In this paper, the physical properties of half-doped manganite La_0.5Ca_0.5MnO₃ with crystallite sizes ranging from 15 to 40 nm are investigated. As expected, ferromagnetic order strengthens at expense of antiferromagnetic one as crystallite size is reduced to 15 nm. However, contrary to previously reported works, an enhancement of saturation magnetization is observed as crystallite size increases from 15 to 22 nm. This unexpected behavior is accompanied by an unusual cell volume variation that seems to induce ferromagnetic-like behavior at expense of antiferromagnetic one. Besides, field cooled hysteresis loops show exchange bias field and coercivity enhancement for increasing cooling fields, which suggest a kind of core-shell structure with AFM-FM coupling for crystallite sizes as small as 15 nm. It is expected that inner core orders antiferromagnetically, whereas uncompensated surface spins behave as spin glass with ferromagnetic-like ordering.