Modulational instability and nano-scale energy localization in ferromagnetic spin chain with higher order dispersive interactions

Kavitha, L.; Mohamadou, Alidou; Parasuraman, E.; Gopi, D.; Akila, N.; Prabhu, A.

doi:10.1016/j.jmmm.2015.11.036

Cited by 46 publications

(13 citation statements)

References 75 publications

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“…DNVMs with frequencies outside the phonon band of the lattice can be used for obtaining new types of DBs by superimposing a localizing function [20,25,[29][30][31][32]. It has been revealed that DNVMs affect the elastic constants of nonlinear lattices [21,33], and the modulational instability of DNVMs with frequencies outside the phonon band results in the formation of chaotic DBs [29,[34][35][36][37][38][39][40][41][42][43]. Recently, it has been demonstrated that DNVMs can be used to assess the accuracy of interatomic potentials [28].…”

Section: Introductionmentioning

confidence: 99%

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice

et al. 2022

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Section: Introductionmentioning

confidence: 99%

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice

et al. 2022

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“…DNVMs in hexagonal lattice [25] were studied in 2D materials [26], for example, in graphene [10,[27][28][29] and boron nitride [30]. Chaotic DBs can emerge in the lattices as a result of modulational instability of DNVMs [31][32][33][34][35][36][37]. Two-dimensional nonlinear lattices appear in a number of applications, for example, in the study of nonlinear excitations in mica [38][39][40][41], and model lattices [42][43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

One-component delocalized nonlinear vibrational modes of square lattices

Ryabov¹,

Chechin²,

Naumov

et al. 2022

Preprint

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All possible one-component delocalized nonlinear vibrational modes (DNVMs) in a square lattice are analyzed. DNVMs are obtained taking into account exclusively the symmetry of a square lattice, and therefore they exist regardless of the type of interactions between particles. In this work, the interactions of the nearest and next nearest neighbors are described by the β-FPU potential. For each DNVM, frequency, kinetic and potential energies are described as functions of amplitude. The mechanical stresses caused by DNVMs and the effect of DNVMs on the stiffness constants of the lattice are presented. DNVMs with higher vibration frequencies have a stronger effect on the mechanical properties of the lattice. Examples of analytical analysis of DNVMs are given. It is found that two of the sixteen one-component DNVMs can have frequencies above the phonon band in the entire range of their amplitudes. These DNVMs can be used to construct discrete breathers by applying localizing functions.

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“…Here we choose an alternative approach related to modulational instability of particular delocalized modes. Such instabilities lead to energy localization in the form of long-living chaotic DBs and subsequent transition to thermal equilibrium [22,[94][95][96][97][98][99][100][101][102][103]. In the course of this transition of a nonlinear chain, the local temperature and the specific heat can be calculated.…”

Section: Introductionmentioning

confidence: 99%

Effect of discrete breathers on the specific heat of a nonlinear chain

Singh,

Morkina,

Korznikova

et al. 2019

Preprint

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Defect-free crystal lattices can accommodate spatially localized, high amplitude atomic vibrations called either discrete breathers (DBs) or intrinsic localized modes (ILMs). This has been explored by a number of molecular dynamics studies and, in few cases, by the first-principles calculations. A number of experimental measurements of crystal vibrational spectra was performed aiming to prove the existence of DBs in thermal equilibrium at elevated temperature. However, the interpretation of these experimental results is still debated. Direct high-resolution imaging of DBs in crystals is hardly possible due to their nanometer size and short lifetime. An alternative way to substantiate the existence of DBs is to evaluate their impact on the measurable macroscopic properties of crystals and validate such prediction. One of such properties is specific heat. In fact, the measurements of heat capacity was done for alpha-uranium by Manley and co-workers in conditions where the presence of DBs was expected. In the present study, employing a one-dimensional nonlinear lattice with an on-site potential, we analyze the effect of DBs on its specific heat. In the most transparent way, this can be done by monitoring the chain temperature in a non-equilibrium process, at the emergence of modulational instability, with total energy of the chain being conserved. For the onsite potential of hard-type (soft-type) anharmonicity, the instability of q = π mode (q = 0 mode) results in the appearance of long-living DBs that gradually dissipate their energy and eventually the system approaches thermal equilibrium with spatially uniform and temporally constant temperature. The variation of specific heat at constant volume is evaluated during this relaxation process. It is concluded that DBs affect specific heat of the nonlinear chain and for the case of hard-type (softtype) anharmonicity they reduce (increase) the specific heat.

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Modulational instability and nano-scale energy localization in ferromagnetic spin chain with higher order dispersive interactions

Cited by 46 publications

References 75 publications

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice

Effect of the stiffness of interparticle bonds on properties of delocalized nonlinear vibrational modes in an fcc lattice

One-component delocalized nonlinear vibrational modes of square lattices

Effect of discrete breathers on the specific heat of a nonlinear chain

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