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In rare-earth permanent magnets (REPM's), trade-off's between intrinsicmagnetic properties are often encountered. A recent example is SmFe$_{12}$where excellent magnetic properties can be achieved at the sacrifice of bulkstructure stability. Bulk structure stability is sustained by the presence ofthe third substitute element as is the case with SmFe$_{11}$Ti, where Tidegrades magnetic properties. It is now in high demand to find out with whichchemical composition a good compromise in the trade-off between structurestability and strong ferromagnetism is reached. We inspect the effects ofrepresentative substitute elements, Zr, Ti, and Co in SmFe$_{12}$ by combiningab initio data with experimental data from neutron diffraction. The trend inthe intrinsic properties with respect to the concentration of substituteelements are monitored and a systematic way to search the best compromise isconstructed. A certain minimum amount of Ti is identified with respect to theadded amount of Co and Zr. It is found that Zr brings about a positive effecton magnetization, in line with recent experimental developments, and we arguethat this can be understood as an effective doping of extra electrons.

(Sm,Zr)Fe$_{12-x}$M$_x$ (M=Zr,Ti,Co) for permanent-magnet applications: Ab initio material design integrated with experimental characterization