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The collective dynamics of magnetic domain wall under electric current is studied in the form of spin transfer torque (STT). The out-of-plane STT induced effective force is obtained based on the Landau-Lifshitz-Gilbert (LLG) equation including microscopic STT terms. The relation between microscopic calculations and collective description of the domain wall motion is established. With our numerical calculations based on tight binding free electron model, we find that the non adiabatic out-of-plane torque components have considerable non-local properties. It turns out that the calculated effective forces decay significantly with increasing domain wall widths.

Ballistic current induced effective force on magnetic domain wall