Calculations of localized modes on surface and impurity layer embedded in a semi-infinite Heisenberg ferromagnet

We investigate the magnetic excitations for the magnetic problem arising from the absence of magnetic translation symmetry in one dimension due to the presence of an impurity layer embedded within a semi-infinite ferromagnet. A Heisenberg model is employed to investigate the possibility that localized modes can occur with an impurity layer implanted within a semi-infinite ferromagnet. No electronic effects are considered. The theoretical approach employs the matching procedure in the mean field approximation and determines the propagating and evanescent spin amplitude fields including the contribution due to an applied field. The results are used to calculate the energies of localized modes associated with the impurity layer and 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. It is shown that more localized modes can occur and the modification of the spin wave spectra can be signaled by the appearance of surface and impurity modes, besides the bulk excitations. Also, the bulk spin fluctuations field, the spin waves localized on the surface as well as on impurity layer depend are shown to depend on the nature of the exchange coupling between spin sites, the values of spin sites and the position of the impurity layer from the surface.     

Magnons localised on surface steps: a theoretical model

We present the solution of the full magnetic problem arising from the absence of magnetic translation symmetry in two dimensions due to an extended magnetic surface step on the surface boundary of an insulating magnetic substrate. The calculation concerns in particular the spin fluctuation dynamics of a magnetic atomic step in the surface of a ferromagnetic simple cubic lattice, the spin order being in the direction normal to surface boundary. Only exchange interactions are considered between the spins in the model. The theoretical approach determines the evanescent spin fluctuation field in the two dimensional plane normal to the direction of the step edge. This field arises owing to the absence of magnetic translation symmetry in this plane, and is completely independent of the form of the surface defect, underlying the general character of the calculation. We show the existence of optical localised magnon modes propagating along the step, their fields being evanescent in the plane normal to the step direction. Received 17 February 1999     

Localised spin modes of decorated magnetic clusters on a magnetic surface

A method for the calculation of the energies of spin modes of surface magnetic clusters on a magnetic surface, using broken translation symmetry in three dimensions (3D), is employed to determine the spin mode energies for a variety of planar clusters. The cluster is considered to be supported on a magnetically ordered substrate such that the localised spins of the cluster and the substrate interact via magnetic exchange. No electronic effects are considered. The analytical approach solves for the 3D evanescent crystal spin field in the bulk and the surface domains around the cluster. This spin field arises owing to the breakdown of magnetic translation symmetry caused by the surface cluster. The analytical approach can be applied to any cluster configuration, underlying the general character of the calculation. In particular, we consider here a 4-, 5-, and 9-atoms planar clusters supported on the surface of a ferromagnetic simple cubic lattice, the spin order being in the direction normal to surface boundary. The method is applied to calculate the spin mode energies of these planar clusters consisting of Gd atoms interacting via Anti-ferromagnetic exchange with an Fe(1 0 0) surface. These results are compared with the calculated energies of the spin modes of the free clusters, and also with those for the same planar clusters when the cluster-substrate exchange is considered hypothetically ferromagnetic.     

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     

Interaction between localized moments in dilute alloys: Correlation effects

The effect of including dynamical correlations between electrons of opposite spins in determining the ground state energy of a pair of magnetically interacting impurity atoms in an otherwise normal metal is discussed. It is found that in the ground state of such a system the spins of the magnetic impurity atoms are aligned antiparallel. In other words, the interaction between the localized states is of antiferromagnetic exchange type. This result differs sharply from that predicted by the Hartree-Fock (H-F) theory, in which the ground state of the system can be either ferro- or antiferromagnetic, depending on the energies of the spin up and spin down electrons relative to the Fermi energy. The calculations are performed using many-body Green's function techniques in thet-matrix approximation.     

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.     

Verification of a new quantum simulation approach through its application to two-dimensional Ising lattices

A new quantum simulation approach has been applied in the present work to the two-dimensional (2D) ferromagnetic and antiferromagnetic Ising lattices to calculate their magnetic structures, magnetizations, free energies and specific heats in the absence of an external magnetic field. Surprisingly, no size effects could be observed in our simulations performed for the Ising lattices of different sizes. Most importantly, our calculated spontaneous thermally averaged spins for the two kinds of systems are exactly same as those evaluated with quantum mean field theory, and the magnetic structures simulated at all chosen temperatures are perfectly ferromagnetic or antiferromagnetic, verifying the correctness and applicability of our quantum model and computational algorithm. On the other hand, if the classical Monte Carlo (CMC) method is applied to the ferromagnetic 2D Ising lattice with S=1, it is able to generate correct magnetization well consistent with Onsager's theory; but in the case of S=1/2, the computational results of CMC are incomparable to those predicted with the quantum mean field theory, giving rise to very much reduced magnetization and considerably underestimated Curie temperature. The difficulty met by the CMC method is mainly caused by its improperly calculated exchange energy of the randomly selected spin in every simulation step, especially immediately below the transition temperature, where the thermal averages of spins are much less than 1/2, however they are assigned to ±1/2 by CMC to evaluate the exchange energies of the spins, such improper manipulation is obviously impossible to lead the code to converge to the right equilibrium states of the spin systems.     

Molecular spin resonance in the geometrically frustrated magnet MgCr2O4 by inelastic neutron scattering

We measured two magnetic modes with finite and discrete energies in an antiferromagnetic ordered phase of a geometrically frustrated magnet MgCr2O4 by single-crystal inelastic neutron scattering, and clarified the spatial spin correlations of the two levels: one is an antiferromagnetic hexamer and the other is an antiferromagnetic heptamer. Since these correlation types are emblematic of quasielastic scattering with geometric frustration, our results indicate instantaneous suppression of lattice distortion in an ordered phase by spin-lattice coupling, probably also supported by orbital and charge. The common features in the two levels, intermolecular independence and discreteness of energy, suggest that the spin molecules are interpreted as quasiparticles (elementary excitations with energy quantum) of highly frustrated spins, in analogy with the Fermi liquid approximation.     

Ferromagnetism in diluted magnetic semiconductor quantum dot arrays embedded in semiconductors

We present an Anderson-type model Hamiltonian with exchange coupling between the localized spins and the confined holes in the quantum dots to study the ferromagnetism in diluted magnetic semiconductor (DMS) quantum dot arrays embedded in semiconductors. The hybridization between the quantum-confined holes in the quantum dots and the itinerant holes in the semiconductor valence band makes possible hole transfer between the DMS quantum dots, which can induce the long range ferromagnetic order of the localized spins. In addition, it makes the carrier spins both in the quantum dots and in the semiconductors polarized. The spontaneous magnetization of the localized spins and the spin polarization of the holes are calculated using both the Weiss mean field approximation and the self-consistent spin wave approximation, which are developed for the present model.Received: 17 Mars 2003, Published online: 30 January 2004PACS: 75.75. + a Magnetic properties of nanostructures - 75.30.Ds Spin waves - 75.50.Dd Nonmetallic ferromagnetic materials - 75.50.Pp Magnetic semiconductors     

中心对称的阻挫磁体中斯格明子直径的调节

在带有垂直各向异性的二维三角晶格磁体中,当同时存在最近邻铁磁性和第三近邻反铁磁性交换作用时,垂直于膜面施加外磁场会使体系内自旋沿着非共面的方向排列,甚至出现拓扑稳定的斯格明子自旋结构.基于蒙特卡罗模拟方法,本文研究了在该二维阻挫磁体中,竞争性交换作用和外磁场对斯格明子直径的影响.与常规非中心对称的手性磁体中的斯格明子性质类似,外磁场会磁化斯格明子外围自旋而减小斯格明子直径.但是,磁体中反铁磁性交换作用的增强会整体压缩斯格明子.本文结合自旋波理论和蒙特卡罗模拟,首次量化了此类阻挫磁体中斯格明子的直径.结果表明:在弱的反铁磁性交换作用磁体中,斯格明子直径随磁场增大而快速线性减小;随着反铁磁性交换作用的增大,斯格明子直径随外磁场增大的减小变得相对平缓,但在强磁场下也会造成斯格明子直径的加速减小;随着反铁磁性交换作用的增强,斯格明子在不同外磁场下的直径的最大值和中值均从逐渐减小到渐趋稳定,而直径的最小值则从快速减小到表现出很大的涨落.这些现象都可以通过分析斯格明子在不同交换作用和外磁场下的构型和磁能变化加以解释.该项工作阐明了在中心对称的阻挫磁体中斯格明子直径的可调节性,不仅完善了我们对斯格明子本身物理机理的认识,同时也为发展基于斯格明子的新一代存储和逻辑器件提供了理论支撑.     

Long time evolution of a spin interacting with a spin bath in arbitrary magnetic field

We introduce a completely different method to calculate the evolution of a spin interacting with a sufficient large spin bath,especially suitable for treating the central spin model in a quantum dot(QD).With only an approximation on the envelope of central spin,the symmetry can be exploited to reduce a huge Hilbert space which cannot be calculated with computers to many small ones which can be solved exactly.This method can be used to calculate spin-bath evolution for a spin bath containing many(say,1000)spins,without a perturbative limit such as strong magnetic field condition,and works for long-time regime with sufficient accuracy.As the spin-bath evolution can be calculated for a wide range of time and magnetic field,an optimal dynamic of spin flip-flop can be found,and more sophisticated approaches to achieve extremely high polarization of nuclear spins in a QD could be developed.     

Effects of the spin–orbit coupling on magnetic and superconducting properties in iron-based superconductors

We analyze the magnetic properties through two-orbital Hubbard model with the spin–orbit coupling (SOC) interaction in the iron-based superconductors. With the help of the Ising approximation for the Hund’s coupling between the itinerant electrons and the localized spins, we give a self-consistent account of the various magnetic orders observed in pnictides and the pairing symmetry. We also calculate the local density of states (LDOS) of the vortex state when a magnetic field is applied. The LDOS without SOC shows no resonant peak at the vortex core center in the superconducting state, while it shows an obvious resonant peak when SOC is applied.     

一维自旋-轨道模型中的畴状轨道液体态

研究了一个一维可解自旋-轨道模型.在大自旋极限下，自旋自由度可以近似用经典自旋来描 述.在没有外磁场情形，系统的基态是伊辛自旋反铁磁背景下的轨道液体态.其低能元激发是 类似于spinon的轨道量子.而在有外磁场情形，系统会出现磁通点阵相.同时，磁通将系统分 割成不连通的轨道液体. 关键词： 自旋轨道系统 畴状轨道液体     

Conductance dips and spin precession in a nonuniform waveguide with spin–orbit coupling

An infinite waveguide with a nonuniformity, a segment of finite length with spin–orbit coupling, is considered in the case when the Rashba and Dresselhaus parameters are identical. Analytical expressions have been derived in the single-mode approximation for the conductance of the system for an arbitrary initial spin state. Based on numerical calculations with several size quantization modes, we have detected and described the conductance dips arising when the waves are localized in the nonuniformity due to the formation of an effective potential well in it. We show that allowance for the evanescent modes under carrier spin precession in an effective magnetic field does not lead to a change in the direction of the average spin vector at the output of the system.     

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.     

Spin-glass surface disorder on the magnetic behaviour of antiferromagnetic small particles

We studied the magnetic properties of an antiferromagnetic small particle of Ising spins. The particle is represented by a two-dimensional array of spins, where the coupling between spins in the core is antiferromagnetic, and its surface is modelled by a shell of spins with competing interactions, simulating a spin-glass type ordering at the surface. We investigated this model by mean-field approximation and Monte Carlo simulations. The magnetic behaviour was studied as a function of the temperature and external magnetic field. Some of the experimental findings observed in real antiferromagnetic nanoparticles, like hysteresis, shifted loops and coercive field, are obtained for this model. We showed that these properties strongly depend on the degree of surface disorder.     

Spin orientation and excitation of magnetic nanocluster on metal surface

The spin orientation and excitation of the ferromagnetic nanocluster on the magnetic metal surface are studied numerically. We show that localized magnetic excitation modes are generated by the spin fluctuation of the cluster, when the ferromagnetic interaction J′ between the cluster and the metal surface is small and the spins in the cluster are oriented in the opposite direction with those of the metal surface by the external field. This magnetic structure is similar to the domain wall (DW) structure of a ferromagnetic wire, both sides of which connect with metal surfaces. As the interaction J′ increases, the sign of the thermal average of the spins in the cluster changes, i.e., the spin-flip takes place. In this time, the magnetic fluctuation of the cluster becomes large and the magnetic excitation energies, except for that of one excitation mode, overlap with the excitation spectrum of the spin wave. We also show that, by the overlap, sharp peaks and dips occur in the excitation spectrum of the spin wave.     

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.     

Effect of interstate interactions on specific heat and magnetic susceptibility in Anderson-localized system

Electron-electron interactions in Anderson-localized states lead to both ferromagnetic (direct exchange) and antiferromagnetic (kinetic-type exchange) interactions among spins of singly occupied states. Specific heat anomaly, in particular its magnetic field dependence, and magnetic susceptibility at low temperatures are calculated by taking into account the coexistence of ferromagnetic and antiferromagnetic interactions among localized spins within a pair model. It is shown that the experimental results on Si:P can be well explained by the present theory.     

Uniform spin wave modes in antiferromagnetic nanoparticles with uncompensated moments

In magnetic nanoparticles the uniform precession (q = 0 spin wave) mode gives the predominant contribution to the magnetic excitations. We have calculated the energy of the uniform mode in antiferromagnetic nanoparticles with uncompensated magnetic moments, using the coherent potential approximation. In the presence of uncompensated moments, an antiferromagnetic nanoparticle must be considered as a kind of a ferrimagnet. Two magnetic anisotropy terms are considered, a planar term confining the spins to the basal plane, and an axial term determining an easy axis in this plane. Excitation energies are calculated for various combinations of these two anisotropy terms, ranging from the simple uniaxial case to the planar case with a strong out-of-plane anisotropy. In the simple uniaxial case, the uncompensated moment has a large influence on the excitation energy, but in the planar case it is much less important. The calculations explain recent neutron scattering measurements on nanoparticles of antiferromagnetic α-Fe₂O₃ and NiO.