We characterized the anti-symmetric exchange coupling, Dzyaloshinskii-Moriy Interaction (DMI),  in ferromagnetic hetero-structure. By measuring asymmetric spin wave dispersion relation with  BLS (Brillouin Light Scattering), we can determine DMI energy density for various materials. Furthermore, we demonstrated another technique to determine DMI energy density by measuring hysteresis loop. With additional in-plane field, the hysteresis loop is shifted depends on the sign and magnitude     of DMI, and the lateral asymmetry of the sample structure.   We also implemented stand alone one-dimensional domain wall simulator,  which can calculate domain wall position, velocity, internal magnetization angle,  and tilting angle of the domain wall under given simulation conditions and material parameters. The simulator adopted all known influences, including three-dimensional external magnetic fields,  spin transfer torque with non-adiabatic contribution, spin Hall effect, Rashba effect, and Dzyaloshinskii-Moriya interaction. Finally, we find that the relation between switching time distribution and damping constant in magnetic  nano-structure by solving Fokker Planck Equations. It has been revealed that the inverse of line width of switching time distribution is proportional to the damping constant.