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By Isaak D. Mayergoyz, Visit Amazon's Giorgio Bertotti Page, search results, Learn about Author Central, Giorgio Bertotti, , Claudio Serpico
As information move premiums bring up in the magnetic recording undefined, advancements in gadget functionality and reliability crucially depend upon the thorough realizing of nonlinear magnetization dynamics at a sub-nanoscale point. This booklet bargains a contemporary, stimulating method of the topic of nonlinear magnetization dynamics by means of discussing vital features similar to the Landau-Lifshitz-Gilbert (LLG) equation, analytical recommendations, and the relationship among the overall topological and structural features of dynamics. a sophisticated reference for the learn and figuring out of nonlinear magnetization dynamics, it addresses events akin to the certainty of spin dynamics briefly time scales and gadget functionality and reliability in magnetic recording. subject matters lined comprise nonlinear magnetization dynamics and the Landau-Lifshitz-Gilbert equation, nonlinear dynamical platforms, spin waves, ferromagnetic resonance and pulsed magnetization switching. The booklet explains easy methods to derive special analytical options for the total nonlinear challenge and emphasises the relationship among the final topological and structural elements of nonlinear magnetization dynamics and the discretization schemes greater suited for its numerical research. it truly is a great study software offering a sophisticated realizing of the learn of magnetization dynamics in occasions of primary and technological curiosity.
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Additional resources for Nonlinear magnetization dynamics in nanosystems
Sample text
In this equation, the conservation of the magnetization magnitude is no longer a constraint. Furthermore, two independent relaxation mechanisms are introduced for the magnetization components parallel and perpendicular to the dc external field. These relaxation mechanisms are controlled by two different time constants, τss and τsl . The relaxation of the magnetization component perpendicular to the applied dc field is attributed to the 30 CHAPTER 2 Basic Equations for Magnetization Dynamics progressive disappearance of the phase coherence in the precession of the individual spins and is therefore referred to as “spin–spin relaxation”.
All these ellipses are centered at the point (ax , ay ). The above family of ellipses is generated by varying the free energy value g0 within an appropriate range. 10). It must be pointed out that only those portions of the ellipses which lie inside the circle m2x + m2y ≤ 1 are accessible to the magnetization dynamics. On the other hand, mz does not appear explicitly in Eq. 8), which means that there exist motions with opposite values of mz resulting in identical projections on the (mx , my )-plane.
As an example, the graph for the phase portrait presented in Fig. 2(a) is shown in Fig. 2(b). This graph representation will prove particularly useful in the discussion of slow-time-scale energy dynamics in slightly dissipative systems (Chapter 5), as well as in the analysis of stochastic magnetization dynamics (Chapter 10). In general, the precessional trajectory on the unit sphere inside the central region (graph edge) Ik will be denoted as Ck (g), and the corresponding period as Tk (g), where g = gL (m; ha ) is the constant energy value along the trajectory.