first report showing a direct correlation between an antiferromagnetic phase transition and slow magnetic relaxation.