This research aims to identify an alternative solution for the Nd₂Fe₁₄B magnet in light of the scarcity of rare-earth (RE) resources. The investigation uses density functional theory (DFT) calculations to assess the effect of partial substitution of Nd with the transition metal (TM) Zr within the ThMn₁₂ structure, focusing specifically on the (Zr_0.5Nd_0.5)Fe₁₁Ti compound. In order to gain a comprehensive understanding, an investigation of intrinsic and magnetic properties, including saturation magnetization (M_S), Curie temperature (T_C) and magnetic anisotropy energy (MAE), is carried out on binary to quinary compounds RFe_11-yTi_y (R: Nd, Zr and Zr_0.5Nd_0.5, y: 0 ≤ y ≤ 1) and (Zr_0.5Nd_0.5)Fe₁₀CoTi. The substitution of Ti at different concentrations for thermodynamic stabilization is studied in ternary and quaternary compounds RFe_12-yTi_y (0 ≤ y ≤ 1). In addition, the influence of Co on phase stability and intrinsic magnetic properties is studied in the quinary compound (Zr_0.5Nd_0.5)Fe₁₀CoTi. Special attention is given to the treatment of the 4f-electrons of Nd and their interaction with the 3d-electrons. Theoretical results are compared with available experimental data, although the limited availability of data, especially for Zr-containing compounds, limits the scope of such comparisons. From the literature and our calculations of binary and ternary compounds, we are encouraged to the quaternary and quinary calculations. Promising magnetic properties of an Nd-lean quaternary compound suitable for engineering applications have been identified. In particular, for the quaternary compound ZrNdFe₂₂Ti₂, calculated values of |BH|_max = 525 kJ/m³ and T_C = 783 K are close to those of the Nd₂Fe₁₄B magnet.

  Methods for evaluating the characteristics of magnetostrictive materials include dynamic magnetic domain observation using a magneto-optical Kerr effect microscope, obtaining B-H curves using a vibrating sample type magnetometer that vibrates a magnetized sample with a DC magnetic field, and so on. Generally, magnetic domains are observed in magnetic materials on flat surfaces. The authors previously researched and developed an inverse magnetostrictive torque sensor in which a magnetostrictive material is deposited on a cylindrical shaft surface. Therefore, to accurately evaluate the characteristics of a torque sensor, it is necessary to observe the magnetic domains while torque is applied on a curved surface. This paper explains that method and presents the results of dynamic domain observation of magnetostrictive materials on the shaft surface using a newly developed magneto-optical Kerr effect microscope.