nonlinear magnetization dynamics in nanosystems, 2009, p.464

[...]... magnetization dynamics, which is a generic case in most engineering applications The chapter contains many examples of numerical modeling of magnetization dynamics problems One such problem is of special theoretical interest This problem is related to the rotationally invariant CHAPTER 1 Introduction 19 magnetization dynamics in uniaxial particles studied in Chapter 7 It is pointed out in that chapter... motions under rotating external field and magnetization self-oscillations caused by spin-polarized current injection Chapter 6 is concerned with the analytical study of precessional switching of magnetization in thin films The physics of this switching is quite different from the conventional damping switching In the case of damping switching, magnetization reversals are produced by applying magnetic fields... randomly perturbed magnetization dynamics by using stochastic processes on graphs This analysis takes advantage of the fact that the randomly perturbed magnetization dynamics has two distinct time scales: the fast time scale of precessional dynamics and the slow time scale of magnetization dynamics caused by damping, thermal fluctuations, and spin-polarized current injection Randomly perturbed magnetization. .. switching” Precessional switching is usually realized in magnetic nanofilms through the following steps The magnetization is initially along the film easy axis and a magnetic field is applied in the film plane almost CHAPTER 1 Introduction 9 orthogonal to the magnetization This field produces a torque which tilts the magnetization out of the film plane This, in turn, results in a strong vertical demagnetizing... stable singledomain magnetization configurations in the free layer The chapter begins with the discussion of the generalization of the LLG equation to the case of spin-polarized current injection Following the work of J.C Slonczewski (based on the semiclassical approach), an additional spin-torque term is introduced in the LLG equation and various mathematically equivalent forms of the resulting equation... notion of precessional switching is defined in precise terms based on the properties of phase portraits of nonlinear magnetization dynamics Namely, it is demonstrated that the application of an external magnetic field results in the modification of the original phase portrait when heteroclinic trajectories are broken into homoclinic trajectories More importantly, new precessional magnetization trajectories... analysis of spatially nonuniform magnetization dynamics, where it leads to complete spatial decoupling in computations The midpoint scheme has been extensively tested by comparing the numerical results obtained by using this scheme with analytical results for P-mode solutions derived in Chapter 7 for the magnetization dynamics driven by circularly polarized rf fields in uniaxially symmetric particles... so-called Suhl instabilities The analytical expression for large magnetization motions (P-modes) in particles with uniaxial symmetry opens the possibility to carry out the analysis of spin-wave perturbations and spin-wave instabilities for spatially uniform large magnetization motions This analysis reveals the remarkable result that the rf input powers capable of inducing spin-wave instabilities are... The presence of eddy currents may be roughly taken into account by renormalizing the damping constant in the LL or LLG dynamics However, magnetization dynamics in metallic systems will not be discussed in detail 27 2.2 Landau–Lifshitz–Gilbert Equation 2.2 LANDAU–LIFSHITZ–GILBERT EQUATION Another equation for the description of magnetization dynamics in ferromagnets has been proposed by Gilbert [284,285]... bath that leads to damping is accounted for by introducing M × (M × Heff ) or M × ∂M/∂t terms and by slightly modifying the precessional term, i.e., by slightly changing γ In this sense, one might say that the true damping is represented by a certain linear combination of terms M × Heff and M×(M × Heff ) or terms M×Heff and M×∂M/∂t According to Eq (2.22), M×Heff can be expressed in terms of M×∂M/∂t and . the topological properties of the phase portrait for the precessional dynamics is by introducing an associated graph, with graph edges representing central regions and graph nodes representing. magnetization in thin films. The physics of this switching is quite different from the conventional damping switching. In the case of damping switching, magnetization reversals are produced by applying magnetic. separatrices. Then, the “unit-disk” representation of the phase portrait of the precessional dynamics is introduced. In this representation, cartesian axes coincide with the principal anisotropy