Current-induced magnetization dynamics

On the application of magnetic field, the magnetic moment undergoes a dynamical precessional motion. The magnetic field does nothing but applies a precessional torque on the angular momentum associated with the magnetic moment. When the angular momentum is changing, so does the magnetic moment. The dynamics of the magnetic moment can be described by the Landau-Lifshitz-Gilbert (LLG) equation:

${d{\bf m}\over dt} = - \gamma {\bf m}\times ({\bf H}_{\rm eff} + {\bf H}_{\rm T}) + \alpha {\bf m}\times{d{\bf m}\over dt}$

where m is the unit vector representing the magnetization direction, H_eff is the effective magnetic field acting on the magnetization, H_Tis the thermal random field that models the thermal fluctuation, α is the magnetic damping parameter. Note: the magnetic moment and the associated angular momentum are two distinctive physical quantities, they are related by the gyromagnetic ratio γ.

Similarly, spin-transfer torque as a torque can also influence the dynamical motion, which is now described by a modified LLG equation:

${d{\bf m}\over dt} = - \gamma {\bf m}\times ({\bf H}_{\rm eff} + {\bf H}_{\rm T}) + \alpha {\bf m}\times{d{\bf m}\over dt} + {\gamma\over\mu_0 M_s}{\bf N}_{\rm st}$

where μ₀ is the magnetic constant, and

${\bf N}_{st} = \eta(\theta){\hbar J\over 2e}({\bf m}\times{\bf m}_0)\times{\bf m}$

is the spin-transfer torque. When m₀ is parallel to the easy axis of m, the effect of the spin-transfer torque is either working against the magnetic damping (anti-damping) or enhance magnetic damping depending on the direction of the applied current. Therefore, when the current polarity and magnitude is appropriate, current-induced magnetization reversal can be achieved. Or sometime, current-induced magnetization dynamics when the damping and anti-damping cancel each other. The reversal can be used as a writing mechanism for the magnetic memory, and the current-induced dynamics can be used as a microwave generator. A typical magnetization reversal trajectory is shown on the below.

For a spin valve, the magnetization in the free layer is susceptible to the applied current, and thus reversal or dynamical motion can be induced. The exact status of the magnetization depends on the applied magnetic field and current (and anisotropy). By solving the modified (stochastic) LLG equation, we may draw a phase diagram. A comparison between experiment [1] and theory [2] is shown below.

References:

[1]. Kiselev, S.I. et al. Microwave oscillations of a nanomagnet driven by a spin-polarized current. Nature 425, 380-383 (2003).
[2]. Xiao, J., Zangwill, A. & Stiles, M.D. Macrospin models of spin transfer dynamics. Phys. Rev. B 72, 014446-13 (2005).