Fig. 2: Structural stability and intrinsic magnetic properties of Sm−Fe−Ti system.

a Heat map of the formation enthalpy of the ternary Sm−Fe−Ti system. Open nodes mark the known elemental and binary phases. Solid nodes represent the present ternary SmFe_12−xM_x (x = 0.5, 1, and 2) phases. Dotted and solid lines are the projections of the convex hull construction into compositional space. b Formation enthalpy H_f and c saturation magnetization μ₀M_s (left) and uniaxial magnetocrystalline anisotropy K_u (right) of SmFe_12−xM_x (x = 0, 0.5, 1, and 2). The corresponding experimental results for SmFe₁₂ measured at 0−300 K^22,23 and SmFe₁₁Ti at 4.2−300 K^15,16,17 are indicated by the open symbols, where the result at 0 K is determined by fitting with low-temperature measurements²².