Spin-Transfer Torque — LLG Equation

In magnetic tunnel junctions, spin-polarized current exerts a torque on the free layer magnetization. The Landau–Lifshitz–Gilbert (LLG) equation with Slonczewski spin-transfer torque is: dm/dt = −γm×H_eff + α·m×(dm/dt) + (ℏJ)/(2eMsd)·m×(m×p̂). The first term drives precession, the second (α) is Gilbert damping, and the third is spin-transfer torque from current density J with polarization p̂. Above a critical current J_c, damping is overcome and the magnetization switches or oscillates.

80
5.0
0.020
m = (1, 0, 0)