151. Lagrangian formulation of the linear autonomous magnetization dynamics in spin-torque auto-oscillators
- Author
-
G. Consolo(1, G. Gubbiotti(2), L. Giovannini(1, and R. Zivieri(1
- Subjects
Complex generalized non-Hermitian Eigenproblem ,Spin transfer torque ,Eigenproblem ,Landau–Lifshitz–Gilbert equation ,01 natural sciences ,Magnetization ,Normal mode ,0103 physical sciences ,Landau-Lifshitz-Gilbert equation ,Auto-oscillators ,Autonomous dynamics ,Lagrange equations ,Micromagnetics ,Rayleigh dissipation function ,010306 general physics ,Eigenvalues and eigenvectors ,010302 applied physics ,Physics ,Magnetization dynamics ,Applied Mathematics ,Spin-transfer torque ,Dissipation ,Computational Mathematics ,Classical mechanics ,Dissipative system - Abstract
A Lagrangian formalism is used to find steady-state solution of the Landau–Lifshitz–Gilbert–Slonczewski equation corresponding to the linear autonomous dynamics of a magnetic auto-oscillatory system subject to the action of a spin-polarized electric current. In such a system, two concurrent dissipative mechanisms, arising from the positive intrinsic dissipation and the negative current-induced one, take place simultaneously and make the excitation of a steady precessional motion of the magnetization vector conceivable. The proposed formulation leads to the definition of a complex generalized non-Hermitian Eigenvalue problem, both in the case of a macrospin model and in the more general case of an ensemble of magnetic particles interacting each other through magnetostatic and exchange interactions. This method allows to identify the spin-wave normal modes which become unstable in the presence of the two competing dissipative contributions and provides an accurate estimation of the value of the excitation threshold current.
- Published
- 2011