The mathematical code that supports the findings of the study is available at https://github.com/mumax/3. 
The MuMax3 scripts in this file correspond to the simulation represented in Fig.4b of the main text.

File "TaPy9nmPt_SOT_parallel.txt" is the script used for modelling the SOT effects in an asymmetric Ta/Py/Pt system with a 9-nm-thin Py layer. (blue line in Fig.4b)
File "TaPy9nmTa_SOT_aniparallel.txt" is the script used for modelling the SOT effects in a symmetric Ta/Py/Ta system with a 9-nm-thin Py layer. (red line in Fig.4b)
File "TaPy9nmPt_SOT_parallel_asymmetric.txt" is the script used for modelling the SOT effects in an asymmetric Ta/Py/Pt system with a 9-nm-thin Py layer. Here, the SOT amplitudes at the two interfaces are considered to be different (black dashed line in Fig.4b)
File "TaPy9nmPt_SOT_zero.txt" is the script to account for the influence of THz field localization (no SOT) on the Ta/Py/Pt system with 9-nm-thin-Py. This spectrum does not show a significant amplitude of spin-wave modes in the spectrum. Thus, the result of this simulation is not presented.

All parameters for the micromagnetic simulations are given in Methods.   