Rare-earth-free permanent magnets have attracted considerable attention due to their favorable properties and applicability for cost-effective, high-efficiency, and sustainable energy devices. However, the magnetic field annealing process, which enhances the performance of permanent magnets, needs to be optimized for different magnetic fields and phases. Therefore, we investigated the effect of composition on the crystallization of amorphous MnBi to the ferromagnetic low-temperature phase (LTP). The optimal compositions and conditions were applied to magnetic field annealing under 2.5 T for elemental Mg- and Sb/Mg pair-substituted MnBi. The optimum MnBi composition for the highest purity LTP was determined to be Mn₅₆Bi₄₄, and its maximum energy product, (BH)_max, was 5.62 MGOe. The Mg-substituted MnBi exhibited enhanced squareness (M_r/M_s), coercivity (H_c), and (BH)_max values up to 0.8, 9659 Oe, and 5.64 MGOe, respectively, whereas the same values for the Sb/Mg pair-substituted MnBi were 0.76, 7038 Oe, and 5.60 MGOe, respectively. The substitution effects were also investigated using first-principles calculations. The density of states and total magnetic moments of Mn₁₆Bi₁₅Mg and Mn₁₆Bi₁₅Sb were similar to those of pure Mn₁₆Bi₁₆. Conversely, the Sb-substituted MnBi resulted in a dramatic enhancement in the anisotropy constant (K) from a small negative value (−0.85 MJ/m³) to a large positive value (6.042 MJ/m³).

The magnetization of most materials decreases with increasing temperature due to thermal deterioration of magnetic ordering. Here, we show that Mn₄C phase can compensate the magnetization loss due to thermal agitation. The Mn–C nanoparticles containing ferrimagnetic Mn₄C and other Mn–C/Mn-O phases were prepared by using the traditional arc-discharge method. A positive temperature coefficient of magnetization (~0.0026 Am² kg⁻¹ K⁻¹) and an exchange bias up to 0.05 T were observed in the samples. We ascribe the exchange bias to the co-existence of ferrimagnetic Mn₄C/Mn₃O₄ and antiferromagnetic α-Mn(C)/MnO phases. The positive temperature coefficient of magnetization of the samples was ascribed to the presence of Mn₄C phase, which is considered as a Néel’s P-type ferrimagnet.