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Effect of $R$-site substitution and the pressure on stability of $R$Fe$_{12}$: A first-principles study

We theoretically study the structural stability of $R$Fe$_{12}$ with the ThMn$_{12}$ structure ($R$: rare-earth elements, La, Pr, Nd, Sm, Gd, Dy, Ho, Er, Tm, Lu, Y, or Sc, or group-IV elements, Zr or Hf) based on density functional theory. The formation energy has a strong correlation with the atomic radius of $R$. The formation energy relative to simple substances decreases as the atomic radius decreases, except for $R=$ Sc and Hf, while that relative to $R_{2}$Fe$_{17}$ and bcc Fe has a minimum for $R=$ Dy. The present results are consistent with recent experimental reports in which the partial substitution of Zr at $R$ sites stabilizes $R$Fe$_{12}$-type compounds with $R=$ Nd or Sm. Our results also suggest that the partial substitution of Y, Dy, Ho, Er, or Tm for Nd or Sm is a possible way to enhance the stability of the ThMn$_{12}$ structure. Under hydrostatic pressure, the formation enthalpy decreases up to $\approx$ 6 GPa and then starts to increase at higher pressures.