Showing papers on "Spin wave published in 1981"

Many-Particle Physics

Abstract: 1. Introductory Material.- 1.1. Harmonic Oscillators and Phonons.- 1.2. Second Quantization for Particles.- 1.3. Electron - Phonon Interactions.- A. Interaction Hamiltonian.- B. Localized Electron.- C. Deformation Potential.- D. Piezoelectric Interaction.- E. Polar Coupling.- 1.4. Spin Hamiltonians.- A. Homogeneous Spin Systems.- B. Impurity Spin Models.- 1.5. Photons.- A. Gauges.- B. Lagrangian.- C. Hamiltonian.- 1.6. Pair Distribution Function.- Problems.- 2. Green's Functions at Zero Temperature.- 2.1. Interaction Representation.- A. Schrodinger.- B. Heisenberg.- C. Interaction.- 2.2. S Matrix.- 2.3. Green's Functions.- 2.4. Wick's Theorem.- 2.5. Feynman Diagrams.- 2.6. Vacuum Polarization Graphs.- 2.7. Dyson's Equation.- 2.8. Rules for Constructing Diagrams.- 2.9. Time-Loop S Matrix.- A. Six Green's Functions.- B. Dyson's Equation.- 2.10. Photon Green's Functions.- Problems.- 3. Green's Functions at Finite Temperatures.- 3.1. Introduction.- 3.2. Matsubara Green's Functions.- 3.3. Retarded and Advanced Green's Functions.- 3.4. Dyson's Equation.- 3.5. Frequency Summations.- 3.6. Linked Cluster Expansions.- A. Thermodynamic Potential.- B. Green's Functions.- 3.7. Real Time Green's Functions.- Wigner Distribution Function.- 3.8. Kubo Formula for Electrical Conductivity.- A. Transverse Fields, Zero Temperature.- B. Finite Temperatures.- C. Zero Frequency.- D. Photon Self-Energy.- 3.9. Other Kubo Formulas.- A. Pauli Paramagnetic Susceptibility.- B. Thermal Currents and Onsager Relations.- C. Correlation Functions.- Problems.- 4. Exactly Solvable Models.- 4.1. Potential Scattering.- A. Reaction Matrix.- B. T Matrix.- C. Friedel's Theorem.- D. Phase Shifts.- E. Impurity Scattering.- F. Ground State Energy.- 4.2. Localized State in the Continuum.- 4.3. Independent Boson Models.- A. Solution by Canonical Transformation.- B. Feynman Disentangling of Operators.- C. Einstein Model.- D. Optical Absorption and Emission.- E. Sudden Switching.- F. Linked Cluster Expansion.- 4.4. Tomonaga Model.- A. Tomonaga Model.- B. Spin Waves.- C. Luttinger Model.- D. Single-Particle Properties.- E. Interacting System of Spinless Fermions.- F. Electron Exchange.- 4.5. Polaritons.- A. Semiclassical Discussion.- B. Phonon-Photon Coupling.- C. Exciton-Photon Coupling.- Problems.- 5. Electron Gas.- 5.1. Exchange and Correlation.- A. Kinetic Energy.- B. Direct Coulomb.- C. Exchange.- D. Seitz' Theorem.- E. ?(2a).- F. ?(2b).- G. ?(2c).- H. High-Density Limit.- I. Pair Distribution Function.- 5.2. Wigner Lattice and Metallic Hydrogen.- Metallic Hydrogen.- 5.3. Cohesive Energy of Metals.- 5.4. Linear Screening.- 5.5. Model Dielectric Functions.- A. Thomas-Fermi.- B. Lindhard, or RPA.- C. Hubbard.- D. Singwi-Sjolander.- 5.6. Properties of the Electron Gas.- A. Pair Distribution Function.- B. Screening Charge.- C. Correlation Energies.- D. Compressibility.- 5.7. Sum Rules.- 5.8. One-Electron Properties.- A. Renormalization Constant ZF.- B. Effective Mass.- C. Pauli Paramagnetic Susceptibility.- D. Mean Free Path.- Problems.- 6. Electron-Phonon Interaction.- 6.1 Frohlich Hamiltonian.- A. Brillouin-Wigner Perturbation Theory.- B. Rayleigh-Schrodinger Perturbation Theory.- C. Strong Coupling Theory.- D. Linked Cluster Theory.- 6.2 Small Polaron Theory.- A. Large Polarons.- B. Small Polarons.- C. Diagonal Transitions.- D. Nondiagonal Transitions.- E. Dispersive Phonons.- F. Einstein Model.- G. Kubo Formula.- 6.3 Heavily Doped Semiconductors.- A. Screened Interaction.- B. Experimental Verifications.- C. Electron Self-Energies.- 6.4 Metals.- A. Phonons in Metals.- B. Electron Self-Energies.- Problems.- 7. dc Conductivities.- 7.1. Electron Scattering by Impurities.- A. Boltzmann Equation.- B. Kubo Formula: Approximate Solution.- C. Kubo Formula: Rigorous Solution.- D. Ward Identities.- 7.2. Mobility of Frohlich Polarons.- A. Single-Particle Properties.- B. ??1 Term in the Mobility.- 7.3. Electron-Phonon Interactions in Metals.- A. Force-Force Correlation Function.- B. Kubo Formula.- C. Mass Enhancement.- D. Thermoelectric Power.- 7.4. Quantum Boltzmann Equation.- A. Derivation of the Quantum Boltzmann Equation.- B. Gradient Expansion.- C. Electron Scattering by Impurities.- D. T2 Contribution to the Electrical Resistivity.- Problems.- 8. Optical Properties of Solids.- 8.1. Nearly Free-Electron System.- A. General Properties.- B. Force-Force Correlation Functions.- C. Frohlich Polarons.- D. Interband Transitions.- E. Phonons.- 8.2. Wannier Excitons.- A. The Model.- B. Solution by Green's Functions.- C. Core-Level Spectra.- 8.3. X-Ray Spectra in Metals.- A. Physical Model.- B. Edge Singularities.- C. Orthogonality Catastrophe.- D. MND Theory.- E. XPS Spectra.- Problems.- 9. Superconductivity.- 9.1. Cooper Instability.- 9.2. BCS Theory.- 9.3. Electron Tunneling.- A. Tunneling Hamiltonian.- B. Normal Metals.- C. Normal-Superconductor.- D. Two Superconductors.- E. Josephson Tunneling.- 9.4. Infrared Absorption.- 9.5. Acoustic Attenuation.- 9.6. Excitons in Superconductors.- 9.7. Strong Coupling Theory.- Problems.- 10. Liquid Helium.- 10.1. Pairing Theory.- A. Hartree and Exchange.- B. Bogoliubov Theory of 4He.- 10.2. 4He: Ground State Properties.- A. Off-Diagonal Long-Range Order.- B. Correlated Basis Functions.- C. Experiments on nk.- 10.3. 4He: Excitation Spectrum.- A. Bijl-Feynman Theory.- B. Improved Excitation Spectra.- C. Superfluidity.- 10.4. 3He: Normal Liquid.- A. Fermi Liquid Theory.- B. Experiments and Microscopic Theories.- C. Interaction between Quasiparticles: Excitations.- D. Quasiparticle Transport.- 10.5. Superfluid 3He.- A. Triplet Pairing.- B. Equal Spin Pairing.- Problems.- 11. Spin Fluctuations.- 11.1. Kondo Model.- A. High-Temperature Scattering.- B. Low-Temperature State.- C. Kondo Temperature.- 11.2. Anderson Model.- A. Collective States.- B. Green's Functions.- C. Spectroscopies.- Problems.- References.- Author Index.

Valence bond description of antiferromagnetic coupling in transition metal dimers

Abstract: A single configuration model containing nonorthogonal magnetic orbitals is developed to represent the important features of the antiferromagnetic state of a transition metal dimer. A state of mixed spin symmetry and lowered space symmetry is constructed which has both conceptual and practical computational value. Either unrestricted Hartree–Fock theory or spin polarized density functional theory, e.g., Xα theory, can be used to generate the mixed spin state wave function. The most important consequence of the theory is that the Heisenberg exchange coupling constant J can be calculated simply from the energies of the mixed spin state and the highest pure spin multiplet.

Itinerant electron magnetism

Abstract: The many theoretical studies of the various magnetic, thermal and magnetoelastic properties for paramagnetic and ferromagnetic transition metals and alloys in the simple itinerant electron model are reviewed. The important amendments to the simple itinerant electron model or Stoner model of magnetism due to the spin wave excitations and spin fluctuations are explained.

Spin Polarization and Atomic Geometry of the Si(111) Surface

Abstract: Based on pseudopotential local spin-density calculations, it is proposed that the minimum-energy Si(111) nonbuckled surface is stable against 2 x 1 buckling distortions. A 2 x 1 antiferromagnetic spin-density wave, localized on the surface, enhances the stability of this structure.

Mean field theory for Heisenberg spin glasses

Abstract: The infinite-ranged spin glass model is studied in the general case of m-component spins. Results for the magnetization laws, the shape of the phase diagram, the nature of the transitions are presented.

Dimerization and Solitons in One-Dimensional XY-Z Antiferromagnets

Abstract: Our previous calculations of the lattice distortion and the formation energy of a soliton in the one-dimensional antiferromagnetic Heisenberg spin-Peierls systems are refined and extended to the case of X Y - Z model. The spin degree of freedom are represented by the phase Hamiltonian with the help of boson representation of fermions introduced by the Jordan-Wigner transformation. Parameters in this phase Hamiltonian are adjusted so that spin wave velocity and exponent of correlation function agree with exact results. This adjustment is shown to give also exact spin susceptibility in the absence of lattice distortion. Based on this phase Hamiltonian of the X Y - Z model localized excitations (solitons) in the presence of lattice distortions are examined in details including the width, the formation energy and the magnetic field dependence.

A New Formalism for High Spin States Applied to the sd-Shell Region

Abstract: A new development within the high spin Nilsson-Strutinsky formalism is presented and applied to certain sd-shell nuclei. The previous method of calculating potential-energy surfaces as a function of angular momentum using interpolated spin values is not satisfactory when studying the individual bands for these light nuclei. In the present research, many-particle many-hole excitations are considered in the rotating system at each deformation in order to calculate the lowest energy at each spin. It is thus possible to calculate not only yrast states but also excited configurations. Potential-energy surfaces in the (, γ)-plane (with each grid point minimized with respect to 4) are calculated at various values of spin, parity and signature. Special attention is paid to the problem of signature splitting ("decoupled bands") and in some cases the two signatures are found to correspond to different shape changes of the nucleus with increasing spin. Detailed investigations of the nuclei 20,22Ne, 24Mg, 27Al and 28Si are presented.

Magnetostatic spin‐wave modes of a heterogeneous ferromagnetic double layer

Abstract: The theory for the magnetostatic spin‐wave modes has previously been presented for homogeneous nonsymmetric double layers [J. Appl. Phys. 51, 4338 (1980)]. It is now extended to the heterogeneous case, where the magnetizations in the two films are allowed to be different. A restriction is still made with respect to inplane magnetization, transverse propagation of the spin waves, and neglect of exchange. Some limiting cases are found to be in agreement with results obtained by other authors. Patterns of the m‐ and b‐fields of some typical modes are also presented.

Have solitons been observed in CsNiF/sub 3/

Abstract: It is shown that a noninteracting--spin-wave theory, in which the central component observed by neutron scattering is attributed to scattering from spin-wave--density fluctuations, gives intensities comparable to, or greater than, the intensities predicted by the soliton theory, and provides a better fit to the variation of the intensity with field, temperature, and wave vector. We conclude that further work is needed to distinguish the soliton contribution to the central-peak intensity from the scattering by pairs of spin waves.

Simulation of the Effects of Paramagnons on a Superconductor by a Simple Rescaling

Abstract: It is shown that under certain conditions a superconductor with spin fluctuations (paramagnons) exhibits the same tunneling characteristics and thermodynamic properties as a superconductor with no paramagnons having the same electron-phonon interaction but scaled down, and an increased effective Coulomb interaction. The condition is that the paramagnon frequency be much higher than any phonon frequency. The effective anisotropy in the electron-phonon interaction is also shown to increase.

Neutron scattering investigation of the temperature dependence of long-wavelength spin waves in ferromagnetic Rb2CrCl4

Abstract: The long-wavelength spin waves in Rb2CrCl4, a nearly two-dimensional ferromagnet, have been investigated at several temperatures below Tc=52.4K using neutron inelastic scattering techniques. The data have been analysed in terms of a Hartree-Fock theory using matching-matrix elements to give correctly the effects of anisotropy. Values for the parameters in the spin Hamiltonian have been found, and the theory accounts well for the energy renormalisation of the spin waves and for the transition temperature and variation of magnetic moment with temperature. Due to weak uniaxial anisotropy terms the spin wave spectrum has a small energy gap of approximately=1K at zero wavevector, which precludes true XY-type behaviour, and a canting of the spins of +or-1.1 degrees from (110) directions is predicted.

Magnetic excitations in chromium. II.

Abstract: Neutron scattering measurements on pure chromium metal have been performed under various conditions of experimental resolution, energy transfer, temperature, and magnetic field. The temperature and energy dependence of the commensurate-diffuse scattering surrounding the (0,0,1) point in reciprocal space has been followed from the spin-flip temperature (${T}_{\mathrm{sf}}$=122 K) to temperatures as high as 700 K, well above the N\'eel point (${T}_{N}$=312 K). Magnetic correlations extending over 11 bcc unit cells persist to these high temperatures. The spectral width of the magnetic scattering is found to increase rapidly with temperature above ${T}_{N}$. The importance of the commensurate-diffuse modes of excitation in the disappearance of the long-range-ordered spin-density-wave (SDW) state at ${T}_{N}$ is discussed. The magnetic field dependence of the excitations in the transversely polarized SDW phase has been investigated and found to be absent. Evidence is also presented for the absence of a spin-wave energy gap greater than 50 \ensuremath{\mu}eV. We have placed the scattering in the paramagnetic phase on an absolute scale by normalizing to the integrated intensities of selected phonons, and have estimated an effective magnetic moment per atom.

Helical Spin Density Wave Due to Antisymmetric Exchange Interaction

Abstract: For the spin systems with both the symmetric exchange interaction (SEI) and the antisymmetric exchange interaction (AEI) (the Dzyaloshinsky-Moriya interaction), the relative stability between the ferromagnetic state (FMS) and the helical spin density wave (HSDW) is discussed phenomenologically. The arguments are made to the spin systems of which the spin structures are described by the spin density S ( r ) varying slowly with the position r and the SEI is favorable to the FMS. For the 21 types of crystal symmetry with the isogonal point groups having no inversion symmetry, the characteristics of the instability of the FMS are investigated. By use of the Landau free energy obtained for crystals with the isogonal point groups T and O , the magnetization process, the magnetic phase diagram, and the intensity of the neutron diffuse scattering are calculated. A comparison between the calculated results and the experiments on MnSi is also given.

On the evolution of higher dimensional Heisenberg continuum spin systems

Abstract: We consider the evolution of a classical Heisenberg ferromagnetic spin chain in its continuum limit in higher spatial dimensions. It is shown that the evolution of a radially symmetric chain could be identified with the motion of a helical space curve as in the linear case. The resulting invariant equations for the curvature (radial energy density) and torsion (related to current density) are shown to be equivalent to a generalized nonlinear Schrodinger equation, similar to the one derived by Ruijgrok and Jurkiewicz recently. Equivalent linear equations as well as special static solutions of point singular type are obtained. Similarity solutions, a class of which belong to Riccati type, are discussed in detail. For general higher dimensions, a potentially useful formulation is presented: Under stereographic projection of the unit sphere of spin, the equation of motion takes a neater form even with the inclusion of anisotropic interactions. Classes of explicit solutions are reported in higher dimensions. Propagating spin waves, static spin waves of point singular nature and of finite energy in some cases are also discussed.

Temperature Dependence of the Spin Dynamics of EuO

Abstract: Neutron-inelastic-scattering techniques have been used to study the spin dynamics of EuO. High-quality single crystals were used so that temperature-dependent line shapes could be obtained at all momentum values. It was found that the magnetic excitations above ${T}_{c}$ changed from Lorentzian-like peaks centered at zero energy near the zone center to rather well-defined spin-wave-like excitations at the zone boundary.

Spin Dynamics in the Amorphous Invar Alloy of Fe 86 B 14

Abstract: The spin waves in an amorphous Invar alloy Fe 86 B 14 11 , have been studied by inelastic neutron scattering. Well defined magnon groups were detected around (0, 0, 0) up to q =0.12 A -1 for various temperatures below T ≤0.9 T c . The spin waves show the dispersions \( \hbar \omega _{q}(T)=E_{0}(T)+D(T)q^{2}\) with D ( T ) varying with temperature according to D ( T )= D (0)(1- a T 5/2 ) with D (0)=118 ±6 (meV A 2 ). The spin wave stiffness at 0 K, D (0), thus determined is almost twice as large as the value D M (0)=68 ±2 (meV A 2 ) determined for the same sample by a magnetization measurement. The spin wave linewidth \( \varGamma \) varies with wave vector q as \(\varGamma=aq^{2}\) and it shows only limited temperature dependence. All of these features are quite similar to those found in the crystalline Invar alloys as Fe 65 Ni 35 and Fe 3 Pt.

Lattice Systems with a Continuous Symmetry III. Low Temperature Asymptotic Expansion for the Plane Rotator Model

Abstract: We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d = 3.

Lattice Systems with a Continuous Symmetry

Abstract: We prove that the expansion in powers of the temperature T of the correlation functions and the free energy of the plane rotator model on a d-dimensional lattice is asymptotic to all orders in T The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures for d= 3.

Pairbreaking in superconductors near and below antiferromagnetic transitions

Abstract: The Abrikosov-Gorkov theory for pairbreaking in superconductors due to a dilute concentration of magnetic impurities is generalized to the case when the magnetic ions are present in a large concentration or on a regular lattice. The case in which the magnetic ions undergo a transition to an antiferromagnetic phase is considered in detail. The physical considerations for increased or decreased pairbreaking over the Abbrikosov-Gorkov value due to the increased range of correlations near the antiferromagnetic transition and due to inelastic scattering of electrons off spin waves in the antiferromagnetic phase are discussed in detail. Recent experimental results are considered in terms of the new theory.

Anomalous spin-wave behavior in the magnetic alloy Fe/sub x/Cr/sub 1-x/

Abstract: Neutron scattering methods are employed to study the temperature and magnetic field dependence of the spin dynamics in the alloy Fe/sub x/Cr/sub 1-x/ for x = 0.34, 0.28, 0.26, 0.24, and 0.22. For x = 0.34 and 0.28, the system orders ferromagnetically and exhibits well-defined spin waves throughout the ferromagnetic phase. For x< or =0.26, ferromagnetism is also present but at low temperatures a spin-glass-like phase exists. For these concentrations the spin-wave excitations are observed within the ferromagnetic phase but as the temperature is lowered towards the spin-glass regime the spin-wave frequency decreases. At low temperatures, within the spin-glass reigme, no well-defined excitations are present, but an intense quasielastic peak is observed. Application of a magnetic field causes a reemergence of the spin-wave excitations.

The paramagnetic state of BCC iron

Abstract: Calculations are reported of the static and dynamic properties of an effective Heisenberg model of Fe with exchange interactions extending to fifth-nearest neighbours. Exchange parameters chosen to fit the spin wave dispersion curve at room temperature lead to little short-range order above Tc and to a neutron scattering function S(q, omega ) which is compatible with Lynn's 'constant omega ' plots. The dispersion curve obtained by plotting the positions of peaks in 'constant omega ' plots is in excellent agreement with the observed one but it does not correspond to propagating spin waves above Tc. The authors' results do not, however, reproduce the observed rapid drop of intensity at low frequency in 'constant q' scans.

Spin Dynamics in Invar (Fe 65 Ni 35 , Fe 3 Pt) and Non Invar (Fe 50 Ni 50 ) Alloys

Abstract: Spin dynamics of a disordered Invar alloy Fe 65 Ni 35 , an ordered Invar alloy Fe 3 Pt as well as a non Invar disordered alloy Fe 50 Ni 50 have been studied by neutron scattering. It has been found that both Invar alloys show common anomalous dynamical properties. Well defined magnon groups could be detected up to the Curie temperature. The spin wave stiffness constant D ( T ) varies with temperature as D ( T )= D 0 (1 - C T 5/2 ). The magnon excitations, however, could explain only about a half of the temrerature variation of magnetization M ( T ) for the Invar alloys, in spite of the fact that the integrated intensity measurements of the magnon spectra suggest that no other excitations take part in M ( T ). M ( T ) of non Invar alloy could be accounted for by the magnon excitations. The magnons in the Invar alloys dampen significantly with increasing temperature as was apparent in the linewidth \(\varGamma (q, T)\) obeying a relation \(\varGamma (q, T)=(\varGamma _{0}+aT^{\alpha })q^{2}\) with α≤1, quit...

Spin waves in triple-q--> structures. Application to USb

Abstract: The spin-wave spectrum in a system with triple-q magnetic structure is calculated. The spin waves differ distinctly from those in the corresponding single-q structure, but agree with the excitations observed by Lander and Stirling in uranium antimonide (USb). Their experiments thus directly verify that the spins in USb are ordered in the triple-q structure.