  Due to the resource criticality of rare-earths (RE), an alternative to the
well-known Nd$_2$Fe$_{14}$B magnets with a lower amount of critical elements is
required. In this work, density functional theory (DFT) calculations to
investigate the influence of partial Nd substitution with more abundant
elements (X: Y and Ce) in ThMn$_{12}$-type (Nd,X)Fe$_{11}$Ti compounds were
performed. In order to have a systematic understanding, the intrinsic magnetic
properties such as the saturation magnetization $M_S$, Curie temperature $T_C$
and magnetocrystalline anisotropy energy, are screened starting from binaries
RFe$_{12}$ (R: Y, Ce and Nd), and only considering the spin magnetic
contribution in case of the $f$ electrons. Ti is considered for the
thermodynamic stabilization and different concentrations of Ti are taken into
account for ternaries RFe$_{12-y}$Ti$_y$ and quaternaries
(Nd,X)Fe$_{12-y}$Ti$_y$ (0.5$\le$ $y$ $\le$1). In addition, the effect of
nitrogenation is examined for each considered compound. In case of
(Nd,Y)Fe$_{11}$Ti, $|BH|$$_{max}$ is found to be 384 kJ/m$^3$ and $T_C$ is
calculated to be 595 K. Similarly, $|BH|$$_{max}$ and $T_C$ are calculated to
be 365 kJ/m$^3$ and 593 K for (Nd,Ce)Fe$_{11}$Ti magnet, respectively. Both 50
% Nd-lean magnets exhibit higher $|BH|$$_{max}$ compared to Sm$_2$Co$_{17}$ and
$T_C$ than Nd$_2$Fe$_{14}$B. For both cases, the theoretical magnetic hardness
factor $\kappa$ is calculated to be 1.20, which qualifies them as good
candidates for RE-lean permanent magnets.
