In the present paper, we study the thickness-dependent characteristics for non-ferromagnetic (LSMO)n/SrTiO3 ((LSMO)n/STO) (001) heterojunctions with n = 3, 6 and 9, using the first-principles method. Either ferrimagnetic or antiferromagnetic ground state is stabilized, depending on the interface stacking sequence and LSMO layer thickness. The estimated potential barrier at LSMO/STO (001) interface is insensitive to the thickness of LSMO layer, and nonstoichiometric La2/3Sr1/3O/TiO2 interfaces embrace a smaller interface barrier. Interestingly, the non-ferromagnetic (LSMO)n/STO (001) heterojunctions with La2/3Sr1/3O/TiO2 interface show a significant enhancement in visible-light absorption as the LSMO layer thickness increases. Our work is helpful for designing the non-ferromagnetic photomagnetoelectric systems and may be interesting for antiferromagnetic spintronics.