Spin excitations in exchange-dominated regime on (1 0 0) and (1 1 0) antiferromagnetic surfaces

Theoretical investigations in the context of Heisenberg model have been made for (1 0 0) and (1 1 0) magnetic surface dynamics for a semi-infinite antiferromagnet geometry. The calculations apply to the exchange dominated regime and are based on a spin-wave operator and matching technique within the framework of non-interacting spin-wave theory. The theoretical formalism developed here does not include either relaxation or reconstruction at the surface and no electronic effects have been considered. Dispersion curves of surface spin-waves are obtained within a single framework by matching the evanescent and travelling solutions, respectively, obtained from the secular equation and satisfying the boundary conditions brought about by the surface. The excitation spectrum of the surface spin-waves has been obtained and compared with that for bulk spin-waves. The quantized bulk modes of the same energy travelling to and away from the surface are related to one another by reflection coefficients, for which sum rules are derived. The numerical results for the evolution of acoustic and optical modes are presented for two different surface planes, namely (1 0 0) and (1 1 0). The findings reported here show that: (i) the reduced coordination number for atoms near the surface as well as the surface orientation play an obvious and crucial part in the surface spin-wave spectra; (ii) the evolutions of bulk as well as surface modes undergo significant changes as a function of the bulk-surface exchange integrals for a given direction of propagation of the spin-wave modes along the surface.     

Spin modes and layer magnetization for surface and impurity layer embedded in a ferromagnet

A theoretical study is made for the role of an impurity layer embedded within a semi-infinite ferromagnet in determining the spectra of (0 0 1) surface spin waves and the layer magnetization for the surface and impurity layer. The calculations are described using simultaneously a closed form of the spin-wave Green's function and the matching procedure in the random-phase approximation. Analytic expressions for the Green's functions are also derived in a low-temperature spin-wave approximation. The theoretical approach determines the bulk and evanescent spin fluctuation fields in the two-dimensional plane normal to the surface. The results are used to calculate the energies of localized modes associated with the impurity layer as well as with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the impurity layer and surface modes. The results derived from the dynamic correlation functions between a pair of spin operators at any two sites are employed to evaluate the spin deviation in the ferromagnet due to the localized modes associated with the surface and with the impurity layer obtained by means of the matching procedure. The correlation functions and the layer magnetization are then illustrated as function of the impurity layer distance from the surface for a given temperature.     

Surface modes with biquadratic coupling and uniaxial anisotropy in semi-infinite Heisenberg antiferromagnet

We address the role and the influence of both biquadratic exchange and uniaxial anisotropy in the study of bulk and surface magnetic excitations for a two-sublattices semi-infinite Heisenberg antiferromagnet. The calculations apply to combined effect and are based on a matching technique within the framework of both non-interacting spin-wave theory and random phase approximation. Emphasis has been laid upon the advantage of handling bulk and surface spin precessional fields, characterized by their symmetry in particular. Analytic expressions for the bulk and surface equations of motion are also derived which enables us to analyze qualitatively the nature of the modes by observing the response of the energy branches to the variation of both biquadratic exchange and single-ion anisotropy field as well as exchange parameters occurring on the surface. Two numerical applications of the theoretical formalism developed in this work are described. First concerns the situation when the free surface model is assumed. The second application considers the existence of surface perturbations and treats the effects of the presence of biquadratic exchange term on the bulk and surface spin-wave spectra showing two kinds of surface propagating modes which depend on the presence or not of the uniaxial anisotropy contribution and also on the variations of the bulk-surface exchange parameters. A significant conclusion which this work reached relates to the checking of the results obtained in the literature by using our own theoretical formalism. We show that this formalism is very well adapted to calculations of localized bulk and surface spin-wave modes associated with the simultaneous presence of biquadratic exchange and uniaxial anisotropy. Also, the results obtained for the bulk spin fluctuations field as well as for the magnetic surface waves, are found to be in qualitative agreement with those obtained in the literature. The analytic formulation presented in this work provides an accurate and practical scheme for calculating the surface spin dynamics under the influence of surface exchange parameters, biquadratic coupling and uniaxial anisotropy terms.     

Surface excitations in magnetic systems with a singlet ground state

We have investigated surface excitations in a system wherein the ionic ground state is a magnetic singlet. The pseudospin formalism is employed to account for the crystal-field and exchange interactions between the ions in a Heisenberg ferromagnet with the singlet-triplet crystal-field-only level scheme. The Hamiltonian was studied in the molecular field approximation to find the possible ground states. Surface excitations for the simple cubic structure were investigated for the (001) surface in the random phase approximation. Analytic expressions have been obtained for the thermodynamic Green functions. For a fully magnetized molecular field ground state, there are in general two bulk bands, the spin-wave and the excitonic. Surface modes were found to exist below the spin-wave band, above the excitonic band and between the bands. The dispersion curves can exist only over one or two limited regions of the two-dimensional wave-vector parallel to the crystal surface.     

Spin excitations in granular structures with ferromagnetic nanoparticles

Spin excitations and relaxation in a granular structure which contains metallic ferromagnetic nanoparticles in an insulating amorphous matrix are studied in the framework of the s-d exchange model. As the d system, we consider the granule spins, and the s system is represented by localized electrons in the amorphous matrix. In the one-loop approximation with respect to the s-d exchange interaction for a diagram expansion of the spin Green’s function, the spin excitation spectrum is found, which consists of spin-wave excitations in the granules and of polarized spin excitations. In polarized spin excitations, a change in the granule spin direction is accompanied by an electron transition with a spin flip between two sublevels of a split localized state in the matrix. We considered polarized spin relaxation (relaxation of the granule spins occurring by means of polarized spin excitations) determined by localized deep energy states in the matrix and the thermally activated electronic cloud of the granule. It is found that polarized spin relaxation is efficient over a wide frequency range. Estimates made for structures with cobalt granules showed that this relaxation could be observed in centimetric, millimetric, and submillimetric wavelength ranges.     

Spin dynamics from time-dependent density functional perturbation theory

We present a new method to model spin-wave excitations in magnetic solids, based on the Liouville–Lanczos approach to time-dependent density functional perturbation theory. This method avoids computationally expensive sums over empty states and naturally deals with the coupling between spin and charge fluctuations, without ever explicitly computing charge-density susceptibilities. Spin-wave excitations are obtained with one Lanczos chain per magnon wave-number and polarization, avoiding the solution of the linear-response problem for every individual value of frequency, as other state-of-the-art approaches do. Our method is validated by computing magnon dispersions in bulk Fe and Ni, resulting in agreement with previous theoretical studies in both cases, and with experiment in the case of Fe. The disagreement in the case of Ni is also comparable with that of previous computations.     

A Cluster-Bethe-Lattice approach to spin-waves in dilute ferromagnets

We study the spin-wave spectra of a dilute ferromagnet within the cluster-Bethe-lattice approximation. Short range order effects for the alloy are included. A study of finite size clusters connected at their edges to Bethe lattices of the same coordination number allows us to determine: (i) the stability condition for the magnetic system; (ii) the continuum spin-wave local density of states; and (iii) the existence of localized states below and above the continuum states.     

Calculations of ferromagnetic surface dynamics using the Green's functions theory and matching procedure

A Heisenberg model is employed to study the spin fluctuation dynamics on a (001) ferromagnetic surface using a new theoretical formalism. The solution of the full magnetic problem arising from the absence of magnetic translation symmetry in one dimension due to the presence of a magnetic surface is presented. The calculations are described using simultaneously a closed form of the spin-wave Green's function and the matching procedure in the random-phase approximation. Analytic expressions for the Green's functions are also derived in a low-temperature spin-wave approximation. The theoretical approach determines the bulk and evanescent spin fluctuation fields in the two dimensional plane normal to the surface. The results are used to calculate the localised modes of magnons associated with the surface. Numerical examples of the modes are given and they are found to exhibit various effects due to the interplay between the bulk and surface modes. It is shown that there may be surface spin-waves that decay in amplitude with distance into the bulk domain. Also the bulk spin fluctuations field as well as the magnons localised at the surface depend on the nature of the bulk-surface coupling exchange. The unstable surface magnetic configurations are illustrated and discussed. The results derived from the dynamic correlation functions between a pair of spin operators at any two sites are employed to evaluate the spin deviation in the ferromagnet due to localised surface modes obtained by the matching procedure as a function of temperature. Received 21 April 2002 / Received in final form 25 October 2002 Published online 14 March 2003     

Spin dynamics in (III,Mn)V ferromagnetic semiconductors: the role of correlations

We address the role of correlations between spin and charge degrees of freedom on the dynamical properties of ferromagnetic systems governed by the magnetic exchange interaction between itinerant and localized spins. For this we introduce a general theory that treats quantum fluctuations beyond the random phase approximation based on a correlation expansion of the Green's function equations of motion. We calculate the spin susceptibility, spin-wave excitation spectrum, and magnetization precession damping. We find that correlations strongly affect the magnitude and carrier concentration dependence of the spin stiffness and magnetization Gilbert damping.     

Exchange Interactions and Curie Temperatures of 3D- and 2D-Ferromagnets

Effective exchange interactions in bulk ferromagnets as well as in magnetic overlayers on Cu(001) covered by a Cu-cap layer of varying thickness were determined from first principles by mapping of corresponding total energies onto the effective Heisenberg model in the framework of the adiabatic approximation and magnetic force theorem. The effective Heisenberg model is then used to determine spin-wave stiffness constants and Curie temperatures evaluated in the framework of the random-phase approximation. Calculations are in a fair agreement with available experimental data for bulk ferromagnets and reproduce an oscillatory Curie temperature of magnetic overlayers as a function of Cu-cap thickness in a qualitative agreement with recent experiments.     

Phase separation in a lattice model of a superconductor with pair hopping

We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.     

Effects of spin-wave energy degeneracy induced by in-plane wave propagation in ferromagnetic thin films

This work presents an investigation of the collapse effect predicted to occur in the spin-wave band structure of magnetic cubic thin films. The system under consideration is described by the Heisenberg model with exchange interactions between the nearest (NN) and next-nearest neighbors (NNN) taken into account. In the collapse effect, which occurs for some specific directions of in-plane propagation of spin waves, the effective coupling between spins in adjacent layers vanishes dynamically and each mode becomes confined to a single atomic plane; this means that all the bulk modes and, independently, all the surface modes become energetically degenerate. This effect of ‘directional collapse’ can only occur when the exchange interactions between NN or NNN include bonds oblique with respect to the direction of in-plane propagation.     

The effect of the single-spin defect on the stability of the in-plane vortex state in 2D magnetic nanodots

The aim of this study is to analyse the stability of the single in-plane vortex state in two-dimensional magnetic nanodots with a nonmagnetic impurity (single-spin defect) at the centre. Small square and circular dots including up to a few thousand of spins are studied by means of a microscopic theory with nearest-neighbour exchange interactions and dipolar interactions fully taken into account. We calculate the spin-wave frequencies versus the dipolar-to-exchange interaction ratio d to find the values of d for which the assumed state is stable. Transitions to other states and their dependence on d and the vortex size are investigated as well, with two types of transition found: vortex core formation for small d values (strong exchange interactions), and in-plane reorientation of spins for large d values (strong dipolar interactions). Various types of localized spin waves responsible for these transitions are identified.     

The effect of bulk impurities on localized surface states

The effect of the occurrence of bulk impurities in a crystal on the existence and localization of surface states is examined by investigating a simple one-dimensional model. It is found that the bulk impurity has a small effect on the existence conditions for localized states associated with the surface, but the degree of localization of the corresponding charge density can be altered appreciably by the presence of such impurities. The penetration depth associated with localized surface levels can be much greater that than estimated for a pure crystal. The charge density associated with the electrons which occupy localized surface states may vary in a real crystal over a broader region near the surface than would be deduced from models of pure crystals. This will affect physical quantities, such as surface impedance, which are dependent on this charge distribution.     

Large wave vector spin waves and dispersion in two monolayer fe on w(110)

We present the first surface spin-wave (SW) dispersion measurements up to the surface Brillouin zone boundary of a two monolayer Fe film on W(110) by using spin-polarized electron energy loss spectroscopy. Pronounced features of SW peaks are observed in the spectra at room temperature. We found that the SW energies in the Fe film are strongly reduced compared to spin waves in bulk Fe and to theoretical predictions. Our results suggest that this reduction is caused by the reduction of exchange interaction within the 2 ML Fe on W(110) as compared to bulk Fe.     

Theory of magnetic multilayers. Exchange interactions and transport properties

The temperature dependence of the local magnetization in the spin-wave regime is discussed and it is shown that it can be used as a sensitive probe of local exchange interactions in magnetic surfaces and overlayers. The present status of the theory of oscillatory exchange interactions through transition and noble metal spacer layers is reviewed. The theory of the giant magnetoresistance observed recently in some antiferromagnetically coupled multilayers is also discussed. It is shown that both the oscillatory exchange and giant magnetoresistance effects can be understood in terms of different distributions of up and down spin d holes in different parts of the layer structure. The total energy and hence the exchange coupling is determined directly by the d band owing to its high density of states and the transport properties more indirectly through the Mott mechanism in which conduction electrons scatter into d band.     

Spin waves in degenerate ferromagnetic semiconductors at low temperatures

Thes-d(f) exchange model of a ferromagnetic semiconductor is considered. With the use of the perturbation expansion in the formal parameter (2S)^–1,S being the magnitude of magnetic ion spin, the magnon Green function is calculated. The spectrum and damping of spin waves in the presence of conduction electrons is investigated. It is demonstrated that the change of sign of the temperature dependent correction to the spin-wave stiffness is possible provided that the Fermi energy exceeds some critical value. This may lead to the increase of the spin-wave stiffness with temperature unlike the case of the Heisenberg ferromagnet. The estimations of this effect for doped EuO and EuS are carried out.     

Localized spin modes on the insulating antiferromagnetic stepped surface model

We present a numerical method to calculate the spin fluctuation dynamics on a stepped surface. The model discussed here consists of an extended antiferromagnetic surface step at the surface boundary of an insulating antiferromagnetic substrate. The stepped surface is formed by two straight steps dropped randomly and the spins moments of the steps and the substrate are considered as local with no electronic effects. The full magnetic problem arising from the absence of translational symmetry due to the presence of a magnetic surface and steps is considered and studied. The calculations concern in particular the energies of localized spin-wave modes near the surface steps and employ the matching procedure in the random-phase approximation and mean field approximation. Only the nearest-neighbor exchange interactions are considered between the spins in the model. The analytical formalism presented here is adapted from an earlier work on the vibrational spectra of two isolated steps, a structure that can be considered as a low dimensional system and solved for the three dimensional evanescent crystal spin field in the bulk and the surface domains around the steps. This spin field arises from the breakdown of the magnetic translation symmetry of the system. The results are used to calculate the spin mode energies associated with the steps and surface terraces. We show the presence of localized acoustic and optical spin wave modes propagating along the surface and the steps as well as the interface surface-steps, their fields are also described as evanescent in the plane normal to the surface step layers and depend on the nature of the exchange interaction near the steps.Received: 9 March 2004, Published online: 30 September 2004PACS: 75.70.Ak Magnetic properties of monolayers and thin films - 75.50.Ee Antiferromagnetics - 75.30.Ds Spin waves - 76.70.Hb Optically detected magnetic resonance (ODMR)     

Spatial structure of an incompressible quantum Hall strip

The incompressible quantum Hall strip is sensitive to charging of localized states in the cyclotron gap. We study the effect of localized states by a density functional approach and find electron density and the strip width as a function of the density of states in the gap. Another important effect is electron exchange. By using a model density functional which accounts for negative compressibility of the QH state, we find electron density around the strip. At large exchange, the density profile becomes nonmonotonic. Both effects, localized states and exchange, lead to a substantial increase of the strip width.     

Electronic state on the surface in the strongly correlated electron systems

In order to clarify the tunneling spectroscopy in high-T_c cuprates, we study electronic state of the surface in the strongly correlated electron systems. First, we obtain Green's function of strongly correlated normal bulk system using the fluctuation exchange (FLEX) approximation. Next, we insert infinite potential into the bulk system and obtain Green's function of surface. We find that the density of states (DOS) in strongly correlated bulk systems are different from that on the surface, and the difference decreases as the magnitude of Coulomb interaction (U) increases.