Josephson current-assisted reversal of a single-domain nanoscale ferromagnet driven by cosine chirp pulse.

We study the microwave-induced magnetization reversal in two systems, the microwave-driven nanomagnet (NM) and the NM coupled to a Josephson junction (JJ) under the microwave field (NM-JJ-MW). The frequency of the applied cosine chirp pulse changes nonlinearly with time to match the magnetization precession frequency. The coupling between the NM and JJ reduces the magnetization switching time as well as the optimal amplitude of the microwave field as a result of manipulating the magnetization via Josephson-to-magnetic energy ratioG. The reversal effect in NM-JJ-MW is sufficiently robust against changes in pulse amplitude and duration. In this system, the increase ofGdecreases the possibility of the non-reversing magnetic response as the Gilbert damping increases without further increase in the external microwave field. We also discuss the magnetic response of the NM driven by the ac field of two JJs in which the time-dependent frequency is controlled by the voltage across the junctions. Our results provide a controllable scheme of magnetization reversal that might help to realize fast memory devices.

Chaotic dynamics from coupled magnetic monodomain and Josephson current.

The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in the absence of an external ac drive, whereas in the superconductor-ferromagnet-superconductor Josephson junction, known as the φ_{0} junction, the magnetic layer effectively provides two extra degrees of freedom that can facilitate chaotic dynamics in the resulting four-dimensional autonomous system. In this work, we use the Landau-Lifshitz-Gilbert model for the magnetic moment of the ferromagnetic weak link, while the Josephson junction is described by the resistively capacitively shunted-junction model. We study the chaotic dynamics of the system for parameters surrounding the ferromagnetic resonance region, i.e., for which the Josephson frequency is reasonably close to the ferromagnetic frequency. We show that, due to the conservation of magnetic moment magnitude, two of the numerically computed full spectrum Lyapunov characteristic exponents are trivially zero. One-parameter bifurcation diagrams are used to investigate various transitions that occur between quasiperiodic, chaotic, and regular regions as the dc-bias current through the junction, I, is varied. We also compute two-dimensional bifurcation diagrams, which are similar to traditional isospike diagrams, to display the different periodicities and synchronization properties in the I-G parameter space, where G is the ratio between the Josephson energy and the magnetic anisotropy energy. We find that as I is reduced the onset of chaos occurs shortly before the transition to the superconducting state. This onset of chaos is signaled by a rapid rise in supercurrent (I_{S}⟶I) which corresponds, dynamically, to increasing anharmonicity in phase rotations of the junction.

Bifurcation structure and chaos in dynamics of nanomagnet coupled to Josephson junction.

Irregular easy axis reorientation features are observed in numerical simulations of the nanomagnet coupled to the Josephson junction. We study magnetization bifurcations and chaos that appear in this system due to the interplay of superconductivity and magnetism. The bifurcation structure of magnetization under the variation of Josephson to magnetic energy ratio as a control parameter demonstrates several precessional motions that are related to chaotic behavior and orbits with different periodicities in the ferromagnetic resonance region. The effect of an external periodic signal on the bifurcation structure is also investigated. The results demonstrate high-frequency modes of a periodic motion and a chaotic response near resonance. Far from the ferromagnetic resonance, we observe a quasiperiodic behavior. The obtained results explain the irregular reorientation of the easy axis and the transitions between different types of motion.

Inertial effects in the dc+ac driven underdamped Frenkel-Kontorova model: Subharmonic steps, chaos, and hysteresis.

The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction.

Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model.

The devil's staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.

Structured chaos in a devil's staircase of the Josephson junction.

The phase dynamics of Josephson junctions (JJs) under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents, and Poincaré sections are analyzed in detail. It is found that the subharmonic Shapiro steps at certain parameters are separated by structured chaotic windows. By performing a linear regression on the linear part of the data, a fractal dimension of D = 0.868 is obtained, with an uncertainty of ±0.012. The chaotic regions exhibit scaling similarity, and it is shown that the devil's staircase of the system can form a backbone that unifies and explains the highly correlated and structured chaotic behavior. These features suggest a system possessing multiple complete devil's staircases. The onset of chaos for subharmonic steps occurs through the Feigenbaum period doubling scenario. Universality in the sequence of periodic windows is also demonstrated. Finally, the influence of the radiation and JJ parameters on the structured chaos is investigated, and it is concluded that the structured chaos is a stable formation over a wide range of parameter values.

Influence of coupling between junctions on breakpoint current in intrinsic Josephson junctions.

We study theoretically the current-voltage characteristics of intrinsic Josephson junctions in high-Tc superconductors. An oscillation of the breakpoint current on the outermost branch as a function of coupling alpha and dissipation beta parameters is found. We explain this oscillation as a result of the creation of longitudinal plasma waves at the breakpoint with different wave numbers. We demonstrate the commensurability effect and predict a group behavior of the current-voltage characteristics for the stacks with a different number of junctions. A method to determine the wave number of longitudinal plasma waves from alpha and beta dependence of the breakpoint current is suggested. We model the alpha and beta dependence of the breakpoint current and obtain good agreement with the results of the simulation.