Excitation Of Discrete Breathers Research Articles

Dark discrete breather modes in a monoaxial chiral helimagnet with easy-plane anisotropy

Nonlinearity and discreteness are two pivotal factors for an emergence of discrete breather excitations in various media. We argue that these requirements are met in the forced ferromagnetic phase of the monoaxial chiral helimagnet $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$ due to the specific domain structure of the compound. The stationary, time-periodic breather modes appear as the discrete breather lattice solutions whose period mismatches with a system size. Thanks to easy-plane single-ion anisotropy intrinsic to $\mathrm{Cr}{\mathrm{Nb}}_{3}\mathrm{S}{}_{6}$, these modes are of the dark type with frequencies lying within the linear spin-wave band, close to its bottom edge. They represent cnoidal states of magnetization, similar to the well-known soliton lattice ground state, with differing but limited number of embedded $2\ensuremath{\pi}$ kinks. The linear stability of these dark breather modes is verified by means of Floquet analysis. Their energy, which is controlled by two parameters, namely, the breather lattice period and amplitude, falls off linearly with a growth of the kink number. These results may pave a path to design spintronic resonators on the base of chiral helimagnets.

Two-dimensional discrete breathers in fcc metals

The interest in discrete breathers (DB), i.e. a time-periodic and spatially localized vibrational mode in a defect free nonlinear lattice, is related to their ability to localize vibrational energy of the order of several eV. In the present work, for the first time, a systematic study of eight nonlinear vibrational modes localized in one spatial dimension and delocalized in the two other dimensions is performed by means of molecular dynamics simulations in defect-free single crystals of fcc metals (Al, Cu and Ni). For this goal, the standard embedded atom method potentials are employed. Calculations are performed at a zero temperature in three-dimensional computational cells. Excitation of DBs takes place via displacement of the specified atoms from their equilibrium lattice sites according to the patterns corresponding to the delocalized nonlinear vibrational modes (DNVMs) found earlier for a two-dimensional triangular lattice. It is revealed that only four out of the eight studied DNVMs can support stable two-dimensional DBs with the lifetimes in the range of 24–47 ps and accumulate vibrational energy of the order of 2 eV per atom. All excited DBs are characterized by a hard type of nonlinearity, i.e. the frequency increases with the increasing oscillation amplitude. Obtained results indicate the presence of a wide variety of nonlinear, spatially localized vibrational modes in three-dimensional lattices of fcc metals.

Excitation of Soliton-Type Waves in Crystals of the A3B Stoichiometry

Using the method of molecular dynamics and taking Ni3Al and Pt3Al as examples, crystals of the A3B composition are considered for the possibility of excitation of soliton-type waves in them. The potentials obtained by the embedded-atom method were used to describe interatomic interactions. It is shown that the harmonic external stimulus can excite waves of the soliton type in a Pt3Al crystal, but not in Ni3Al. Such compression–expansion waves are generated because of excitation of discrete breathers with soft nonlinearity that cannot exist in a Ni3Al crystal near the affected region. The detected waves are capable of propagating to thousands of nanometers along the Pt3Al crystal without losses of integrity and speed. The shape of the obtained wave corresponds to the kink solution of the sine-Gordon equation. The aggregate amount of energy transferred by a wave is determined by the number of rows of atoms involved in fluctuations; this may involve dozens and hundreds of electron volts.

Discrete breathers in biatomic crystals of AB and A 3 B composition

The conditions for the existence of discrete breathers (DBs) in biatomic crystals of AB and A 3 B composition are established, and their properties are studied by means of molecular mechanics using the examples of CuAu and Pt3Al, respectively. The phonon spectra of the crystals are analyzed, and a gap in the phonon spectrum of CuAu is obtained via considerable homogeneous elastic strain. There is a gap in the phonon spectrum of the Pt3Al crystal at zero strain, due to the considerable difference between the atomic weights of its components. The frequencies at which discrete breathers can exist in the considered crystals are determined. The energy localized on different types of DBs is estimated. The propagation of a current pulse through Pt3Al resulting in the excitation of DBs with mild nonlinearity is simulated.

Discrete breathers in alpha-uranium

Uranium is an important radioactive material used in the field of nuclear energy and it is interesting from the scientific point of view because it possesses unique structure and properties. There exist several experimental reports on anomalies of physical properties of uranium that have not been yet explained. Manley et al. [Phys. Rev. Lett. 96, 125501 (2006); Phys. Rev. B 77, 214305 (2008)] speculate that the excitation of discrete breathers (DBs) could be the reason for anisotropy of thermal expansion and for the deviation of heat capacity from the theoretical prediction in the high temperature range. In the present work, with the use of molecular dynamics, the existence of DBs in α-uranium is demonstrated and their properties are studied. It is found that DB frequency lies above the phonon band and increases with DB amplitude. DB is localized on half a dozen of atoms belonging to a straight atomic chain. DB in uranium, unlike DBs in fcc, bcc and hcp metals, is almost immobile. Thus, the DB reported in this study cannot contribute to thermal conductivity and the search for other types of DBs in α-uranium should be continued. Our results demonstrate that even metals with low-symmetry crystal lattices such as the orthorhombic lattice of α-uranium can support DBs.

Dynamics of Discrete Breathers in the Pt<sub>3</sub>Al Crystal

By method of molecular dynamics discrete breathers with soft and hard types of non-linearity in the Pt3Al crystal are studied. Obtained graphs characterize the spatial localization of the discrete breathers, the dependence of the frequency on the oscillation amplitude and the amount of energy localized on the discrete breathers. It is shown that the collision of moving discrete breathers may lead to the energy exchange between the breathers with some portion of the energy given to the Pt3Al lattice. The probability of excitation of discrete breathers in thermodynamic equilibrium is estimated.

Дискретные бризеры в кристалле CuAu

Molecular dynamics observed discrete breathers (DB) in CuAu crystal. To analyze the possible existence of DB had been calculated phonon density of states of the considered crystal. A function of formation of initial conditions for the excitation of discrete breather with a hard type of the nonlinearity in CuAu crystal. It is shown that it can be received in a close-packed row Cu atoms along the [110] direction. The conditions for the excitation of discrete breathers, as well as its dependence on the amplitude of the frequency. It is found that more than 0.55 Å is virtually no change in frequency is increased when the initial amplitude. An energy profile discrete breather with a hard type of nonlinearity. The basic directions of dispersion DB Energy. The conditions of formation of discrete breather with a mild type of the nonlinearity due to deformation of the crystal and the mass underestimation of copper atoms. It was found that the discrete breather with a mild type of the nonlinearity may exist in the gap of the phonon spectrum of the crystal under deformation or under-weight copper. The results indicate that DB soft type of nonlinearity is mainly localized on a single atom of copper and several tens sschestvuet wobble periods. Despite this, he is able to collectively focus the energy of about 0.9 eV, while the DB with a hard type of non-linearity is mainly localized to 6 atoms and their total energy of up to 2.1 eV.

Energy localization on the Al sublattice of Pt3Al with L12 order

A three-dimensional molecular-dynamics model of Pt3Al with L12 order was developed and found to support the excitation of discrete breathers (DBs) and energy localization on the Al sublattice. For an initial lattice temperature of 0 K, large-amplitude DBs polarized along [100] are found to be very weakly damped, retaining most of their initial energy for more than 1000 cycles, while DBs polarized along [111] damped out over ∼15 cycles. Because the DBs and their dissipation channels are confined to the Al sublattice, long-lived nonequilibrium states with large energy differences between the Al and Pt sublattices occur. Since collisions during irradiation more efficiently generate lattice vibrations in light atoms than heavy atoms, such nonequilibrium states may occur and alter the relaxation processes occurring during radiation damage.

О локализации энергии нелинейных и линейных колебаний атомов в модельной кристаллической решетке состава А3В

A three- dimensional molecular-dynamics model of Pt3Al with L12 order was developed and found to support the excitation of discrete breathers (DBs) and energy localization on the Al sublat-tice. For an initial lattice temperature of 0 K, large-amplitude DBs polarized along [100] are found to be very weakly damped, retaining most of their initial energy for more than 1000 cycles, while DBs polarized along [111] damped out over ~15 cycles. Because the DBs and their dissipation channels are confined to the Al sublattice, long-lived states with large energy differences between the Al and Pt sublattices occur.<br />

Spontaneous excitation of discrete breathers in crystals with the NaCl structure at elevated temperatures

The density of phonon states at various temperatures has been calculated for crystals with the NaCl structure with equal and strongly differing weights of anions and cations. It has been shown that, in the crystal with a considerable difference in the weights of components, a wide band gap exists in the spectrum of phonon states, which leads to spontaneous excitation of nonlinear localized vibrational modes—gap discrete breathers having frequencies inside the band gap, if the temperature is sufficiently high. It has been found that the peak of the density of phonon states lying above the spectrum of linear vibrations appears at elevated temperatures, which can indicate the existence of discrete breathers with corresponding frequencies. It has been noted that, previously, the existence of gap discrete breathers in the NaI crystal at 555 K was shown experimentally. The presented results bring up the question of the theoretical justification and experimental observation of the breathers with frequencies above the phonon spectrum.

Lifetime of gap discrete breathers in diatomic crystals at thermal equilibrium

Crystals having a gap in a phonon spectrum can support so-called gap discrete breathers (DBs), i.e., nonlinear localized vibrational modes existing in perfect crystals and having frequencies within the gap. In our recent work, for a two-dimensional crystal with stoichiometry A3B, we have demonstrated that if the atomic weight of the components is related as MA MB , then there is a wide gap in the phonon spectrum and the gap DBs can be easily excited. The situation is opposite if the above condition is not satisfied. In the present work the gap DBs are studied at thermal equilibrium, whereas in the previous study the temperature was zero. We demonstrate that in the crystal supporting DBs, in contrast to the opposite case, the lifetime of high-energy light atoms grows with temperature. The possible role of gap DBs in the thermally activated formation of vacancy and interstitial atom pairs (Frenkel pairs) was studied. We have measured the time needed for the appearance of a Frenkel pair as a function of temperature for the crystals supporting and not supporting DBs. A minor difference in waiting time of Frenkel pair nucleation was found in these two cases. We argue that, for the model and its parameters considered in the present work, the main mechanism of thermally activated Frenkel pair formation is the cooperative motion of atoms rather than the excitation of DBs.

Dissipative Breathers in rf SQUID Metamaterials

The existence and stability of dissipative breathers in rf SQUID (Superconducting Quantum Interference Device) arrays is investigated numerically. In such arrays, the nonlinearity which is intrinsic to each SQUID, along with the weak magnetic coupling of each SQUID to its nearest neighbors, result in the formation of discrete breathers. We analyze several discrete breather excitations in rf SQUID arrays driven by alternating flux sources in the presence of losses. The delicate balance between internal power losses and input power, results in the formation of dissipative discrete breather (DDB) structures up to relatively large coupling parameters. It is shown that DDBs may locally alter the magnetic response of an rf SQUID array from paramagnetic to diamagnetic or vice versa.

Discrete breathers in ac-driven nanoelectromechanical shuttle arrays

We investigate the dynamics of electrically ac-driven nanoelectromechanical shuttle arrays. The electromechanical coupling enforces long-range interactions. We find multistability regimes upon changing the voltage and frequency. We show that the instability driven by parametric amplification of sinusoidal mechanical waves leads to the creation of spatially localized mechanical oscillations, discrete breathers, and subsequently to an abrupt change in the electrical transport properties. In particular, we find current rectification, which is induced by the excitation of discrete breathers. This is of potential interest and use for nanomechanical sensor application.

Discrete Breathers in Nonlinear Magnetic Metamaterials

Magnetic metamaterials composed of split-ring resonators or U-type elements may exhibit discreteness effects in THz and optical frequencies due to weak coupling. We consider a model one-dimensional metamaterial formed by a discrete array of nonlinear split-ring resonators where each ring interacts with its nearest neighbors. On-site nonlinearity and weak coupling among the individual array elements result in the appearance of discrete breather excitations or intrinsic localized modes, both in the energy-conserved and the dissipative system. We analyze discrete single and multibreather excitations, as well as a special breather configuration forming a magnetization domain wall and investigate their mobility and the magnetic properties their presence induces in the system.

Resonant plasmon scattering by discrete breathers in Josephson junction ladders

We study the resonant scattering of plasmons (linear waves) by discrete breather excitations in Josephson junction ladders. We predict the existence of Fano resonances, and find them by computing the resonant vanishing of the transmission coefficient. We propose an experimental setup of detecting these resonances, and conduct numerical simulations which demonstrate the possibility to observe Fano resonances in the plasmon scattering by discrete breathers in Josephson junction ladders.

Two-dimensional discrete breathers: construction, stability, and bifurcations

We develop a methodology for the construction of two-dimensional discrete breather excitations. Application to the discrete nonlinear Schrodinger equation on a square lattice reveals three different types of breathers. Considering an elementary plaquette, the most unstable mode is centered on the plaquette, the most stable mode is centered on its vertices, while the intermediate (but also unstable) mode is centered at the middle of one of the edges. Below the turning points of each branch in a frequency-power phase diagram, the construction methodology fails and a continuation method is used to obtain the unstable branches of the solutions until a triple point is reached. At this triple point, the branches meet and subsequently bifurcate into the final state of an extended phonon mode.