M. d’Aquino

Midpoint numerical technique for stochastic Landau-Lifshitz-Gilbert dynamics

The implicit midpoint time-integration technique is applied to the stochastic Landau-Lifshitz-Gilbert (LLG) equation. The numerical scheme converges to the Stratonovich solution in the limit of vanishing time step. It preserves the magnetization magnitude and the main energy balance properties of the LLG equation independently of the time step. The numerical technique is then applied to the study of superparamagnetic state in a small spheroidal particle, and the numerical results are compared with the theory.

Thermal stability in spin-torque-driven magnetization dynamics

In this article, thermal fluctuations in spin-torque-driven magnetization dynamics are described phenomenologically by introducing a Gaussian white noise term in the Landau-Lifshitz-Slonczewski equation. The ensuing stochastic magnetization dynamics is studied by considering the Fokker-Planck equation for the probability distribution of magnetization. The corresponding Fokker-Planck for the energy probability distribution is then derived in the limit of small fluctuations by averaging with respect to fast-time-scale precessional dynamics. By using this equation the stationary probability distribution of energy is analytically determined. This distribution has peaks around stable stationary states as well as around self-oscillatory regimes. On this basis, we define an effective potential barrier controlling switching between stable equilibrium states and self-oscillatory regimes.

Power spectrum of current-induced magnetization dynamics in uniaxial nanomagnets

Nanomagnets with uniaxial symmetry driven by spin polarized currents are considered, in which anisotropy, applied field, and spin polarization are all aligned along the symmetry axis. Thermal fluctuations are taken into account by adding a Gaussian white noise stochastic term to the equation for the deterministic dynamics. The corresponding Fokker-Planck equation is derived and it is solved by using separation of variable and eigenfunction expansion techniques. From the solution of the Fokker-Planck equation, the autocorrelation function and the power spectral density of magnetization are computed. The position and the linewidth of the peaks in the power spectral density are discussed in detail.

Quasiperiodic magnetization dynamics in uniformly magnetized particles and films

We study Landau–Lifshitz–Gilbert (LLG) magnetization dynamics in uniformly magnetized uniaxial particles and films subject to circularly polarized electromagnetic fields. Rotational invariance of the system and the introduction of an appropriate rotating reference frame permit one to reduce the problem to the study of an autonomous dynamical system on the unit sphere. Quasiperiodic magnetization dynamics correspond to limit cycles of this reduced dynamical system. A perturbation technique based on the Poincare–Melnikov method is applied to predict the existence, the number, the shape, and the stability of these limit cycles for small value of the damping constant in the LLG equation.

Model of phase locking in spin-transfer-driven magnetization dynamics

A simplified model of phase locking is discussed, which can be fully solved in analytical terms with no limitations as to the intensity of the coupling mechanism responsible for the locking. A nanomagnet with uniaxial symmetry is considered, jointly driven by a spin-polarized current, a dc magnetic field along the symmetry axis, and a radio-frequency circularly polarized magnetic field. The conditions are determined under which locking occurs between current-induced oscillations and the action of the rf field. The locking effect exhibits hysteresis as a function of the current.

Numerical integration of Landau–Lifshitz–Gilbert equation based on the midpoint rule

The midpoint rule time discretization technique is applied to Landau–Lifshitz–Gilbert (LLG) equation. The technique is unconditionally stable and second-order accurate. It has the important property of preserving the conservation of magnetization amplitude of LLG dynamics. In addition, for typical forms of the micromagnetic free energy, the midpoint rule preserves the main energy balance properties of LLG dynamics. In fact, it preserves LLG Lyapunov structure and, in the case of zero damping, the system free energy. All the above preservation properties are fulfilled unconditionally, namely, regardless of the choice of the time step. The proposed technique is then tested on the standard micromagnetic problem No. 4. In the numerical computations, the magnetostatic field is computed by the fast Fourier transform method, and the nonlinear system of equations connected to the implicit time-stepping algorithm is solved by special and reasonably fast quasi-Newton technique.

Current-driven chaotic magnetization dynamics in microwave assisted switching of spin-valve elements

The switching process of a uniformly magnetized spin-valve is considered. The system is subject to external dc applied fields and injected radio-frequency (RF) spin-polarized currents. The possibility of using the RF power to obtain a reduced coercivity of the particle is related to the onset of chaotic magnetization dynamics for moderately low values of the RF current amplitude. Perturbation technique for the estimation of the reduced coercive field is developed and applied to the microwave assisted switching of the particle. Numerical simulations confirm the predictions of the theory.

Spin-wave analysis of uniaxial nanopillar devices

The spin-wave instability of self-oscillations in uniaxial nanopillar devices is studied. It is demonstrated that under certain conditions these self-oscillations are stable with respect to spin-wave perturbations. This theoretical result is consistent with experimentally observed stability of large angle self-oscillations driven by spin-polarized current injection.

Large Hysteresis effect in Synchronization of Nanocontact Vortex Oscillators by Microwave Fields.

Current-induced vortex oscillations in an extended thin-film with point-contact geometry are considered. The synchronization of these oscillations with a microwave external magnetic field is investigated by a reduced order model that takes into account the dynamical effects associated with the significant deformation of the vortex structure produced by the current, which cannot be taken care of by using the standard rigid vortex theory. The complete phase diagram of the vortex oscillation dynamics is derived and it is shown that strong hysteretic behavior occurs in the synchronization with the external field. The complex nonlinear nature of the synchronization manifests itself also through the appearance of asymmetry in the locking frequency bands for moderate microwave field amplitudes. Predictions from the reduced order model are confirmed by full micromagnetic simulations.

Micromagnetic study of phase-locking in spin-transfer nano-oscillators driven by currents and ac fields

The magnetization dynamics of a spin-transfer nano-oscillator is studied for a system subject to the combined action of dc spin-polarized electric current and microwave circularly polarized applied field. The uniform mode theory is developed for a spin-valve with an arbitrary orientation of the polarizer. The theory enables one to predict the control parameters for the synchronization between the magnetization self-oscillation and the external microwave field. Full micromagnetic simulations are performed with the predicted control parameters, and they demonstrate the hysteretic nature of the synchronization in very good agreement with the theory.