Spintronics applications for high-density non-volatile memories require simultaneous optimization of the perpendicular magnetic anisotropy (PMA) and current-induced magnetization switching. These properties determine, respectively, the thermal stability of a ferromagnetic memory cell and a low operation power consumption, which are mutually incompatible with the spin transfer torque as the driving force for the switching. Here, we demonstrate a strategy of alloy engineering to overcome this obstacle by using electrically induced orbital currents instead of spin currents. A non-equilibrium orbital density generated in paramagnetic γ-FeMn flows into CoPt coupled to the magnetization through spin-orbit interaction, ultimately creating an orbital torque. Controlling the atomic arrangement of Pt and Co by structural phase transition, we show that the propagation length of the transferred angular momentum can be modified concurrently with the PMA strength. We find a strong correlation to the phase transition-induced changes of d orbitals with mₗ = ±1 and mₗ = ±2 character. The close link of orbital hybridization to the dynamic orbital response and magnetic properties offers new possibilities to realize optimally designed orbitronics memory and logic applications. This dataset contains the DFT calculations for the electronic structure of CoPt in L1₁ and A1 structures that are discussed the corresponding publication.