Recently, room temperature ferromagnetism (RTFM) was found in simple oxide semiconductor nanoparticles. However, there are few reports on antiferromagnetic insulators. Therefore, in this study, the relationship between antiferromagnetism as the core property and RTFM was investigated. Specifically, Cr₂O₃ with T_N = 308 K was focused. The Cr₂O₃ nanoparticles exhibited hysteresis at 300 K and 340 K. In other words, RTFM is independent of the core magnetism. Additionally, saturation magnetization (M_s) and coercive force (H_c) had magnetic interactions between the core and the surface.