  This research aims to identify an alternative solution for the
Nd$_2$Fe$_{14}$B 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 ThMn$_{12}$ structure, focusing specifically on the
(Zr$_{0.5}$Nd$_{0.5}$)Fe$_{11}$Ti compound. In order to gain a comprehensive
understanding, an investigation of intrinsic and magnetic properties, including
saturation magnetisation ($M_S$), Curie temperature ($T_C$) and magnetic
anisotropy energy (MAE), is carried out on binary to quinary compounds
RFe$_{11-y}$Ti$_{y}$ (R: Nd, Zr and Zr$_{0.5}$Nd$_{0.5}$, y: $0 \leq y \leq 1$)
and (Zr$_{0.5}$Nd$_{0.5}$)Fe$_{10}$CoTi. The substitution of Ti at different
concentrations for thermodynamic stabilisation is studied in ternary and
quaternary compounds RFe$_{12-y}$Ti$_y$ ($0 \leq y \leq 1$). In addition, the
influence of Co on phase stability and intrinsic magnetic properties is studied
in the quinary compound (Zr$_{0.5}$Nd$_{0.5}$)Fe$_{10}$CoTi. Special attention
is given to the treatment of the 4$f$-electrons of Nd and their interaction
with the 3$d$-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. Based on the
literature and the calculations of binary and ternary compounds, the
calculations of quaternary and quinary compounds are encouraged. Promising
magnetic properties of an Nd-lean quaternary compound suitable for engineering
applications have been identified.
