All-$d$ Heusler alloys are promising candidates for advanced spintronic and magnetoelastic applications, yet many lack the intrinsic large anomalous Hall conductivity (AHC) and magnetostriction required for practical device integration. In this work, we systematically investigate the topological transport and magnetostrictive properties of 81 heavy-element substituted Co-based all-$d$ Heusler alloys ${\mathrm{Co}}_{2}YZ\left(R\right)$ $(Y=\mathrm{Cr},\mathrm{Mn},\mathrm{Fe};Z=\mathrm{Sc},\mathrm{Ti},\mathrm{V}; \text{and} R=\mathrm{Re},\mathrm{Os},\mathrm{Ir},\mathrm{Pt})$ using first-principles calculations. We demonstrate that the fractional substitution of $5d$ transition metals serves as a highly effective strategy to tune the electronic structure via strong spin-orbit coupling (SOC). Our calculations identify eight materials exhibiting giant AHC values exceeding 1000 S/cm, with ${\mathrm{Co}}_2{\mathrm{Mn}}_{0.75}{\mathrm{Os}}_{0.25}\mathrm{Sc}$ and ${\mathrm{Co}}_2{\mathrm{Mn}}_{0.75}{\mathrm{Re}}_{0.25}\mathrm{V}$ approaching 1500 S/cm. Detailed symmetry and electronic structure analyses reveal that this massive AHC originates from the SOC-induced gap opening of Weyl nodal lines near the Fermi level, which generates an extended distribution of large Berry curvature. Furthermore, the introduction of strong SOC significantly enhances the magnetocrystalline anisotropy energy, transforming alloys with initially negligible magnetostriction into high-performance magnetoelastic materials. Notably, ${\mathrm{Co}}_2{\mathrm{Fe}}_{0.75}{\mathrm{Os}}_{0.25}\mathrm{Ti}$ and ${\mathrm{Co}}_2{\mathrm{FeSc}}_{0.75}{\mathrm{Ir}}_{0.25}$ exhibit giant magnetostriction coefficients of 752 and 609 ppm, respectively. Our findings establish heavy-element substitution as a robust, dual-purpose approach for the design and realization of multifunctional topological magnetic materials.

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• Magnetism
• Spintronics
• Heusler alloy
• Topological materials
• Transition metals
• Density functional calculations
• Density functional theory