M. d'Aquino

Theory of Injection Locking for Large Magnetization Motion in Spin-Transfer Nano-Oscillators

We study magnetization dynamics in spin-transfer devices subject to DC and microwave injected currents. When the frequency of the injected current is sufficiently close to the self-oscillation frequency of the device, phase-locking occurs. This phenomenon is theoretically studied by using Landau-Lifshitz equation with Slonczewski spin-torque term. By exploiting separation of time scales and using averaging technique, we derive equations which are applicable to the study of phase-locking for arbitrary large magnetization motion. The stability diagram in the (detuning, ac current)-plane is determined and it is shown that phase locking is hysteretic at sufficiently large ac currents.

Geometrical analysis of precessional switching and relaxation in uniformly magnetized bodies

Precessional switching and relaxation in a single-domain particle or film is studied by using the Landau-Lifshitz-Gilbert equation. The analysis of the switching process is based on the explicit knowledge of two integrals of motion for the magnetization dynamics in the conservative case. The knowledge of these integrals of motions enables one to carry out the geometrical analysis of the system and give the complete phase portrait. The relaxation process which occurs after the magnetization is reversed is analyzed by using geometrical methods and it is showed that the dynamical system exhibits entanglement of separatrices and riddled basins of attraction.

Analytical Description of Quasi-Random Magnetization Relaxation to Equilibrium

The Landau-Lifshitz (LL) dynamics of a uniformly magnetized particle is considered. The LL equation is written in the form of a Hamiltonian perturbed dynamical system. By using suitable averaging technique, the equation for the slow dynamics of the energy is derived. The averaging technique breaks up in the case of separatrix crossing. It is shown that, in the limit of small damping, the separatrix crossing can be described by using a probabilistic approach.

Thermal Stability in Uniaxial Nanomagnets Driven by Spin-Polarized Currents

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. It is shown that the deterministic dynamics and the thermal relaxation are both governed by an effective potential including the effect of current injection

Forces in magnetic fluids subject to stationary magnetic fields

In this paper, we study the stationary magnetic field effect of linear magnetic fluid. The fluid mechanical stress are taken into account by a properly defined fluid pressure. The expression of pressure is not unique and depends on which expression of the electromagnetic force density is considered.

Full Micromagnetic Numerical Simulations of Thermal Fluctuations

Thermal fluctuations for fine ferromagnetic particles are studied with the full micromagnetic analysis based on numerical integration of the spatially discretized Langevin-Landau-Lifshitz equation. These results can be used as a basis for the formulation of a standard problem to test the implementation of thermal fluctuations in numerical micromagnetic codes. To this end an example of micromagnetic analysis of thermal fluctuations in an ellipsoidal magnetic nanoparticle is presented.

A novel formulation for the numerical computation of magnetization modes in complex micromagnetic systems

The small oscillation modes in complex micromagnetic systems around an equilibrium are numerically evaluated in the frequency domain by using a novel formulation, which naturally preserves the main physical properties of the problem. The Landau-Lifshitz-Gilbert (LLG) equation, which describes magnetization dynamics, is linearized around a stable equilibrium configuration and the stability of micromagnetic equilibria is discussed. Special attention is paid to take into account the property of conservation of magnetization magnitude in the continuum as well as discrete model. The linear equation is recast in the frequency domain as a generalized eigenvalue problem for suitable self-adjoint operators connected to the micromagnetic effective field. This allows one to determine the normal oscillation modes and natural frequencies circumventing the difficulties arising in time-domain analysis. The generalized eigenvalue problem may be conveniently discretized by finite difference or finite element methods depending on the geometry of the magnetic system. The spectral properties of the eigenvalue problem are derived in the lossless limit. Perturbation analysis is developed in order to compute the changes in the natural frequencies and oscillation modes arising from the dissipative effects. It is shown that the discrete approximation of the eigenvalue problem obtained either by finite difference or finite element methods has a structure which preserves relevant properties of the continuum formulation. Finally, the generalized eigenvalue problem is solved for a rectangular magnetic thin-film by using the finite differences and for a linear chain of magnetic nanospheres by using the finite elements. The natural frequencies and the spatial distribution of the natural modes are numerically computed.

Magnetization self-oscillations induced by spin-polarized currents

The effect of a spin-polarized current on magnetization dynamics is described by the Landau-Lifshitz-Gilbert (LLG) equation with the addition of Slonczewski spin-transfer term. Detailed predictions about the existence, position, and stability of magnetization self-oscillations induced by the spin-polarized current are obtained by an analytical perturbative method for different levels of current injection and externally applied field. The two cases of opposite direction of current flow are discussed.

Three-Dimensional Computation of Magnetic Fields in Hysteretic Media With Time-Periodic Sources

In this paper, we present a 3-D numerical model of an integral formulation for the efficient computation of 3-D magnetic fields in hysteretic media with (time) periodic sources. The hysteretic medium is described by an isotropic vector generalization of the classical scalar Jiles-Atherton model. The nonlinear algebraic system is solved using Picard-Banach iterations in the frequency domain. The full matrices arising after the discretization of the main (linear) operators are suitably compressed and distributed among the nodes of a parallel computer system. The numerical model is applied for the nondestructive micromagnetic characterization (of mechanical properties) in metallic materials. In particular, the problem of estimating incremental permeability is analyzed.

Spin-Wave Instabilities in Spin-Transfer-Driven Magnetization Dynamics

We study the stability of magnetization precessions induced in spin-transfer devices by the injection of spin-polarized electric currents. Instability conditions are derived by introducing a generalized, far-from-equilibrium interpretation of spin waves. It is shown that instabilities are generated by distinct groups of magnetostatically coupled spin waves. Stability diagrams are constructed as a function of external magnetic field and injected spin-polarized current. These diagrams show that the application of larger fields and currents has a stabilizing effect on magnetization precessions. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.