Surface magnon-polaritons at a dielectric/graphene/gyromagnetic interface in a perpendicular applied magnetic field.

We present a theoretical study of the surface magnon-polaritons at an interface formed by vacuum and a gyromagnetic medium (that can be either ferromagnetic or antiferromagnetic), when there is a graphene layer deposited between the media at the interface and a magnetic field is applied perpendicular to the interface. The retarded-mode dispersion relations are calculated by considering a superposition of transverse magnetic and transversal electric electromagnetic waves in both media. Our results reveal the appearance of the surface magnon-polariton modes (with frequencies typically of a few GHz) that do not exist in the absence of graphene at the interface. Also, a typical magnon-polariton dispersion relation with damping is revealed, including a resonant frequency that depends on the applied magnetic field. The effects of varying the doping levels, which modify the Fermi energies in the graphene, and varying the perpendicular applied magnetic field are presented, revealing a strong influence exerted by the presence of graphene on the surface magnon-polariton modes. Other effects include the control of the slope of the dispersion curves (with respect to the in-plane wave vector) for the modes as the Fermi energies of the graphene sheet are changed and the distinctive localization properties for the emerging surface modes.

Unusual behaviour of the spin-phonon coupling in the quasi-one-dimensional antiferromagnet RbCoCl3.

We present an experimental and theoretical study for the lattice vibrational (phonon) modes in the quasi-one-dimensional (or chain-like) antiferromagnet RbCoCl3 at low temperatures both above and below the two different magnetic phase transitions. Clear evidence is found for the role of spin-phonon interactions in providing a temperature-dependent contribution for the frequencies of the E1g and E2g symmetry phonons that occur with frequencies comparable to those of the spin wave excitations (magnons) in this compound. The behaviour in RbCoCl3, as studied here by Raman scattering experiments, is quite different from that typically observed in rutile-structure antiferromagnets where the spin-phonon coupling has been well characterized. The theory is modified to take account of the strong Ising-like component in the spin Hamiltonian. This enables the spin-phonon coupling parameters to be deduced, with the analysis also revealing the onset of an extra frequency shift for the phonons below the transition temperature TN1 = 28 K associated with magnetic ordering along the Co chains.

Damping of dipole-exchange spin waves in ferromagnetic thin films at elevated temperatures.

A non-bosonic technique, based on the drone-fermion perturbation method and a high-density expansion, is employed to study the spin-wave (SW) scattering processes in a ferromagnetic thin film with exchange and dipole-dipole interactions. Specifically, the diagrammatic contributions to the spin-spin Green's functions are evaluated within a 1/zperturbation expansion, wherezis the number of spins interacting with any given spin. The results are used to calculate the SW damping at temperatures below the Curie temperatureTC. It is found that, apart from the usual contributions due to three-magnon and four-magnon processes in the film, which are dominant at relatively low temperatures (consistent with boson expansion methods), there is an additional mechanism that becomes important for temperatures above about12TCThis is spin disorder damping, previously studied in bulk magnetic materials; it occurs when a spin wave is scattered by the instantaneous disorder produced when a longitudinal spin component undergoes a large thermal fluctuation. Numerical estimates are presented for thin films of Permalloy and EuO.

Magnon-polaritons in ferromagnetic magnonic crystals with graphene at the interfaces.

We present a theoretical study for the surface and bulk magnon-polaritons in magnonic crystals (or semi-infinite layered superlattices), which are formed from an array of ferromagnetic materials and nonmagnetic spacers with graphene sheets interposed between them. The external medium is taken to be vacuum. The Fermi energies in the graphene can be varied by employing different electronic doping levels, resulting in a strong influence exerted by the presence of graphene on the surface magnon-polariton modes. These effects include localization of the modes and control of the group velocities of the modes as the Fermi energies of the graphene sheets are varied, along with an important role for the phenomenological damping in the graphene sheets.

Magnon-polaritons in graphene/gyromagnetic slab heterostructures.

We present a theoretical study for the surface magnon-polaritons in structures formed by graphene layer(s) on an insulating gyromagnetic medium (that can be either ferromagnetic or antiferromagnetic) surrounded by vacuum. We consider different doping levels to vary the Fermi energies in the graphene, including both semi-infinite and slab magnetic samples. Our results reveal a strong influence, exerted by the presence of graphene, on the surface magnon-polariton modes. The effects include control of the group velocities for the modes as the Fermi energies of the graphene sheet are varied, modified nonreciprocal and reciprocal mode propagation properties depending on the type of magnetic material, and distinct localization properties for the emerging surface modes.

Interplay between intra- and inter-nanowires dynamic dipolar interactions in the spin wave band structure of Py/Cu/Py nanowires.

We have studied both experimentally and theoretically the reprogrammable spin wave band structure in Permalloy(10 nm)/Cu(5 nm)/Permalloy(30 nm) nanowire arrays of width w = 280 nm and inter-wire separation in the range from 80 to 280 nm. We found that, depending on the inter-wire separation, the anti-parallel configuration, where the magnetizations of the two Permalloy layers point in opposite directions, is stabilized over specific magnetic field ranges thus enabling us to directly compare the band structure with that of the parallel alignment. We show that collective spin waves of the Bloch type propagate through the arrays with different magnonic bandwidths as a consequence of the interplay between the intra- and inter-nanowire dynamic dipolar interactions. A detailed understanding, e.g. whether they have a stationary or propagating character, is achieved by considering the phase relation (in-phase or out-of-phase) between the dynamic magnetizations in the two ferromagnetic layers and their average value. This work opens the path to magnetic field-controlled reconfigurable layered magnonic crystals that can be used for future nanoscale magnon spintronic devices.

Squeezing and time evolution of magnon states under perpendicular pumping.

The coherent magnon state representation is employed to investigate the quantum-statistical behavior of the nonlinear excitation of magnons in ferromagnets. Both the long-range magnetic dipole-dipole and short-range exchange interactions are included, along with a static longitudinal applied field and a microwave pumping field in the perpendicular orientation. Within a microscopic (or Hamiltonian-based) approach the total Hamiltonian is transformed from spin operators to a normal-mode set of boson creation and annihilation operators. When the three-magnon interactions are included, it is found that the microwave pumping field may be used to control the nonlinear statistical properties of the system. From a study of the time evolution of the system we deduce the average number of magnons, the super-Poissonian statistical behavior, and the occurrence of magnon squeezing. We also compare the results with the case where the microwave pumping field is in the parallel orientation, and it is found that there are important differences in the time dependence.

Role of interbranch pumping on the quantum-statistical behavior of multi-mode magnons in ferromagnetic nanowires.

Theoretical studies are reported for the quantum-statistical properties of microwave-driven multi-mode magnon systems as represented by ferromagnetic nanowires with a stripe geometry. Effects of both the exchange and the dipole-dipole interactions, as well as a Zeeman term for an external applied field, are included in the magnetic Hamiltonian. The model also contains the time-dependent nonlinear effects due to parallel pumping with an electromagnetic field. Using a coherent magnon state representation in terms of creation and annihilation operators, we investigate the effects of parallel pumping on the temporal evolution of various nonclassical properties of the system. A focus is on the interbranch mixing produced by the pumping field when there are three or more modes. In particular, the occupation magnon number and the multi-mode cross correlations between magnon modes are studied. Manipulation of the collapse and revival phenomena of the average magnon occupation number and the control of the cross correlation between the magnon modes are demonstrated through tuning of the parallel pumping field amplitude and appropriate choices for the coherent magnon states. The cross correlations are a direct consequence of the interbranch pumping effects and do not appear in the corresponding one- or two-mode magnon systems.

Quantum statistics for a two-mode magnon system with microwave pumping: application to coupled ferromagnetic nanowires.

A microscopic (Hamiltonian-based) method for the quantum statistics of bosonic excitations in a two-mode magnon system is developed. Both the exchange and the dipole-dipole interactions, as well as the Zeeman term for an external applied field, are included in the spin Hamiltonian, and the model also contains the nonlinear effects due to parallel pumping and four-magnon interactions. The quantization of spin operators is achieved through the Holstein-Primakoff formalism, and then a coherent magnon state representation is used to study the occupation magnon number and the quantum statistical behaviour of the system. Particular attention is given to the cross correlation between the two coupled magnon modes in a ferromagnetic nanowire geometry formed by two lines of spins. Manipulation of the collapse-and-revival phenomena for the temporal evolution of the magnon number as well as the control of the cross correlation between the two magnon modes is demonstrated by tuning the parallel pumping field amplitude. The role of the four-magnon interactions is particularly interesting and leads to anti-correlation in some cases with coherent states.

Localization of the electronic excitations in single-walled carbon nanotubes with embedded line impurities.

A matrix operator formalism is used to study the excitations in long, single-walled carbon nanotubes with the dynamic electronic properties described by a tight-binding model where the interactions between atoms take place via nearest-neighbour hopping. Defects in the form of substitutional impurity atoms are introduced to study the localized electronic modes of the nanotube as well as the propagating modes of the pure (host) material. The impurities are assumed to have the form of one or more line defects parallel to the nanotube axis. Two geometric configurations are investigated corresponding to the longitudinal axis of the nanotube being parallel to either a zigzag or an armchair direction of the graphene lattice. A tridiagonal matrix technique is employed to solve the electronic operator equations that provide a description of the frequencies of the discrete modes of the system and their spatial amplitudes. Numerical examples are presented for different nanotube diameters and spatial configurations of the impurity lines.

The effect of lattice structure on dipole-exchange spin waves in ultrathin ferromagnetic films.

Calculations are reported relating to the dipole-exchange spin waves in ultrathin ferromagnetic films with different lattice structures such as simple cubic, body-centred cubic and face-centred cubic, using a microscopic, or Hamiltonian-based, theory. Both the short-range exchange and the long-range dipolar interactions are included in the Hamiltonian, together with an external magnetic field applied either parallel or perpendicular to the film surfaces. The use of phenomenological dipole-exchange boundary conditions, as in macroscopic theories, is avoided. Comparisons between our results and macroscopic theories generally give good agreement in a small wavevector limit. At larger wavevectors for the microscopic theory, it is found that the frequencies and the localization properties of the discrete spin waves show a sensitive dependence on the lattice structure.

Spin waves in nickel nanorings of large aspect ratio.

The spin dynamics of high-aspect-ratio nickel nanorings in a longitudinal magnetic field have been investigated by Brillouin spectroscopy and the results are compared with a macroscopic theory and three-dimensional micromagnetic simulations. Good agreement is found between the measured and calculated magnetic field dependence of the spin wave frequency. Simulations show that as the field decreases from saturation, the rings switch from a "bamboo" to a novel "twisted bamboo" state at a certain critical field, and predict a corresponding dip in the dependence of the spin wave frequency on the magnetic field.

Spin-wave quantization in ferromagnetic nickel nanowires.

The dynamical properties of uniform two-dimensional arrays of nickel nanowires have been investigated by inelastic light scattering. Multiple spin waves are observed that are in accordance with dipole-exchange theory predictions for the quantization of bulk spin waves. This first study of the spin-wave dynamics in ferromagnetic nanowire arrays reveals strong mode quantization effects and indications of a subtle magnetic interplay between nanowires. The results show that it is important to take proper account of these effects for the fundamental physics and future technological developments of magnetic nanowires.

Segregation of photosystems in thylakoid membranes as a critical phenomenon.

The distribution of the two photosystems, PSI and PSII, in grana and stroma lamellae of the chloroplast membranes is not uniform. PSII are mainly concentrated in grana and PSI in stroma thylakoids. The dynamics and factors controlling the spatial segregation of PSI and PSII are generally not well understood, and here we address the segregation of photosystems in thylakoid membranes by means of a molecular dynamics method. The lateral segregation of photosystems was studied assuming a model comprising a two-dimensional (in-plane), two-component, many-body system with periodic boundary conditions and competing interactions between the photosystems in the thylakoid membrane. PSI and PSII are represented by particles with different values of negative charge. The pair interactions between particles include a screened Coulomb repulsive part and an exponentially decaying attractive part. The modeling results suggest a complicated phase behavior of the system, including quasi-crystalline phase of randomly distributed complexes of PSII and PSI at low ionic screening, well defined clustered state of segregated complexes at high screening, and in addition, an intermediate agglomerate phase where the photosystems tend to aggregate together without segregation. The calculations demonstrated that the ordering of photosystems within the membrane was the result of interplay between electrostatic and lipid-mediated interactions. At some values of the model parameters the segregation can be represented visually as well as by analyzing the correlation functions of the configuration.

A two-dimensional many-body system with competing interactions as a model for segregation of photosystems in thylakoids of green plants.

We address the segregation of photosystems I (PSI) and II (PSII) in thylakoid membranes by means of a molecular dynamics method. We assume a two-dimensional (in-plane) problem with PSI and PSII being represented by particles with different values of negative charge. The pair interactions between particles include a screened Coulomb repulsive part and am exponentially decaying attractive part. Our modeling results suggest that the system may have a complicated phase behavior, including a quasi-crystalline phase at low ionic screening, a disordered phase and, in addition, a possible "clotting" agglomerate phase at high screening where the photosystems tend to clot together. The relevance of the observed phenomena to the stacking of thylakoid membranes is discussed.

Diagrammatic approach to calculation of the fluctuation correlation matrix in a metabolic system.

We present here a simple diagrammatic approach for the time evolution of the fluctuations in metabolite concentrations around the steady state. A fluctuation correlation matrix is introduced to characterise the response in the concentrations of metabolites to a singular initial fluctuation in one of the metabolites. We show how the temporal evolution of the correlation matrix can be represented in the form of a series with individual terms corresponding to pathways on a metabolic graph. The basic properties of such graphs are studied and it is shown how each term in the series can be evaluated. A Monte-Carlo procedure is outlined to calculate the fluctuation correlation matrix. We discuss various properties of the graphical representation and discuss links to information theory that arise from it.

Mapping of statistical physics to information theory with application to biological systems.

The problem of achieving a mapping of formalisms in statistical physics and theoretical biology to information theory is discussed using an example for canonical ensembles. We extend the meaning of the Handscomb Monte-Carlo method to a general recipe for the transformation from a "configuration" space to a "sentence" space. The ensemble of "sentences" and its corresponding source uncertainty function are introduced. A possible mapping procedure based on a generalization of the Handscomb representation is described. For a biological illustration, we present a way to introduce a pathway representation to describe metabolic processes in living systems.