Phonon Scattering via an Atomic Well in Free Standing Thin Solid Films

Abstract

A theoretical model is presented for the study of the scattering of phonons at an extended inhomogeneous boundary separating thin solid monatomic films. The model system consists of two solid films with otherwise stress-free surfaces on either side of an atomic well boundary. The coherent reflection and transmission scattering cross sections for phonons incident from the interior of the thin films on the inhomogeneous atomic well boundary are calculated in accordance with the Landauer-Büttiker coherent scattering description, using the matching method with nearest and next-nearest neighbor elastic force constants. This is done specifically for two different cases of elastic interactions on the boundary to investigate the consequences of their softening and hardening for the coherently scattered spectra. The numerical results yield an understanding for the effects on coherent phonon conductance due to phonon incidence and to the elastic nature of the boundary. The coherent reflection and transmission scattering cross sections show characteristic spectral features that are invariant with the change of the boundary force constants, depending solely on the cutoff frequencies for the propagating phonons and on incidence angle. They also show the Fano resonances that result from the interactions of propagating phonons with the localized vibrational Rayleigh-like modes on the boundary, depending on the boundary elastic force constants. The evolution of the system average conductance per phonon mode with incidence illustrates an interesting effect. An experimental observable this average conductance remains constant at half a phonon in intensity over significant frequency intervals. The effect is remarkable inasmuch as it permits in principle the possibility of a constant intensity phonon source.

Phonons transmission by thin films sandwiched between two similar fcc structures

“…To calculate scattering properties of the two sandwiched systems, we use a method specifically developed to investigate electronic transport through phase-coherent structures [16][17][18]. Transport coefficients are calculated as a function of phonon frequency within the Landauer-Buttiker formalism [19] by employing an exact recursive matching technique.…”

Spin Waves Transmission via a Molecular Junction Connecting Two Quasi-2d Heisenberg Ferromagnets

“…11,18 At temperatures well below the magnetic order-disorder transition the z components of the spins may be approximated as S A and S B for the film and molecule, respectively. For sites p ≡ (n, s, −1), (n, s, 0), and (n, s, 1) inside the ferromagnetic films far from the molecular junction, the system of equations for spin dynamics may be cast in matrix form…”

“…We can hence distinguish between two different types of solutions: (i) the propagating spin wave modes in the films described by the condition |Z(ν)| = 1, with Z(ν) = exp(±iφ x ), where φ x = q x a, and q x denotes the reciprocal lattice wave vectors along the x direction, and (ii) those corresponding to the condition |Z(ν)| < 1, describing the evanescent modes. 11,18 The evanescent modes do not transport any energy, but are necessary for a complete description of the scattering problem at the boundary.…”

“…They can become important for the coherent transport of other types of elementary excitations in low dimensional systems, as phonons and magnons. 11,12,18 At low temperatures, the devices are mesoscopic in the sense that their quantum states must be described by coherent wave functions extending over the entire system, and quantum-mechanical interference effects become (a) A schematic representation of a molecular junction connecting two semi-infinite ultrathin two-dimensional Heisenberg ferromagnetic films made up of three atomic layers each, with magnetic exchange interactions between nearest neighbors. For simplicity we take the same distance a between adjacent sites.…”

Spin wave ballistic transport properties of [Co1−cGdcAshokan1, Khater2, Ghantous3 et al. 2015Journal of Magnetism and Magnetic MaterialsSelf Cite10060View full textAdd to dashboardCite

“…A detailed analysis is presented to account for both the propagating and evanescent modes of the system, and the phase field matching theory (PFMT) is used to compute the scattering cross sections within the Landauer-Büttiker formalism [21,22]. The PFMT is a method originally developed for the scattering of phonons, magnons and more recently of electrons for a variety of nanosystems [19,20,[23][24][25][26][27][28][29][30]. It is equivalent to the non-equilibrium Green's function method but is a more transparent theoretical tool.…”