Solitonic Transport in Magnetic Nanoparticle Systems

Project leaders

Stefano Ruffo, Ramaz Khomeriki

Agreement

GEORGIA - SRNSF - Shota Rustaveli National Science Foundation

Call

CNR-SRNSF 2016-2017

Department

Physical sciences and technologies of matter

Thematic area

Physical sciences and technologies of matter

Status of the project

New

Research proposal

The investigations of assembly of magnetic nanoparticles [1-3] became one of the hot topics of physics since the development of technology calls for the realization of smaller and smaller magnetic units. In this connection, there exists an intense interest to engineer new materials and devices, such as strong magnets for high-end electronics [4], logic gates [5], thermally stable magnetic memories [6] and soft magnetic materials for magnetic sensors [6]. However, in order to reveal the full potential of these materials, quantitative theoretical and experimental study of propagation of magnetic excitations (localized and/or delocalized) is essential. In our recent work [7], funded by joint grant from CNRS and SRNSF, we have studied the propagation and tunneling of localized modes through multiferroic interfaces. In another recent work of ours [8] we have investigated the long-range interaction induced ordering in needle shaped three-dimensional classical spin systems with purely dipolar interactions. In this project we aim at combining the experience cumulated these studies with another work done more recently[9] where we investigate soliton propagation through long-range interacting systems and, in particular, in chains of magnetic nanoparticles.

The first step along this line will be the examination of a chain of anharmonic oscillators coupled by long-range forces. The problem of propagation of nonlinear excitations in such systems has not been studied yet; up to now only the localizations in systems with nearest neighbor couplings have been considered. Thus, we will examine the coupled equations which follow from the Hamiltonian for the chain of anharmonic oscillators. Interesting effects are expected in the long-range case, particularly, the phase and group velocities should diverge in the long wavelength limit. Let us remark that long-range forces are present in dipolar systems and, thus, after performing simulations and getting estimates for characteristic soliton parameters we will switch to magnetic nanoparticle systems and check the possibility of soliton propagation there.

For the analytical treatment of nanoparticle magnetic chains we start with the full dipolar Hamiltonian: for instance, we will consider the case of Cobalt nanoparticles with magnetic moment 20 Bohr's magneton and separation length 20nm. For computer simulations we will use landau-Lifshitz-Gilbert equation driving it by one end with the signal compatible with the envelope soliton shape. One should seek for appropriate parameters to ensure a good fit with the real experimental situation.

Our analytical approach is based on the reduction of the dynamical equations for anharmonic latices and dipolar systems to the exactly solvable Nonlinear Schroedinger Equation in order to write down an approximate analytical soliton solution of the problem. The method of reduction is an universal Reductive Perturbation Method on which we have published several papers in the past (see e.g. Refs. [7,10]).

Thus the project activities could be divided into two main tasks: 1) Analytical reduction of a long-range anharmonic oscillator model to the Nonlinear Schroedinger Equation and comparison of the solution with the results of numerical experiments. By this we will prove the applicability of the Reductive Perturbation Method to long-range systems; 2) Using the scheme developed for the long-range oscillator chain, we will examine a magnetic nanoparticle chain and arrays for the same purpose, i.e. to find an approximate form of solitary solution. The results will be compared with direct numerical simulations on the Landau-Lifshitz-Gilbert equation.

It should be especially emphasized that, besides the applied character of the proposed research, the results could be interesting from the point of fundamental research as well, as far as dynamical properties to be studied in the present project could characterize other long-range interacting systems (gravitational and Coulomb forces). Therefore the research proposed here could be among the few, if not the first, experimentally testable prediction of the dynamical properties of long-range interacting systems.

R E F E R E N C E S

[1] M. Varon, M. Beleggia, T. Kasama, R. J. Harrison, R. E. Dunin-Borkowski, V. F. Puntes & C. Frandsen, "Dipolar Magnetism in Ordered and Disordered Low-Dimensional Nanoparticle Assemblies", Scientific Reports. 3, 1234 (2013).
[2] Sugawara, A. & Scheinfein, M. R. "Room-temperature dipole ferromagnetism in linear-self-assembling mesoscopic Fe particle arrays", Phys. Rev. B 56, R8499-R8502 (1997).
[3] Russier, V. "Calculated magnetic properties of two-dimensional arrays of nanoparticles at vanishing temperature", J. Appl. Phys. 89, 1287-1294 (2001).
[4] Jones, N. "The pull of stronger magnets", Nature 472, 22-23 (2011).
[5] Cowburn, R. P. & Welland, M. E. "Room temperature magnetic quantum cellular automata", Science 287, 1466-1468 (2000).
[6] Zeng, H., Li, J., Liu, J. P., Wang, Z. L. & Sun, S. H. "Exchange-coupled nanocomposite magnets by nanoparticle self-assembly", Nature 420, 395-398 (2002).
[7] L. Chotorlishvili, R. Khomeriki, A. Sukhov, S. Ruffo, J. Berakdar, "Dynamics of Localized Modes in a Composite Multiferroic Chain", Phys. Rev. Lett, 111, 117202 (2013).
[8] G. Miloshevich, Th. Dauxois, R. Khomeriki, S. Ruffo, "Dipolar needles in the microcanonical ensemble: Evidence of spontaneous magnetization and ergodicity breaking", Europhys. Lett., 104, 17011 (2013).
[9] G. Miloshevich, J.P. Nguenang, Th. Dauxois, R. Khomeriki, S. Ruffo, "Instabilities and relaxation to equilibrium in long-range oscillator chains", Phys. Rev. E 91, 032927, (2015).
[10] R. Khomeriki, S. Lepri, S. Ruffo, "Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model", Physical Review E, 70, 066626.

Research goals

In the present project we aim at investigate the physics of long-range interacting systems on the particular example of magnetic dipolar interactions. In conventional materials, dipolar magnetism is generally considered negligible, however there are relevant experimental activities concerning ''meta-materials'' where atoms are replaced by nanoparticles, for which dipolar interactions overwhelm inter-particle exchange coupling leading to dipolar magnetic ordering at room temperatures and, possibly, the manifestation of the exotic phenomena typical of long-range systems such as ensemble inequivalence, negative specific heat, temperature jumps and ergodicity breaking. Via numerical simulations, we will mimic realistic experimental situations in magnetic nanoparticle systems finding signatures of propagation of long range localized modes, giving thus specific experimental predictions. Analytical schemes that we have developed will be used for constructing weakly nonlinear solutions and then verifying the results via direct numerical simulations of the Landau-Lifshitz-Gilbert equation with realistic experimental parameters. The italian side will be concentrated mainly on the theoretical aspects of long-range interacting systems, while Georgian side will conduct numerical simulations on the model equations.

Last update: 15/09/2025