Bifurcation magnetic resonance in films magnetized along hard magnetization axis

We study low-frequency ferromagnetic resonance in a thin film magnetized along the hard magnetization axis performing an analysis of magnetization precession dynamics equations and numerical simulation. Two types of films are considered: polycrystalline uniaxial films and single-crystal films with cubic magnetic anisotropy. An additional (bifurcation) resonance initiated by the bistability, i.e. appearance of two closely spaced equilibrium magnetization states is registered. The modification of dynamic modes provoked by variation of the frequency, amplitude, and magnetic bias value of the ac field is studied. Both steady and chaotic magnetization precession modes are registered in the bifurcation resonance range.     

Nonlinear dynamic magnetization regimes in (100) ferrite-garnet films

To study the nonlinear dynamics of a uniformly precessing magnetization in perpendicularly magnetized (100) ferrite-garnet films, equations of motion are numerically solved over a wide ac field frequency range. Bifurcation changes in the magnetization precession and the states of dynamic bistability have been detected. The conditions of high-amplitude regular and stochastic dynamic regimes are revealed, and the possibilities of controlling these precession regimes by applied magnetic fields are shown.     

Switching of precession regimes under the conditions of dynamic bistability of magnetization

The dynamics of the magnetization of a single-crystal film under the conditions of dynamic bistability has been investigated using numerical simulation. It has been shown that the use of an additional alternating magnetic field has made it possible to suppress the dynamic bistability of magnetization and to implement one of the two precession regimes depending on the field frequency. Multiple switching between magnetization precessions with different amplitudes can be performed directly from one regime to the other regime due to the corresponding change in the frequency of the additional magnetic field.     

Influence of additional perturbation on dynamical bistability in thin magnetic films

Bistable states in the precession dynamics of thin magnetic films with the stripe-domain structure have been investigated on the basis of a numerical solution of the equation of motion for magnetization. It has been found that weak additional perturbation due to chaotic and low-frequency harmonic oscillations of the magnetic field can substantially change the probability of the dynamical bistability regime and lead to the elimination of bistability establishing only one of the regimes.     

Stochastic resonance between the limiting cycles of precession dynamics

A new type of stochastic resonance that arises between two precession modes under dynamic bistability conditions and is excited by an alternating magnetic field, including a harmonic signal and a white noise, has been studied using a numerical analysis of the uniform magnetization precession in a thin film. The spectrum of the steady-state dynamics of the system at stochastic resonance has been investigated, and its distinctive features have been revealed for the longitudinal and transverse orientations of the additional alternating field.     

Magnetization stochastic dynamics in exchange-coupled layered structure

The stochastic and self-oscillation regimes established under the action of a longitudinal high-frequency magnetic field in a multilayer magnetic structure with antiferromagnetic exchange coupling are considered. A bifurcation diagram revealing the types of magnetization dynamic states is constructed in various frequency intervals. Poincaré diagrams are constructed for the stochastic regimes.     

Dynamics of a magnetic moment of finite dipolar lattices in the AC field

Dynamic regimes of a magnetic moment of 2 × 2, 3 × 3, and 4 × 4 square dipole lattices in the linearly and circularly polarized ac magnetic field and the perpendicular static field have been investigated. The possibility of regular and chaotic precession dynamics of the magnetic moment of the lattices has been demonstrated. A shift of the main magnetic resonance owing to the dipole–dipole interaction and additional resonances have been revealed. Quasiperiodic regimes and bistability states with a metastable chaotic attractor have been discovered.     

Average transient period for precession regimes in magnetic films with dynamic bistability

The average transient time of regular regimes corresponding to the dynamic bistability state is studied using analysis of uniform precession of magnetization of a thin magnetic film. The possibility of controlling the transient process parameter by an additional ac magnetic field in the form of a harmonic of noise signal is established. A new type of stochastic resonance is detected, which corresponds to the probability of high-amplitude precession and is manifested during a short noise action.     

Nonlinear regimes of resonance precession of the magnetization in a (111) iron-garnet film

The special features of precessional motion under ferromagnetic resonance conditions with perpen-dicular magnetization of the film are investigated on the basis of a numerical solution of the equations of motion of magnetization in a (111) type iron garnet film. Several nonlinear magnetization precession regimes exist for fixed values of the crystallographic and induced anisotropies. Depending on the value of the magnetizing field and the amplitude of the microwave field, precession occurs around the normal to the film with the third harmonic of the fundamental frequency making a small or large contribution to the nutation motion and with a small or large amplitude of the precession angle. Precession regimes around one of three symmetric directions different from the direction of the normal are possible. Narrow ranges of the static field, where dynamical bistability and regimes with a period which is a multiple of the period of the microwave field are realized, exist.     

Equilibrium states and quasi-static magnetization switching of a multilayer structure

The equilibrium orientations of magnetic moments that correspond to various values and directions of the biasing field are found in a set of magnetic films with cubic crystalline anisotropy and uniaxial induced anisotropy. The films are coupled by exchange interaction of the antiferromagnetic type. Field intervals are established where noncollinear and bistability states causing orientational phase transitions and hysteresis exist. Ninety degree magnetization switching (per switching cycle) of the magnetic moments of the films, as well as an orientational phase transition of bifurcation character, is discovered. Hysteresis loops for 180° in-plane magnetization switching are constructed.     

Magnetization dynamics under nonlinear ferromagnetic resonance conditions in a (111) film

The equation of motion of magnetization of a garnet ferrite (111) film is solved numerically. It is shown that different regimes of the resonance precession of magnetization are realized depending on the bias and microwave fields; the regimes differ in amplitude and in the shape of their magnetization precession trajectories. In addition, bifurcations occur which lead to an abrupt change in amplitude, to bistability, and to precession with a period that is a multiple of the microwave-field period.     

Specific features in precession dynamics of magnetization of a uniaxial magnetic film

The precession dynamics of the magnetization of a film with in-plane uniaxial anisotropy in the case of its biasing along the hard magnetization axis has been analyzed by numerically solving the Landau-Lifshitz equations. It has been revealed that the ferromagnetic resonance spectrum near the magnetic anisotropy field exhibits an additional peak, which is associated with the angular bistability due to the presence of two symmetric angular equilibrium positions. The trajectories of precession motion during biasing along the hard magnetization axis differ substantially from the trajectories corresponding to the biasing along the easy axis.     

Equilibrium values and dynamics of the net magnetic moment of a system of magnetic dipoles

Equilibrium states of different systems formed by coupled spherical bodies with dipole magnetic moments have been investigated using a numerical analysis. The bistable states and the corresponding values of the net magnetic moment are determined for a number of planar and three-dimensional systems of dipoles, and the conditions providing the existence of orientational configurations of coupled dipoles involved in the bistability are analyzed. The disturbances of the magnetic moment due to the quasi-static passage of an additional dipole and the dynamic modes excited by a homogeneous alternating magnetic field and represented by periodic, quasi-periodic, and chaotic oscillations of the magnetic moment of the system are considered for several types of systems. The bifurcation diagrams of the dynamic modes are constructed, and the specific features typical of the systems under consideration are revealed.     

Regular and chaotic dynamics of the dipole moment of square dipole arrays

Dipole lattices, which represent square dipole arrays, are investigated. Various types of equilibrium configurations of arrays are obtained, and conditions are shown under which these configurations are established. On the basis of parametric bifurcation diagrams, the main types of regular and chaotic oscillation regimes of the total dipole moment of a system are considered and their dependence on the amplitude, frequency, and polarization of an alternating field, as well as on the initial equilibrium configuration of arrays, is analyzed. Scenarios of the onset of chaotic regimes are demonstrated, including those that occur via the establishment and variation of quasiperiodic oscillations of the dipole moment of a system. The dynamic bistability state is revealed in which a stochastic resonance—an increase in the response of a system to a harmonic signal in the presence of noise—can be implemented.     

Stochastic resonance in a laser with saturable absorber

Summary We have investigated, experimentally and theoretically, the occurrence of stochastic resonance (SR) in a laser with saturable absorber: a non-linear optical system presenting optical bistability and self-pulsed regimes for the laser output intensity. In the optical-bistability regime we have obtained an excellent demonstration of SR by studying Fourier spectra and residence time distributions; operating just below the Hopf bifurcation that originates pulsed periodic regime we have obtained experimental evidence of the SR phenomenon. For operation close to the Hopf bifurcation, the theoretical analysis (performed through numerical simulations) has demonstrated that simultaneous presence of noise and periodic forcing generates excursions far from equilibrium; from the locking between these excursions and periodic forcing the SR phenomenon may arise. Paper presented at the International Workshop “Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena”, Elba, 5–10 June 1994.     

Bifurcation and Stability Analysis of the Equilibrium States in Thermodynamic Systems in a Small Vicinity of the Equilibrium Values of Parameters

The dynamic behavior of thermodynamic system, described by one order parameter and one control parameter, in a small neighborhood of ordinary and bifurcation equilibrium values of the system parameters is studied. Using the general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, we performed an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The peculiarities of the transition to an unstable state of the system are discussed, and the estimates of the transition time to the unstable state in the neighborhood of ordinary and bifurcation equilibrium values of parameters are given. The influence of an external field on the dynamic behavior of thermodynamic system is analyzed, and the peculiarities of the system dynamic behavior are discussed near the ordinary and bifurcation equilibrium values of parameters in the presence of external field. The dynamic process of magnetization of a ferromagnet is discussed by using the general methods of bifurcation and stability analysis presented in the paper.     

The role of emitter quasi-bound state and scattering on intrinsic bistability in resonant tunneling diodes

Usually, numerical self-consistent calculations predict a much larger intrinsic bistability region than actually is measured in resonant tunneling diodes (RTDs). In addition, numerical calculations have shown that scattering in the well reduces bistability. We used a unified treatment of current flowing from continuum states and emitter quasi-bound states to show numerically and analytically that not only the scattering in the quantum well but also the scattering in the emitter reduces bistability. Moreover, within the Hartree approximation, bistability occurs by tunneling resonantly between emitter quasi-bound state and well quasi-bound state as a pitchfork bifurcation.     

Equilibrium configurations and transitions between them in annular magnetic nanodipole systems

The equilibrium states of annular systems of magnetic dipoles have been studied by computer simulation. The bistability conditions under which the total magnetic moment of one of equilibrium configurations is zero, while the magnetic moment of another equilibrium configuration lies in the ring plane and is close to the sum of the magnetic moments of dipoles in the system, have been determined. The realization of other equilibrium configurations has also been demonstrated. We analyze transitions between equilibrium configurations by acting on the system by longitudinal and circular static fields, as well as transitions from the configuration with the maximal magnetic moment of the system to the configuration with zero total magnetic moment after the relaxation of oscillatory regimes excited by a varying field.     

Regular and chaotic precession of magnetization in magnetic films with a stripe domain structure

Based on a numerical solution of the equations of motion found over a wide range of frequencies of an alternating magnetic field, the nonlinear precession dynamics of magnetization are studied in thin-film structures of the (100) type with a stripe domain structure in a perpendicular bias field. The conditions are determined under which high-amplitude regular and chaotic dynamic regimes occur. Bifurcational variations in the precession of coupled magnetic moments and dynamic-bistability states are detected. The specific features of the spectrum of Lyapunov exponents and of time analogs of Poincaré cross sections of trajectories in chaotic regimes are considered.     

Tensile stress influence on coercive properties in Fe-rich cold-drawn amorphous wires

Magnetization reversal process has been studied in ferromagnetic amorphous wires of nominal composition Fe_77.5B₁₅Si_7.5 prepared by the cold-drawing technique. Conventional hysteresis loops were measured by the fluxmetric method in the presence of the tensile stress. The measurements have been performed by short movable coils. Application of tensile stress results in increase of the remanent magnetization and decrease of the switching field. When the tensile stress is high enough, the shape of hysteresis loop is perfectly rectangular that is associated with quick enough reversals of magnetization. These hysteresis loops could be considered as quasi-magnetically bistable, but it is not exactly the standard bistability. The experiments with short movable coils have demonstrated that two domain walls (in contrast with the case of the standard bistability) propagation is responsible for the remagnetization process of the inner core.