Size-dependent multiple magnetic phases and exchange bias effect in hole-doped double perovskite La_1.6Sr_0.4NiMnO₆

La_1.6Sr_0.4NiMnO₆ nanoparticles of different sizes (18–150 nm) have been prepared by a sol–gel method, and the size effects on their magnetic properties are investigated. It is found that there is a ferromagnetic (FM) transition at T_C ∼ 245 K for the sample with particle size D ∼ 150 nm. As the particle size decreases, a spin glass (SG) transition appears at T_G ∼ 60 K and becomes more obvious. Meanwhile, the T_C shifts to a lower temperature and the FM transition becomes indistinct. The size dependent saturation magnetization M_S, which is in the range 0.78 ∼ 1.27 μ_B/f.u., shows a non-monotonic variation with a maximum of 1.27 μ_B/f.u. at the particle size D_C ∼ 42 nm. The exchange bias (EB) effect is clearly observed for D > 32 nm and becomes indistinct as D ⩽ 32 nm. As the particle size decreasing, the EB field H_E decreases and becomes near nil at D_C. Meanwhile, the coercive field H_C first increases to a maximum at D_C and then decreases. All the results indicate the coexistence of AFM APBs related to the anti-site disorders, FM domains, and SG phase in La_1.6Sr_0.4NiMnO₆ nanoparticles. The magnetic properties of the nanoparticles are understood by a complex core-shell model, i.e. both AFM APBs and FM domains coexist in the core, and the SG phase mainly resides on the surface (shell) of each particle, which reveals that the size effects on the FM phase, AFM APBs and surface SG phase in grain are different, even are opposite. The nanometer size effect is a crucial factor to influence the magnetic properties of La_1.6Sr_0.4NiMnO₆ nanoparticles. (paper)