arXiv subjects

S. Murugesh

Publications and source records attributed to S. Murugesh.

14 recordsLinked to original sources

arXiv2020

Exact and non-exact Fermi-Pasta-Ulam-Tsingou recurrences in a Heisenberg ferromagnet

We visualize the Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in a classical Heisenberg ferromagnetic (HF) spin chain by exploiting its gauge eq uivalence to the nonlinear Schrödinger equation (NLSE). We discuss two types of spatially periodic breather excitations in the spin chain, that are associated with: (I) Akhmediev breather, and (II) Galilean transformed Akhmediev breather. The recurrence in the former is exact in the sense that the initial and final states are identical. In the later, the spin chain undergoes an additional global rotation during the rec urrence process, which makes the initial and final states distinguishable. Both the complex solutions (I) and (II) nevertheless show a definit e phase shift during the recurrence process. A one-to-one correspondence between HF spin chain and the NLSE seems missing by virtue of the clo seness of the FPUT recurrence.

nlin.PS↗

arXiv2019

Rogue breather modes: Topological sectors, and the `belt-trick', in a one-dimensional ferromagnetic spin chain

We present explicit solutions for breather soliton modes of excitation in the one-dimensional Heisenberg ferromagnetic spin chain. We identify a characteristic geometrical feature of these breather modes wherein a helicoidal configuration of spins is continuously transformed to one which differs from the initial helicoid by a total twist of `2'. This is a curious manoeuvre popularly known as the `belt trick', an illustration of the simple connectedness of the $\rm{SU}(2)$ group manifold, and its rotation period $4π$. We show that this effectively splits the configuration space of the ferromagnetic chain in one-dimension into two topological sectors, distinguished by their total twist -- either `0', or `1'. Further, the energy lower bound of the two sectors is separated by a finite gap varying inversely with the size of the lattice.

nlin.SI↗

arXiv2017

Knot soliton solutions for the one-dimensional non-linear Schrödinger equation

We identify that for a broad range of parameters a variant of the soliton solution of the one-dimensional non-linear Schr\"{odinger} equation, the {\it breather}, is distinct when one studies the associated space curve (or soliton surface), which in this case is knotted. The signi ficance of these solutions with such a hidden non-trivial topological element is pre-eminent on two counts: it is a one-dimensional model, and the no nlinear Schrödinger equation is well known as a model for a variety of physical systems.

nlin.PS↗

arXiv2016

Spin breather and rogue formations in a Heisenberg ferromagnetic system

We construct explicit spin configurations for the breather solution of a one-dimensional Heisenberg ferromagnetic spin system. This corresponds to the breather soliton solution of the gauge equivalent nonlinear Schrödinger equation. There are three broad cases, wherein the solution shows distinct behavior. Of particular interest to our study is the rogue behavior in spin field terms.

nlin.PS↗

arXiv2014

Spin-Transfer-Torque Driven Magneto-Logic OR, AND and NOT Gates

We show that current induced magneto-logic gates like AND, OR and NOT can be designed with the simple architecture involving a single nano spin-valve pillar, as an extension of our recent work on spin-torque-driven magneto-logic universal gates, NAND and NOR. Here the logical operation is induced by spin-polarized currents which also form the logical inputs. The operation is facilitated by the simultaneous presence of a constant controlling magnetic field, in the absence of which the same element operates as a magnetoresistive memory element. We construct the relevant phase space diagrams for the free layer magnetization dynamics in the monodomain approximation and show the rationale and functioning of the proposed gates. The flipping time for the logical states of these non-universal gates is estimated to be within nano seconds, just like their universal counter parts.

cond-mat.mes-hall↗

arXiv2014

Spin-Transfer-Torque Driven Magneto-Logic Gates Using Nano Spin-Valve Pillars

We propose model magneto-logic NOR and NAND gates using a spin valve pillar, wherein the logical operation is induced by spin-polarized currents which also form the logical inputs. The operation is facilitated by the simultaneous presence of a constant controlling magnetic field. The same spin-valve assembly can also be used as a magnetic memory unit. We identify regions in the parameter space of the system where the logical operations can be effectively performed. The proposed gates retain the non-volatility of a magnetic random access memory,(MRAM). We verify the functioning of the gate by numerically simulating its dynamics, governed by the appropriate Landau-Lifshitz-Gilbert equation with the spin-transfer torque term. The flipping time for the logical states is estimated to be within nano seconds.

cond-mat.mes-hall↗

arXiv2013

Synchronization and chaos in spin-transfer-torque nano-oscillators coupled via a high speed Op Amp

We propose a system of two coupled spin-torque nano-oscillators (STNOs), one driver and another response, and demonstrate {using numerical studies} the synchronization of the response system to the frequency of the driver system. To this end we use a high speed operational amplifier in the form of a voltage follower which essentially isolates the drive system from the response system. We find the occurrence of 1:1 as w ell as 2:1 synchronization in the system, wherein the oscillators show limit cycle dynamics. An increase in power output is noticed when the two oscillators are locked in 1:1 synchronization. Moreover in the cro ssover region between these two synchronization dynamics we show the existence of chaotic dynamics in the slave system. The coupled dynamics under periodic forcing, using a small ac input current in addition to that of the dc part, is also studied. The slave oscillator is seen to retain its qualitative identity in the parameter space in spite of being fed in, at times, a chaotic signal. Such electrically coupled STNOs will be highly useful in fabricating commercial spin-valve oscillators with high power output, when integrated with other spintronic devices.

cond-mat.mes-hall↗

arXiv2009

Bifurcation and chaos in spin-valve pillars in a periodic applied magnetic field

We study the bifurcation and chaos scenario of the macro-magnetization vector in a homogeneous nanoscale-ferromagnetic thin film of the type used in spin-valve pillars. The underlying dynamics is described by a generalized Landau-Lifshitz-Gilbert (LLG) equation. The LLG equation has an especially appealing form under a complex stereographic projection, wherein the qualitative equivalence of an applied field and a spin-current induced torque is transparent. Recently chaotic behavior of such a spin vector has been identified by Zhang and Li using a spin polarized current passing through the pillar of constant polarization direction and periodically varying magnitude, owing to the spin-transfer torque effect. In this paper we show that the same dynamical behavior can be achieved using a periodically varying applied magnetic field, in the presence of a constant DC magnetic field and constant spin current, which is technically much more feasible, and demonstrate numerically the chaotic dynamics in the system for an infinitely thin film. Further, it is noted that in the presence of a nonzero crystal anisotropy field chaotic dynamics occurs at much lower magnitudes of the spin-current and DC applied field.

cond-mat.other↗

arXiv2008

Spin-transfer torque induced reversal in magnetic domains

Using the complex stereographic variable representation for the macrospin, from a study of the nonlinear dynamics underlying the generalized Landau-Lifshitz(LL) equation with Gilbert damping, we show that the spin-transfer torque is effectively equivalent to an applied magnetic field. We study the macrospin switching on a Stoner particle due to spin-transfer torque on application of a spin polarized current. We find that the switching due to spin-transfer torque is a more effective alternative to switching by an applied external field in the presence of damping. We demonstrate numerically that a spin-polarized current in the form of a short pulse can be effectively employed to achieve the desired macro-spin switching.

cond-mat.other↗

arXiv2005

Equatorial and related non-equilibrium states in magnetization dynamics of ferromagnets: Generalization of Suhl's spin-wave instabilities

We investigate the nonlinear dynamics underlying the evolution of a 2-D nanoscale ferromagnetic film with uniaxial anisotropy in the presence of perpendicular pumping. Considering the associated Landau-Lifshitz spin evolution equation with Gilbert damping together with Maxwell equation for the demagnetization field, we study the dynamics in terms of the stereographic variable. We identify several new fixed points for suitable choice of external field in a rotating frame of reference. In particular, we identify explicit equatorial and related fixed points of the spin vector in the plane transverse to the anisotropy axis when the pumping frequency coincides with the amplitude of the static parallel field. We then study the linear stability of these novel fixed points under homogeneous and spin wave perturbations and obtain a generalized Suhl's instability criterion, giving the condition for exponential growth of P-modes under spin wave perturbations. Two parameter phase diagrams (in terms of amplitudes of static parallel and oscillatory perpendicular magnetic fields) for stability are obtained, which differ qualitatively from those for the conventional ferromagnetic resonance near thermal equilibrium and are amenable to experimental tests.

nlin.CD↗

arXiv2004

Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems

The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems. Typical examples include dynamics of filament vortices in ordinary and superfluids, spin systems, phases in classical optics, various systems encountered in physics of soft matter, etc. Such interrelations between geometric evolution and physical systems have yielded considerable insight into the underlying dynamics. We present a succinct tutorial analysis of these developments in this article, and indicate further directions. We also point out how evolution equations for moving surfaces are often intimately related to soliton equations in higher dimensions.

nlin.PS↗

arXiv2001

New geometries associated with the nonlinear Schrödinger equation

We apply our recent formalism establishing new connections between the geometry of moving space curves and soliton equations, to the nonlinear Schrödinger equation (NLS). We show that any given solution of the NLS gets associated with three distinct space curve evolutions. The tangent vector of the first of these curves, the binormal vector of the second and the normal vector of the third, are shown to satisfy the integrable Landau-Lifshitz (LL) equation ${\bf S}_u = {\bf S} \times {\bf S}_{ss}$, (${\bf S}^2=1$). These connections enable us to find the three surfaces swept out by the moving curves associated with the NLS. As an example, surfaces corresponding to a stationary envelope soliton solution of the NLS are obtained.

nlin.PS↗

arXiv2001

Kinematics of the Three Moving Space Curves Associated with the Nonlinear Schrödinger Equation

Starting with the general description of a moving curve, we have recently presented a unified formalism to show that three distinct space curve evolutions can be identified with a given integrable equation. Applying this to the nonlinear Schrödinger equation (NLS), we find three sets of coupled equations for the evolution of the curvature and the torsion, one set for each moving curve. The first set is given by the usual Da Rios-Betchov equations. The velocity at each point of the curve that corresponds to this set is well known to be a local expression in the curve variables. In contrast, the velocities of the other two curves are shown to be nonlocal expressions. Each of the three curves is endowed with a corresponding infinite set of geometric constraints. These moving space curves are found by using their connection with the integrable Landau- Lifshitz equation. The three evolving curves corresponding to the envelope soliton solution of the NLS are presented and their behaviors compared.

nlin.SI↗

arXiv2001

New connections between moving curves and soliton equations

Lamb has identified a certain class of moving space curves with soliton equations. We show that there are two other classes of curve evolution that may be so identified. Hence three distinct classes of curve evolution are associated with a given integrable equation. The nonlinear Schrödinger equation is used to illustrate this explicitly.

nlin.PS↗