Lagrangian formulation of the linear autonomous magnetization dynamics in spin-torque auto-oscillators
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 dissipat...
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| Published in | Applied mathematics and computation Vol. 217; no. 21; pp. 8204 - 8215 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier Inc
01.07.2011
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0096-3003 1873-5649 |
| DOI | 10.1016/j.amc.2011.02.043 |
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| 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. |
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| AbstractList | 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. |
| Author | Giovannini, L. Zivieri, R. Consolo, G. Gubbiotti, G. |
| Author_xml | – sequence: 1 givenname: G. surname: Consolo fullname: Consolo, G. email: cnsgcr@unife.it organization: Department of Physics and CNISM, University of Ferrara, Via G. Saragat 1, 44122 Ferrara, Italy – sequence: 2 givenname: G. surname: Gubbiotti fullname: Gubbiotti, G. organization: Istituto Officina dei Materiali del CNR (CNR-IOM), Research unit of Perugia, c/o Department of Physics, Via A. Pascoli, I-06123 Perugia, Italy – sequence: 3 givenname: L. surname: Giovannini fullname: Giovannini, L. organization: Department of Physics and CNISM, University of Ferrara, Via G. Saragat 1, 44122 Ferrara, Italy – sequence: 4 givenname: R. surname: Zivieri fullname: Zivieri, R. organization: Department of Physics and CNISM, University of Ferrara, Via G. Saragat 1, 44122 Ferrara, Italy |
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| Keywords | Lagrange equations Complex generalized non-Hermitian Eigenproblem Spin-transfer torque Landau–Lifshitz–Gilbert equation Autonomous dynamics Auto-oscillators Rayleigh dissipation function Micromagnetics Lagrangian Complex generalized non-Hermitian Lagrange equation Numerical analysis Landau―Lifshitz―Gilbert equation Applied mathematics Dissipative system Eigenvalue problem Eigenproblem Steady state solution Landau Lifshitz equation |
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| Snippet | A Lagrangian formalism is used to find steady-state solution of the Landau–Lifshitz–Gilbert–Slonczewski equation corresponding to the linear autonomous... A Lagrangian formalism is used to find steady-state solution of the Landau-Lifshitz-Gilbert-Slonczewski equation corresponding to the linear autonomous... |
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| SubjectTerms | Auto-oscillators Autonomous Autonomous dynamics Complex generalized non-Hermitian Eigenproblem Dissipation Dynamical systems Dynamics Exact sciences and technology Excitation Global analysis, analysis on manifolds Lagrange equations Landau–Lifshitz–Gilbert equation Magnetization Mathematical analysis Mathematical models Mathematics Micromagnetics Numerical analysis Numerical analysis. Scientific computation Rayleigh dissipation function Sciences and techniques of general use Spin-transfer torque Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds |
| Title | Lagrangian formulation of the linear autonomous magnetization dynamics in spin-torque auto-oscillators |
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