Phase Field Matching Theory Research Articles

The importance of long range Fe–Fe interactions in magnetically ordered 2D Fe0.2Ni0.8/Ni(001) and Fe0.3Ni0.7/Ni(001) alloy systems

We develop a theoretical approach to study the magnonic properties of the 2D ordered surface Fe–Ni alloys with 20% and 30% Fe on a face-centered cubic Ni(001) surface substrate. The surface alloy nanostructures in stable equilibrium are determined by computing the lowest energy configurations of constitutive supercells of the ordered alloys. The magnetic exchange constants of the ground state of the stable systems are calculated to define their Heisenberg Hamiltonians using the DFT Spin-Polarized Relativistic Korringa–Kohn–Rostoker (SPRKKR) method and considering Fe–Fe interactions up to third nearest neighbors. To determine the propagating exchange spin-wave modes, evanescent modes, and the consequent magnonic properties, the spin dynamics of the magnetic surface alloy nanostructures are solved using the phase field matching theory (PFMT). Our results indicate that the Fe–Fe exchange interactions up to third nearest neighbors are vital for accurately describing their magnonics. In particular, the exchange interactions influence the form of dispersion branches for the high-energy spin-wave modes of the Fe–Ni surface alloys considered. Appropriate Green’s functions are also derived from the PFMT method to compute the local densities of states (LDOS) for the atomic sites at the surface boundary. For the case of 20% Fe surface alloy, the Fe–Fe exchange interactions shift the Fe LDOS peaks to lower frequency intervals. We also distinguish the emergence of remarkable LDOS peaks for the he case of the 30% Fe surface alloy at specific Ni sites. These peaks change positions under second and third nearest neighbor Fe–Fe interactions, heralding new accessible spin-wave channels. Our results contribute to establishing a systematic understanding of the magnonics of the magnetic surface alloys of transition metal (TM) materials. This new knowledge will enable the study of the quantum transport of spin waves at interfacial alloy nanojunctions composed of such materials. The present DFT-PFMT theoretical approach is general and can be applied to other surface TM alloy magnetic nanostructures.

Theoretical computation of the phononic vibrational dynamics of Au3Pd, AuPd, and AuPd3 nanostructures at the [AunPdm]/Au(110) bimetallic ordered surface alloy systems

In this work we develop a calculation for the surface phononic dynamical properties of the three ordered bimetallic surface alloy nanostructures [AunPdm]/Au(110) where [AunPdm] = Au3Pd, AuPd, and AuPd3, for the appropriate concentrations of palladium atoms in the proportions 25 %, 50 %, and 75 %, respectively, at the surface boundaries. They are ordered equilibrium structures, which have been characterized, by Atanasov and Hou (2009). Using the phase field matching theory (PFMT), and the Green's function formalism, the surface phonon dispersion curves are computed, in the harmonic approximation, along the high-symmetry directions ΓX, XS, SY and YΓ of the Brillouin zone of the corresponding surface alloy nanostructure. The local vibration densities of states (LDOS) are also calculated for these systems. The results reveal that the number and the dynamic behavior of the surface phonon and resonance modes, are very sensitive to the concentration of the palladium adsorbate atoms in the [AunPdm] nanostructures. The number and characteristics of these modes are modified at the surface and shifted to higher energies as the concentration increases. These phononic results can greatly contribute to our understanding of the dynamic effects underlying potential technological applications of these surface alloy nanostructures.

Vibrational wave scattering in disordered ultra-thin film with integrated nanostructures

Abstract A theoretical model, the phase-field matching theory, has been used to investigate the localized states, their associated states, the local vibrational density of states, the coherent conductance, and the associated thermal conductivity of the perturbed ultra-thin film quasi-dimensional crystalline lattice. The defect disrupts the system’s translational symmetry in the perpendicular direction to it, which is axis Ox, and induces a localized state in its behavior that is not present in the bulk, scattering the incident elastic wave. The model was analyzed for three different cases of elastic parameters: softening, homogeneous, and hardening. The purpose is to investigate how the local dynamics can respond to changes in the microscopic environment in the perturbed domain. The analysis of the total phononic conductance spectra and the local vibrational densities states identifies distinguishing characteristics and demonstrates the sensor’s potential use in nondestroyed control.

Computation of the lattice dynamics for the low-coverage Au/Cu(111) ordered metallic surface alloy system

The lattice dynamics of the ordered Au/Cu(111) surface alloy system are investigated, in particular for the low-coverage ordered Cu(111)-Au 3×3 R30° surface alloy structure. The computations are developed using the phase field matching theory (PFMT) and the Green's functions (GF) formalism. Dispersion branches for surface phonons and resonances along the directions of high symmetry ΓM‾, MK‾, and KΓ‾ of the two-dimensional (2D) surface Brillouin zone (BZ) of the system, are computed. The vibration local densities of states (LDOS) are also determined for representative atomic sites at the surface alloy boundary. The lattice dynamics of the Cu(111)-Au 3×3 R30° surface reveal novel surface phonon and resonance dispersion branches that could be of potential interest for electronic, chemical, and spintronic applications, notably via electron-phonon interactions at this surface.

Electronic quantum scattering across molecular junctions: Oligoacenes and oligophenyl graphene strips

The use of molecular junctions has shown a constant development in the miniaturization of electronic devices. Because, understanding electron transport plays a key factor to develop potential applications in nanoelectronic. Additionally, in most recent studies, the Green functions were used as a powerful formalism to study electronic transport across atomic junctions.In this contribution, we involve an alternative model, based on the phase-field matching theory (PFMT) to investigate the electronic transport properties cross-molecular junctions. We focus on electric characterization and quantum scattering properties of Oligophenyl and Oligoacenes, both are examples of 1D-graphene nanoribbons. We show the impact of the PFMT by using a simple model system of two groups of semi-infinite monatomic chains of Gold (Au) or Silicon (Si), sandwiched together by molecular nanocontacts (Oligophenyl or Oligoacenes). The coherent transmission/reflection coefficients are calculated based on Landauer-Büttiker scattering matrix. The mathematical background of the PFMT is illustrated, we will consider the transport properties by using the Gold electrode instead of semi-infinite monatomic chains. In particular, we will investigate the effect of embedded atoms and magnetic fields across the molecular junction. The results exhibit an oscillation behavior of the transport properties under the presence of a magnetic field at the junction area.

Spin dynamics and magnonic characteristics of a magnetically ordered fcc Fe-Ni alloy monolayer on an fcc Ni slab substrate

We investigate the surface spin dynamics and magnonic characteristics of a magnetically ordered fcc Fe-Ni alloy monolayer on a Ni magnetic slab substrate. The calculations are performed using the Heisenberg Hamiltonian representation for the magnetic ground state of the system. Using the Spin Polarized Relativistic Korringa-Kohn-Rostoker (SPRKKR) method, the relevant magnetic exchange parameters are computed, taking into account the nearest and next nearest Fe-Fe interactions. This establishes the appropriate Heisenberg Hamiltonian. The Phase Field Matching Theory (PFMT) is applied to compute the spin dynamics and surface magnonics of the system, and thus determine the spin wave eigenmodes localized at the surface but propagating in its plane with surface group velocities; these intrinsic eigenmodes constitute basic elements for the magnonic characteristics of the system. The inclusion of the Fe-Fe interactions alters the highest magnonic mode compared to the case when such interactions are absent. The localized densities of states (LDOS) for the irreducible representative magnetic sites at the surface nanostructure are extracted from our computed PFMT Green’s functions. The model is general, and can be applied to different ultrathin layered magnetic alloys on magnetically ordered substrates.

AN APPROACH BASED ON LANDAUER–BÜTTIKER FORMALISM TO COMPUTE THE ELECTRONIC LOCALIZED STATES AT SURFACE BOUNDARIES

In this contribution, we provide a theoretical model to study the effect of different cutting edges on the appearance of localized electronic states. The system under study is a three-dimensional atomic chain that ends with an open cut forming a semi-infinite structured layer in the (1 0 0), (1 1 0) and (1 1 1) directions. We investigate the surface electronic characteristics of the monoatomic chain of a simple cube (sc), orthorhombic (orth), and tetragonal (tetr) structures. We have adopted in our approach the tight-binding approximation to build up the surface Hamiltonian matrix. Additionally, the number of secular equation, at the surface, has been determined by using phase field matching theory (FPMT). In fact, the Hamiltonian system obtained from different cutting orientations provides an inhomogeneous system. To solve the surface eigenvalue problem, we integrate the calculation of the scattering reflection probabilities as given in Landauer–Büttiker formalism. Next, based on the computed scattering probabilities, we build up the surface core states which provide the surface Hamiltonian matrix which can be solved numerically. Our model calculation has been applied to the following elements: (i) fluorite (F), manganese (Mn), polonium (Po), bromine (Br), indium (I), tin (Sn), and protactinium (Pa). The results emphasize the influence of cutting direction on the electronic characteristic of surface and on the scale of energy values. We report the appearance of new electronic curves that characterize the surface states. Those surface states are localized down, within, and above the bulk spectrum. They also provide different characteristic features, of the metals under study, in a given cutting orientation. Furthermore, we have integrated the calculation of non-structured cuts on the outer layers. The relaxation effect on the surface is a standard process which leads to stabilize the changes in the internal energy until the equilibrium. The spacing geometry caused by the relaxation on the surface could be determined by using the molecular dynamic algorithm. We account in this case the lift of degeneracy and the rise of additional localized branches within and outside the bulk range.

Magnonic ballistic transport across Fe-Ni alloy nanojunctions between Fe/Co leads using Phase Field Matching and Ising Effective Field Theory approaches

We analyze the scattering and ballistic transport of spin waves (SW) of Fe/Co leads across iron-nickel alloy nanojunctions, for different nanojunction nickel concentrations. The analytical and numerical analysis is developed for variable thicknesses n of the (100) atomic layers of the homogeneous Fe-Ni alloy nanojunctions, where 1 ≤ n ≤ 7. The ordered magnetic states are treated in the virtual crystal approximation (VCA) and computed using the Ising EFT-MFT method. The spin dynamics and the SW scattering at the nanojunctions are examined by implementing the phase field matching theory (PFMT) for the Heisenberg Hamiltonian. Ballistic coherent reflection and transmission probabilities of the SWs incident from the Fe/Co leads onto the nanojunctions, are calculated using the Landauer-Büttiker formalism. Resonance assisted maxima of the ballistic SW transmission spectra are also along various directions of the Brillouin zone. The characteristics of these maxima can be modified by varying several factors including the nanojunction thickness, the number of layers, the propagation path, the alloy concentrations and temperature.

Fabry–Perot magnonic ballistic coherent transport across ultrathin ferromagnetic lamellar bcc Ni nanostructures between Fe leads

We propose thermodynamically stable systems of ultrathin lamellar bcc Ni nanostructures between bcc Fe leads, Fe[Ni(n)]Fe, based on the available literature for bcc Ni overlayers on Fe(001) surfaces, and establish the necessary criteria for their structural and ferromagnetic order, for thicknesses n ≤ 6 bcc Ni monatomic layers. The system is globally ferromagnetic. A theoretical model is presented to investigate and understand the ballistic coherent scattering of Fe spin-waves, incident from the leads, at the ferromagnetic bcc Ni nanostructure. The NiNi and NiFe exchange are computed using the Ising effective field theory (EFT), and the magnetic ground state of the system is constructed in the Heisenberg representation. We compute the spin-wave eigenmodes localized on the bcc Ni nanostructure, using the phase field matching theory (PFMT), illustrating the effects of symmetry breaking on the confinement of localized spin excitations. The reflection and transmission scattering properties of spin-waves incident from the Fe leads, across the embedded Ni nanostructures are investigated within the framework of the same PFMT methodology. A highly refined Fabry–Perot magnonic ballistic coherent transmission spectra is observed for these Fe[Ni(n)]Fe systems.

Vibrational properties at the ordered metallic surface alloy system Au(110)-1×2-Pd

We present a calculation for the vibrational properties of the ordered surface alloy Au(110)-1×2-Pd on a crystalline substrate of Au. The surface phonon dispersion curves and the local vibrations densities of states (LDOS) are calculated in the harmonic approximation for the system, using the phase field matching theory (PFMT) method and associated real space Green’s functions. In particular, it is shown that the surface alloy presents optic vibrational modes above the Au bulk bands, along the directions of high-symmetry [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] of the corresponding two-dimensional Brillouin zone. Measurements of the surface phonon dispersion branches can hence be made by different techniques such as helium atom scattering (HAS) to compare with. The calculated LDOS for Au and Pd atomic sites in the four top surface atomic layers span a wider range of frequencies than those for the individual Au(110) or Pd(110) metallic surfaces. These LDOS provide a spectral signature for the progressive transition from the surface dynamics to that of the Au crystal bulk. Knowledge of these LDOS for the surface alloy can also serve as an input for modeling the diffusion and reaction rates of chemical species at its surface.

Computation of magnons ballistic transport across an ordered magnetic iron-cobalt alloy nanojunction between iron leads

A model is presented to analyze the spin waves scattering and ballistic transport at the iron-cobalt magnetically ordered alloy nanojunction between iron leads. The B2 structure considered for the ordered alloy with equal amounts of Fe and Co is bcc, where l=3,7, and 11 for the number of (100) atomic layers between the bcc structure of the iron leads. To analyze the spin dynamics and spin wave scattering at the nanojunction boundary, the phase field matching theory is implemented in the Heisenberg Hamiltonian representation. The coherent ballistic reflection and transmission probabilities of spin waves from the iron leads incident onto the nanojunction boundary are calculated in accordance with the Landauer- Büttiker description, and numerical results are presented for the ballistic spin waves transport across the nanojunction over the full range of their frequencies. The results are of particular interest for experiments for spin waves wavelengths greater than the nanojunction width. They demonstrate, furthermore, the possibility of the resonance assisted maxima for the spin waves transmission and reflection spectra owing to the interactions between the incident spin waves and the modes on the nanojunction, leading to inhomogeneous broadened Fabry-Perot type resonances, in contrast to other considered nanojunctions where localized modes give Fano type resonances. This effect is general and may be observed at different characteristic frequencies and corresponding incident angles. The eigenvectors of these modes are calculated for certain frequencies to illustrate the spin precession configurations of the representative nanojunction atoms for both the propagating and localized modes.

Spin wave ballistic transport properties of [formula omitted] nanojunctions between Co leads

The spin wave (SW) ballistic transport properties are investigated for nanojunction systems composed of thin [Co1−cGdc]ℓ′[Co]ℓ[Co1−cGdc]ℓ′ layered nanostructures between cobalt leads. The nanojunction is considered as a homogeneous random alloy of concentrations c on an hcp crystal lattice. ℓ corresponds to the numbers of the hcp (0001) atomic planes per given layer. The phase field matching theory (PFMT) is used to investigate the spin dynamics of the nanojunction system in the virtual crystal approximation (VCA), valid in particular for submicroscopic SW wavelengths. The model calculations yield the spin modes localized on the nanojunction, normal to its plane, in their propagating and resonant forms. The eigenvectors of these modes are calculated for certain cases to illustrate the spin precession configurations on the nanojunction. The VCA-PFMT approach yields a general model, and is used to calculate the SW ballistic scattering and transport across the nanojunction for spin waves incident from the Co leads onto the nanojunction. The results demonstrate resonance Fano assisted maxima in the SW transmission spectra due to interactions between incident lead spin waves and localized spin resonances on the nanojunction. It is shown that these maxima change with nanojunction thickness and alloy concentration. The spectral transmission results for low frequency SWs are of specific interest, in particular they correspond to submicroscopic wavelengths which present an interest for current research of magnonic devices.

Ballistic transport of spin waves incident from cobalt leads across cobalt–gadolinium alloy nanojunctions

Calculations are presented for the scattering and ballistic transport of spin waves (SW) incident from cobalt leads, on ultrathin ferrimagnetic cobalt–gadolinium ‥Co][Co(1−c)Gd(c)]ℓ[Co‥ nanojunction systems. The nanojunction [Co(1−c)Gd(c)]ℓ itself is a randomly disordered alloy of thickness ℓ hcp lattice planes between matching hcp planes of the Co leads, at known stable concentrations c≤0.5 for this alloy system. To compute the spin dynamics, and the SW scattering and ballistic transport, this alloy nanojunction is modeled in the virtual crystal approximation (VCA), valid in particular at the length scale of the nanojunction for submicroscopic SW wavelengths. The phase field matching theory (PFMT) is applied to compute the localized and resonant magnons on the nanojunction. These magnons, characteristic of the embedded nanostructure, propagate in its symmetry plane with spin precession amplitudes that decay or match the spin wave states in the semi-infinite leads. The eigenvectors of these magnon modes are calculated for certain cases to illustrate the spin precession configurations on the nanojunction. The VCA-PFMT approach is also used to calculate the reflection and transmission spectra for the spin waves incident from the Co leads on the nanojunction. The results demonstrate resonance assisted maxima for the ballistic SW transmission spectra due to interactions between the incident spin waves and the nanojunction magnon modes. These properties are general for variable nanojunction thicknesses and alloy stable concentrations c≤0.5. In particular, the positions of the resonance assisted maxima of spin wave transmission can be modified with nanojunction thickness and alloy concentration.

Quantum conductance of silicon-doped carbon wire nanojunctions

Unknown quantum electronic conductance across nanojunctions made of silicon-doped carbon wires between carbon leads is investigated. This is done by an appropriate generalization of the phase field matching theory for the multi-scattering processes of electronic excitations at the nanojunction and the use of the tight-binding method. Our calculations of the electronic band structures for carbon, silicon, and diatomic silicon carbide are matched with the available corresponding density functional theory results to optimize the required tight-binding parameters. Silicon and carbon atoms are treated on the same footing by characterizing each with their corresponding orbitals. Several types of nanojunctions are analyzed to sample their behavior under different atomic configurations. We calculate for each nanojunction the individual contributions to the quantum conductance for the propagating σ, Π, and σ∗electron incidents from the carbon leads. The calculated results show a number of remarkable features, which include the influence of the ordered periodic configurations of silicon-carbon pairs and the suppression of quantum conductance due to minimum substitutional disorder and artificially organized symmetry on these nanojunctions. Our results also demonstrate that the phase field matching theory is an efficient tool to treat the quantum conductance of complex molecular nanojunctions.

Electronic conductance via atomic wires: a phase field matching theory approach

A model is presented for the quantum transport of electrons, across finite atomic wire nanojunctions between electric leads, at zero bias limit. In order to derive the appropriate transmission and reflection spectra, familiar in the Landauer-B\"{u}ttiker formalism, we develop the algebraic phase field matching theory (PFMT). In particular, we apply our model calculations to determine the electronic conductance for freely suspended monatomic linear sodium wires (MLNaW) between leads of the same element, and for the diatomic copper-cobalt wires (DLCuCoW) between copper leads on a Cu(111) substrate. Calculations for the MLNaW system confirm the correctness and functionality of our PFMT approach. We present novel transmission spectra for this system, and show that its transport properties exhibit the conductance oscillations for the odd- and even-number wires in agreement with previously reported first-principle results. The numerical calculations for the DLCuCoW wire nanojunctions are motivated by the stability of these systems at low temperatures. Our results for the transmission spectra yield for this system, at its Fermi energy, a monotonic exponential decay of the conductance with increasing wire length of the Cu-Co pairs. This is a cumulative effect which is discussed in detail in the present work, and may prove useful for applications in nanocircuits. Furthermore, our PFMT formalism can be considered as a compact and efficient tool for the study of the electronic quantum transport for a wide range of nanomaterial wire systems. It provides a trade-off in computational efficiency and predictive capability as compared to slower first-principle based methods, and has the potential to treat the conductance properties of more complex molecular nanojunctions.

Magnons coherent transmission and its heat transport at ultrathin insulating ferromagnetic nanojunctions

A model calculation is presented for the magnons coherent transmission and corresponding heat transport at magnetic insulating nanojunctions. The system consists of a ferromagnetically ordered ultrathin insulating junction between two semi-infinite ferromagnetically ordered leads. Spin dynamics are analyzed using the equations of motion for the spin precession displacements, valid for the range of temperatures of interest. Coherent scattering cross-sections at the junction boundary are calculated using the phase field matching theory, for all the incidence angles on the boundary from the lead bands, for arbitrary angles of incidence, at variable temperatures, and for different nano thicknesses of the ultrathin junction. The model is general; it is applied in particular to the Fe/Gd/Fe system with a sandwiched ferromagnetic Gd junction. It yields also the thermal conductivity due to the magnons coherent transmission between the two leads when these are maintained at slightly different temperatures. The calculation is carried out for state of the art values of the exchange constants, and elucidates the relation between the coherent scattering transmission of magnons and their thermal conductivity, for different thicknesses.