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Interaction of an external impurity with the surface intrinsic mode in a Heisenberg chain
No full textIn this paper we have demonstrated the existence of surface intrinsic localized modes in one-dimensional classical spin systems. These modes have frequencies above the top of the magnon band and are more localized than the corresponding modes that were found in the lattice dynamics. By numerical methods we have studied the forward evolution in time. These entities are stable in time for many time steps. Also, we consider the interaction of these surface excitations with an external dipolar field. We have first considered the case in which the external dipole is parallel to the spins of the bulk. According to the distance of the impurity from the surface we find that at a particular distance a new surface mode appears, that we have called a mixed mode because it is formed by a localized state at the surface plus a plane wave. At large distances the dipole traps the surface mode, while at small distances the external impurity potential is so strong that all the spins are forced to be aligned in the z direction. For the case in which the external magnetic dipole is antiparallel to the bulk spins there are no mixed modes and the external impurity is so strong that the surface modes are trapped at large distances, and the bulk modes are trapped at very short distances
Theory of kink and domain-wall excitations in translationally invariant lattices with quartic anharmonicity
No full textA theoretical investigation has been made of localized excitations having the form of kinks or domain walls in translationally invariant monatomic lattices with harmonic and quartic anharmonic interactions between nearest-neighbor atoms. Antisymmetric kinks are found for negative values of the anharmonic coefficient. Symmetric kinks are found to be poorly defined for translationally invariant anharmonic potentials. In the case of domain walls, stable solutions were obtained only for negative values of the anharmonic coefficient. These results are compared with those for on-site quartic anharmonicity
Surface localized modes in anharmonic systems at low dimensionality
No full textIn this paper we discuss in detail the localized vibrational modes in monoatomic and diatomic one-dimensional chains induced by anharmonicity. Analysis of the effects of the quartic anharmonic interactions in the Vibrational spectrum shows, in the monoatomic case, the appearance of surface modes, not allowed in the harmonic field, and of high-frequency modes. In the diatomic case we found two types of surface mode, the first reminiscent of the harmonic one and the second entirely due to the anharmonicity, and two localized gap modes arising from the top of the acoustic branch with odd parity centered on a heavy atom and even parity centered on a light atom. The introduction of cubic anharmonicity produces odd and even gap localized modes arising from the bottom of the optical branch and affects the surface modes
Localized modes in an anharmonic diamond-structure chain
No full textIn this paper we study localized vibrational modes in a chain of atoms with the same mass, but with two alternating force constants between nearest neighbors. This model simulates a row of atoms in the [111] direction of a diamond or silicon crystal. Cubic and quartic anharmonicity are included in the potential. The harmonic and quartic anharmonic terms produce intrinsic localized modes with frequencies above the optical branch and in the gap. The inclusion of cubic terms with negative coefficients reduces the frequencies, leads to new localized modes in the gap, and introduces static distortions of the chain. Modes of both even and odd parity occur. Surface modes occur when the localization is near a free end
Intrinsic localized modes in the bulk and at the surface of anharmonic diatomic chains
No full textIntrinsic localized vibrational modes in a diatomic anharmonic chain are discussed in detail. We consider a finite (even or odd) number of particles interacting with nearest-neighbor harmonic and cubic and quartic anharmonic potentials. For suitable values of the potential parameters we find two odd parity modes localized about light and heavy atoms, respectively, with frequencies above the top of the optical branch. In the gap there are localized modes arising from the top of the acoustic branch with odd parity if they are centered on a heavy atom and even parity if centered on a light atom. There are also two localized modes originating from the bottom of the optical branch. The odd parity mode is centered on a light atom, while the even parity mode is centered on a heavy atom. In addition, we have found two types of surface modes. One is the anharmonic version of the surface mode occurring in a finite diatomic harmonic chain with frequency in the gap, and the other is entirely due to the anharmonicity. The latter mode has its frequency above the top of the optical branch. A comparison with other work is given
EVOLUTION AND STABILITY OF SELF-LOCALIZED MODES IN A NONLINEAR INHOMOGENEOUS CRYSTAL-LATTICE
No full textThe evolution and stability of self-localized modes in an inhomogeneous crystal lattice are discussed. After establishing the basic equations, appropriate time and space scales are introduced, together with a power threshold. A mathematical stability theory, based upon an averaged Lagrangian analysis, concludes that the system is stable for any mass defect, if the perturbation is symmetric. For asymmetric perturbations, only single-peaked stationary states are stable. Finally, numerical simulations are presented that not only support the theoretical work of the earlier sections but show clearly the evolution of the solutions from a range of input conditions
Theory of the anharmonic linewidths of surface phonons in aluminum
No full textA theoretical investigation has been made of the linewidth of the Rayleigh mode on the Al(111) surface due to cubic anharmonic interactions between atoms. The normal-mode frequencies and eigenvectors for the harmonic crystal were calculated by using a model containing central interactions extending up to tenth-nearest neighbors and three-body interactions extending up to second-nearest neighbors. This model reproduces with great accuracy the experimental bulk-phonon frequencies as well as the surface-phonon frequencies. The linewidths were evaluated along the SIGMA-BAR direction as a function of the lateral momentum transfer and at the MBAR point as a function of the temperature. The results compare favorably with recent experimental data
COMPARISON BETWEEN PHENOMENOLOGICAL AND PSEUDOPOTENTIAL FORCE-CONSTANTS FOR THE LATTICE-DYNAMICS OF AL
No full textIn this paper we present a critical comparison of,calculations of phonon-dispersion curves for aluminum, based on pseudopotential and empirical force-constant methods. The former method is.based on both perturbative and nonperturbative evaluations of the total energy of the crystal. In the perturbative approach the total energy is evaluated to second order in the electron-ion interaction with a local pseudopotential. In the nonperturbative approach the electron-ion interaction is treated exactly using a non-local ab initio pseudopotential. In the empirical force-constant method the total energy is represented by a sum of two-body and three-body terms, the latter being restricted to interactions among triplets of nearest neighbors and of nearest and next-nearest neighbors. All models include physical mechanisms for ensuring the breakdown of the Cauchy relation. We show that in each method convergence of the calculated phonon frequencies requires the inclusion of long-range interactions. The radial-force constants obtained by the empirical and perturbative pseudopotential methods are very similar for the first three shells of neighbors. On the other hand, the tangential force constants differ markedly, a reflection of the different physical mechanisms that come into play in the various models in the establishment of equilibrium
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