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To guide improved properties coincident with reduction of critical materialsin permanent magnets, we investigate via density functional theory (DFT) theintrinsic magnetic properties of a promising system,$R$(Fe$_{1-x}$Co$_{x}$)$_{11}$Ti$Z$ with $R$=Y, Ce and interstitial doping($Z$=H, C, N). The magnetization $M$, Curie temperature $T_\text{C}$, andmagnetocrystalline anisotropy energy $K$ calculated in local densityapproximation to DFT agree well with measurements. Site-resolved contributionsto $K$ reveal that all three Fe sublattices promote uniaxial anisotropy inYFe$_{11}$Ti, while competing anisotropy contributions exist in YCo$_{11}$Ti.As observed in experiments on $R$(Fe$_{1-x}$Co$_{x}$)$_{11}$Ti, we find acomplex nonmonotonic dependence of $K$ on Co content, and show that anisotropyvariations are a collective effect of MAE contributions from all sites andcannot be solely explained by preferential site occupancy. With interstitialdoping, calculated $T_\text{C}$ enhancements are in the sequence of N$>$C$>$H,with volume and chemical effects contributing to the enhancement. The uniaxialanisotropy of $R$(Fe$_{1-x}$Co$_{x}$)$_{11}$Ti$Z$ generally decreases with Cand N; although, for $R$=Ce, C doping is found to greatly enhance it for asmall range of 0.7$<$$x$$<$0.9.

Intrinsic magnetic properties of {$R$(Fe$_{1-x}$Co$_{x}$)$_{11}$Ti$Z$} ($R$ = Y and Ce; $Z$ = H, C, and N)