Spin-rotational Invariance Research Articles

Anomalous spin-wave excitations in a one-dimensional Dzyaloshinski–Moriya antiferromagnet

The dynamics of a one-dimensional Heisenberg antiferromagnet with a small Dzyaloshinski–Moriya component to the exchange interaction is considered. The spin rotational invariance within the easy plane is broken by the application of a weak magnetic field in the easy plane. The nature of the spin-wave excitations of the quantum spin system is investigated, and pronounced anomalies in the single-spin-wave spectrum at fields comparable to the anisotropy in the exchange interaction are found. These anomalies are of quantum character and are related to the resonance between the single-spin-wave and the two-spin-wave excitations. The implications for the two-spin-wave bound states are discussed.

Heavy-fermion state in the Anderson lattice.

To investigate theoretically the heavy-fermion state in cerium and uranium compounds, the low-energy excited states in an Anderson lattice are studied at absolute zero. The coupled Dyson equations for both the Green's functions of the f electron and the spin fluctuations are set up in the case of the finite correlation interaction energy. The vertex functions are approximately determined to fulfill the Ward-Takahashi relations which originate from the spin-rotational invariance, in the low-energy region. In the spectral density of the f-electron Green's function which is numerically calculated, it is found that a sharp peak corresponding to the state of quasifermions with heavy masses appears near the Fermi level, and a broad peak similar to the resonance peak in Kondo impurity systems appears in a relatively-high-energy region. As the temperature increases, the quasifermion peak diminishes and changes to the resonance peak.

Magnetic properties of the Anderson lattice

A formulation for the Anderson lattice is presented. Using the Ward-Takahashi relations which stem from the spin-rotational invariance of the system, we construct a set of coupled equations of the f-electron and the spin-fluctuation Green's functions in a form invariant under the spin-rotation.

Dynamical unification of fermions and gauge bosons for internal symmetry and gravity

Internal-symmetry gauge bosons and the tetrad fields of gravity with their respective nontrivial local transformation behaviour are constructed by more basic gauge fermions. A physically sensible mass scale Λ2 for a parametrization for the small-distance behaviour of the theory is closely related to Newton’s and Sommerfeld’s constants. Local invariances determine uniquely the renormalizable gauge fermion self-interactions. The very quantization can be interpreted as a dynamical breakdown of a local spin rotation invariance and leads to spin-spin four-fennion interaction in a dynamical Higgs mechanism.

Surface spin waves in the Hubbard model

A general random-phase-approximation (RPA) equation for the surface susceptibility of an itinerant ferromagnet is derived. The surface is treated as a perturbation to the bulk problem. It is shown that the resulting secular equation for surface spin waves has the same structure as for magnetic insulators. It is demonstrated that the spin-rotational invariance of the Hubbard Hamiltonian imposes an important self-consistency condition on the surface perturbation to the bulk susceptibility. The previous calculations which do not satisfy this self-consistency condition are critically reviewed. The secular equation for surface spin waves is solved explicitly for a strong itinerant ferromagnet containing a plane of impurities with an excess intra-atomic repulsion $\ensuremath{\Delta}U$ modeling the surface. The unenhanced surface susceptibility is treated exactly in the surface plane and approximated by the bulk susceptibility outside the plane. This approximation is shown to be asymptotically exact within RPA for a ferromagnet with exchange splitting much larger than the bandwidth. Surface spin waves in this model split off the bottom of the bulk spin-wave band for a magnetically weaker surface ($\ensuremath{\Delta}U<0$) and they deviate downward from the bulk band only to the order ${q}_{\ensuremath{\parallel}}^{4}$ (${q}_{\ensuremath{\parallel}}$ is the wave vector parallel to the surface). The attenuation of long-wavelength surface spin waves is exponential and their attenuation length is proportional to the square of the wavelength. All these properties are in qualitative agreement with the properties of surface spin waves in magnetic insulators. The similarities and differences between surface spin waves in metals and insulators are discussed in the light of the modern approach to magnetic excitations in bulk itinerant ferromagnets.

Ward-Takahashi Identities in Itinerant Electron Ferromagnetism. I: Zero Temperature Case

A systematic calculation of the Ward-Takahashi identities in 1tmerant electron ferro­ magnetism is presented by making use of the functional integral method. The 1/h-singularity of the magnon Green's function for vanishing energy and momentum plays the significant role. Here h denotes a ficticious infinitesimal magnetic field applied to the system. The identities for the multi point vertex functions corresponding to the processes in which the electron, magnon and longitudinal spin fluctuation interact are given. The electron and magnon pole term contributions to these identities are discussed. § I. Introduction So far a number of theoretical works have been made to clarify the effects of the electron-magnon interaction in itinerant electron ferromagnetism. ll. 2) Any theo­ ry in this field is required to keep the rotational invariance when we make quan­ titative discussion. It is well-known that such invariance is conveniently described in the frame of the Ward-Takahashi identities (hereafter referred to as \VTI). In a previous paper,') we have proposed a systematic approach to calculating WTI in ferromagnetically ordered state making use of the functional integral method. In our treatment, a ficticious infinitesimal magnetic field h is introduced to create the ordered state. h is taken as zero after the end of calculation. The ordered state does not have the spin rotational invariance, and as a result of such breakdown of symmetry, the magnon appears as a Goldstone boson in order to recover the original symmetry. In deriving WTI, the 1/h-singularity of the magnon Green's function for vanishing energy and momentum plays the significant role. The pur­ pose of this paper is to present WTI with the help of the above method for multi point vertex functions in which the electron, magnon (transversal spin fluctuation), and longitudinal spin fluctuation interact with each other and themselves. In order to analyze the electron and magnon propagators, we need at least three point vertex functions which correspond to the magnon emission or absorption

Spin density functional theory for the spin wave stiffness coefficient in ferromagnets

The spin density functional theory is used to derive a variational principle (lower bound) for the wavevector dependent static transverse ferromagnetic spin susceptibility chi +-(q) for a general exchange-correlation energy functional. This variational principle is a direct consequence of the Hohenberg and Kohn minimum energy theorem for the ground state. The importance of spin rotational invariance is stressed in choosing the trial function so that the variational expression for chi +-(q) has the correct behaviour for small q. Noting the relationship between the spin wave stiffness coefficient D and chi +-(q), a rigorous upper bound for D is derived for general ferromagnetic systems. The relationships between the present general theory for D and recent theories based on the local exchange model are discussed.

Remarks on coupled spin and charge fields in the Hubbard hamiltonian

This paper deals with the combined effect of spin and charge fluctuations on the thermodynamic properties of an itinerant electron paramagnet described by the Hubbard Hamiltonian. Firstly, we discuss the functional integral formulation of the partition function. We argue that a correct formulation must preserve the spin rotational invariance of the Hamiltonian. As a consequence, the Landau-Ginzburg-Wilson free energy functional contains both spin and charge fluctuation fields, with coupling terms of the form ρM2, ρ2 M2, etc... where p is a charge (scalar) field, and M is a vector spin field with 3 components. The relevant coupling between spin and charge fields is [FORMULA] where n(e) is the density of states, eF is the Fermi level, and u is the intra-atomic Coulomb integral. It is pure imaginary. Next, we exploit the similarity between the free energy which we obtain and various other cases of coupled fields, such as metamagnets, or other phenomenological functionals. The role of constraints such as charge neutrality is discussed, with respect to critical properties, using the renormalization group method.

Electron correlations in itinerant strong ferromagnetism

The problem of fully exploiting the requirement of spin rotation invariance to study the structure of the electron self-energy in itinerant strong ferromagnetism is considered. A model is derived which describes the effect of electron-magnon interaction in terms of a spinon self-energy.

Low-temperature behavior of the spin-wave energy in the itinerant electron model of ferromagnetism

An exact microscopic formula for the transverse dynamical susceptibility is derived from the spin rotation invariance properties of the model. The same properties allow the definition on a microscopic basis of the effective magnon-magnon interaction. As a concrete application of the above general results we calculate the low-temperature behavior of the spin-wave energy due to magnon-magnon interaction in the long-wavelength limit. For Ni in the parabolic band approximation and strong ferromagnetism limit we haveC2(K)=8.3×10−5T5/2K2 meV.

Spin-rotation invariance and the structure of correlation functions in magnetic systems

We analyze, in the framework of the functional approach to statistical mechanics, general properties of correlation functions in ordered magnetic systems. The aim of this paper is to investigate what consequences can be derived from the requirement of invariance of the theory under local infinitesimal spin rotation. The extension of the method that we introduce, to include anisotropic Hamiltonians, is discussed, and the case of the anisotropy described by an internal field is worked out. Our main results are a set of generalized Ward identities, a microscopic definition of the stiffness constant as a static limit of a local response function, and an exact asymptotic expression for the correlation functions of interest, for zero temperature and small wave length and frequency. Modifications to the hydrodynamic expression for correlation functions in the case where anisotropy is present are also discussed.