arXiv subjects

A. E. Botha

Publications and source records attributed to A. E. Botha.

13 recordsLinked to original sources

arXiv2024

Hysteresis and chaos in anomalous Josephson junctions without capacitance

Usually, overdamped Josephson junctions do not exhibit chaotic behavior in their phase dynamics, either because the phase space dimension is less than three (as in the case of a single overdamped ac-driven junction) or due to the general tendency of systems to become less chaotic with increasing dissipation (as in the case of coupled overdamped junctions). Here we consider the so-called $φ_0$ superconductor/ferromagnet/superconductor Josephson junction in which the current flowing through the junction may induce magnetization dynamics in the ferromagnetic interlayer. We find that due to the induced magnetization dynamics, even in the overdamped limit, i.e. for a junction without capacitance, the junction may exhibit chaos and hysteresis that in some cases leads to multiple branches in its current-voltage characteristics. We also show that pulsed current signals can be used to switch between the different voltage states, even in the presence of added thermal noise. Such switching could be used in cryogenic memory components.

cond-mat.supr-con↗

arXiv2022

Simulation of the Einstein-de Haas effect combining molecular and spin dynamics

The spin and lattice dynamics of a ferromagnetic nanoparticle are studied via molecular dynamics and with semi-classical spin dynamics simulations where spin and lattice degrees of freedom are coupled via a dynamic uniaxial anisotropy term. We show that this model conserves total angular momentum, whereas spin and lattice angular momentum are not conserved. We carry out simulations of the the Einstein-de Haas effect for a Fe nanocluster with more than 500 atoms that is free to rotate, using a modified version of the open-source spinlattice dynamics code (SPILADY). We show that the rate of angular momentum transfer between spin and lattice is proportional to the strength of the magnetic anisotropy interaction. The addition of the anisotropy allows full spin-lattice relaxation to be achieved on previously reported timescales of \sim 100 ps and for tight-binding magnetic anisotropy energies comparable to those of small Fe nanoclusters.

cond-mat.mtrl-sci↗

arXiv2021

Bifurcation structure and chaos in nanomagnet coupled to Josephson junction

Recently an irregular easy axis reorientation demonstrating the Kapitza pendulum features were observed in numerical simulations of nanomagnet coupled to the Josephson junction. To explain its origin we study the magnetization bifurcations and chaos which appear in this system due to interplay of superconductivity and magnetism. The bifurcation structure of the magnetization under the variation of Josephson to magnetic energy ratio as a control parameter demonstrates several precessional motions. They are related to chaotic behavior, bistability, and multiperiodic orbits in the ferromagnetic resonance region. Effect of external periodic drive on the bifurcation structure is investigated. The results demonstrate high-frequency modes of periodic motion and chaotic response near resonance. Far from the ferromagnetic resonance we observe a quasiperiodic behavior.

cond-mat.supr-con↗

arXiv2020

Analytical criteria for magnetization reversal in $φ_0$ Josephson junction

The $φ_0$ Josephson junctions formed by ordinary superconductors and a magnetic non-centrosymmetric interlayer are studied. We derive an analytical solution for the magnetization dynamics induced by an arbitrary current pulse and formulate the criteria for magnetization reversal. Using the obtained results, the form and duration of the current pulse are optimized. The agreement between analytical and numerical investigations is reached in the case of a large product of the ratio Josephson to magnetic energy, strength of spin-orbit interaction and a minimal value of the current pulse. The obtained results allow one to predict magnetization reversal at the chosen system parameters.

cond-mat.supr-con↗

arXiv2019

Directional bonding explains high conductance values of atomic contacts in bcc metals

Atomic-sized junctions of iron, created by controlled rupture, present unusually high values of conductance compared to other metals. This result is counter-intuitive since, at the nanoscale, body-centered cubic metals are expected to exhibit lower coordination than face-centered cubic metals. In this work, classical molecular dynamics simulations of contact rupture, using an interatomic potential that accounts for directional bonding, yield highly-coordinated stable structures before rupture, unlike an isotropic bonding potential, which results in the expected stable single-atom contacts. Density functional theory electronic transport calculations show that conductance values of these highly coordinated and highly stable structures, can explain the experimentally measured values for conductance of body-centered cubic atomic contacts, thus revealing the important role of directional bonding in these metals.

cond-mat.mes-hall↗

arXiv2018

Devil's Staircases in SFS Josephson Junctions

We study the effect of coupling between the superconducting current and magnetization in the superconductor/ferromagnet/superconductor Josephson junction under an applied circularly polarized magnetic field. Manifestation of ferromagnetic resonance in the frequency dependence of the amplitude of the magnetization and the average critical current density is demonstrated numerically. The IV-characteristics show subharmonic steps that form devil's staircases, following a continued fraction algorithm. The origin of the found steps is related to the effect of the magnetization dynamics on the phase difference in the Josephson junction. The dynamics of our system is described by a generalized RCSJ model coupled to the Landau-Lifshitz-Gilbert equation. In the suplement we justify analytically the appearance of the fractional steps in IV-characteristics of the superconductor/ferromagnet/superconductor Josephson junction.

cond-mat.supr-con↗

arXiv2018

Re-orientation of easy axis in $φ_0$ junction

We study theoretically a dynamics of $φ_0$ junction with direct coupling between magnetic moment and Josephson current which shows features close to Kapitza pendulum. We have found that starting with oscillations along $z$-axis, the character of magnetization dynamics changes crucially and stable position of magnetic moment $\vec m$ is realized between $z-$ and $y$-axes depending on parameters of the system. Changes in critical current and spin-orbit interaction lead to the different stability regions for magnetization. An excellent agreement between analytical and numerical results is obtained for low values of the Josephson to magnetic energy ratio.

cond-mat.supr-con↗

arXiv2016

Characteristic distribution of finite-time Lyapunov exponents for chimera states

It is shown that probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a characteristic shape. Such distributions could be used as a signature of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. In such cases, the characteristic distribution may be obtained indirectly, via embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist, unnoticed.

nlin.CD↗

arXiv2014

Computer Assisted 'Proof' of the Global Existence of Periodic Orbits in the Rössler System

The numerical optimized shooting method for finding periodic orbits in nonlinear dynamical systems was employed to determine the existence of periodic orbits in the well-known Rössler system. By optimizing the period $T$ and the three system parameters, $a$, $b$ and $c$, simultaneously, it was found that, for any initial condition $(x_0,y_0,z_0) \in \Re^3$, there exists at least one set of optimized parameters corresponding to a periodic orbit passing through $ (x_0,y_0,z_0)$. After a discussion of this result it was concluded that its analytical proof may present an interesting new mathematical challenge.

nlin.CD↗

arXiv2014

Optimized shooting method for finding periodic orbits of nonlinear dynamical systems

An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the additional advantage of being relatively simple to implement. It is also applicable to both autonomous and non-autonomous systems. As an example of its use, it is employed to find periodic orbits in the Rössler system, a coupled Rössler system, as well as an eight-dimensional model of a flexible rotor-bearing; problems which have been treated previously via two related methods. The results agree with the previous methods and are seen to be more accurate in some cases. A simple implementation of the method, written in the Python programming language, is provided as an Appendix.

nlin.CD↗

arXiv2014

Structured Chaos in a Devil's Staircase of the Josephson Junction

The phase dynamics of Josephson junctions under external electromagnetic radiation is studied through numerical simulations. Current-voltage characteristics, Lyapunov exponents and Poincare 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 Josephson junction 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.

cond-mat.supr-con↗

arXiv2013

Devil's Staircases and Continued Fractions in the Josephson Junctions

The detailed numerical simulations of the IV-characteristics of Josephson junction under external electromagnetic radiation show devil's staircases within different bias current intervals. We have found that the observed steps form very precisely continued fractions. Increasing of the amplitude of radiation shifts the devil's staircases to higher Shapiro steps. The algorithm of appearing and detection of the subharmonics with increasing radiation amplitude is proposed. We demonstrate that subharmonic steps registered in the famous experiments by A. H. Dayem and J. J. Wiegand [Phys. Rev 155, 419 (1967)] and J. Clarke [Phys. Rev. B 4, 2963 (1971)] also form continued fractions.

cond-mat.supr-con↗

arXiv2012

Manifestation of Resonance-Related Chaos in Coupled Josephson Junctions

Chaotic features of systems of coupled Josephson junctions are studied. Manifestation of chaos in the temporal dependence of the electric charge, related to a parametric resonance, is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. The number of junctions in the stack strongly influences the fine structure in the current voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency over a range of conditions and parameters. General features of the system are analyzed by means of a linearized equation and the criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.

cond-mat.supr-con↗