Green's function study of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system

The magnetic properties of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system on a square lattice are investigated by using the double-time temperature-dependent Green's function technique. In order to decouple the higher order Green's functions, Anderson and Callen's decoupling and random phase approximations have been used. The nearest- and next-nearest-neighbor interactions and the single-ion anisotropies are considered and their effects on compensation and critical temperature are studied.     

Callen's postulates and the riemannian space of thermodynamic states

It is shown that the property uniquely fixed for a thermodynamical system by Callen's postulates is the riemannian structure of its thermodynamic state space.     

Many‐body Green's function theory for thin ferromagnetic films: exact treatment of the single‐ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many‐body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second‐ and fourth‐order uniaxial single‐ion anisotropy, and the magnetic dipole‐dipole coupling. The single‐ion anisotropy terms can be treated exactlyby introducing higher‐order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest‐order Green's functions. RPA‐like approximations are used to decouple the exchange interaction terms in both the low‐order and higher‐order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.     

Exact Green's function of the equations of quantum mechanics in an electromagnetic field. I

An exact Green's function of the Cauchy problem in arbitrary (nonparallel) stationary homogeneous electrical and magnetic fields is constructed for the Klein-Gordon-Fock and Dirac equations and for the Pauli equation in arbitrary nonstationary fields, on the basis of a single approach using the method of the canonical Maslov operator (extension of the WKB method to the multidimensional case) and a Fock idea about the proper time in relativitic mechanics.     

Theory of the free full-circle arc

A theoretical investigation of the full-circle arc located between two planes is presented. The circular arc shape is due to an applied magnetic field. The basic equations for conservations of mass, momentum, energy, and charge, as well as Maxwell's equations and the equation of state lead to a coupled set of partial differential equations. By means of Green's formula, this set is transformed into a set of integral equations. Using the analytically known Green's function, the system may be solved by an iteration procedure. For a simplified arc model, the quantities of interest are computed: The temperature distribution, the mass flow field, and the external magnetic field necessary to maintain this arc configuration.     

Exact function of the equations of quantum mechanics in an electromagnetic field. II

The zero term of the quasiclassical asymptotic (?→ 0) of the Klein-Gordon-Fock equation as symmetrized by Feynman (V. V. Belov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 45 (1975)), giving the exact Green's function of the Cauchy problem in arbitrary (nonparallel) steady homogeneous electric and magnetic fields, is constructed. The exact Green's function for the Dirae equation in an arbitrary, steady electromagnetic field and for the Pauli equation (semirelativistic Schrödinger equation) in the nonsteady-state case is constructed in an analogous manner.     

Zur Quantentheorie der Transportprozesse im Magnetfeld. III

In the presence of a transversal magnetic field the electric thermoelectric and thermal transportcoefficients are calculated, taking into account phonon drag. The calculations are based on the model of free electrons, phonons, and impurity scatterers. Starting from Kubo's formulae, and using truncation technique for Green's functions an integral equation (generalized transport equation) is developed. It is solved in the case of strong magnetic field. If phonon drag is neglected Titeica type formulae hold for all transportcoefficients. Phonon drag reduces the values in the sense that the electron-phonon-relaxation time is replaced by the sum of the electron-phonon- and phonon-scatterer-relaxation time.     

Symmetry Reductions,Group‐Invariant Solutions,and Conservation Laws of a (2+1)‐Dimensional Nonlinear Schrödinger Equation in a Heisenberg Ferromagnetic Spin Chain

Nonlinear spin excitations in ferromagnetic spin chains are studied for spintronic and magnetic devices including magnetic‐field sensors and for high‐density data storage. Here, (2+1)‐dimensional nonlinear Schrödinger equation is investigated, which describes the nonlinear spin dynamics for a Heisenberg ferromagnetic spin chain. Lie point symmetry generators and Lie symmetry groups of that equation are derived. Lie symmetry groups are related to the time, space, scale, rotation transformations, and Galilean boosts of that equation. Certain solutions, which are associated with the known solutions, are constructed. Based on the Lie symmetry generators, the reduced systems of such an equation are obtained. Based on the polynomial expansion and through one of the reduced systems, group‐invariant solutions are constructed. Soliton‐type group‐invariant solutions are graphically investigated and effects of the magnetic coupling coefficients, that is, α₁, α₂, α₃, and α₄, on the soliton's amplitude, width, and velocity are discussed. It is seen that α₁, α₂, α₃, and α₄ have no influence on the soliton's amplitude, but can affect the soliton's velocity and width. Lax pair and conservation laws of such an equation are derived.     

Resistance minimum of the Kondo-type in non-dilute magnetic systems

Using Nagaoka's decoupled equations of motion for double-time Green's functions an approximate integral equation is derived and solved numerically for the self-energy of conduction electrons in intermetallic compounds containing a non-dilute and translationally symmetric system of magnetic rare-earth ions. These latter are assumed to interact with an antiferromagnetics-f exchange parameter with the conduction electrons. The resistivity is computed and compared with experimental values for CeAl₂ and CeAl₃.     

Radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to circumferential magnetic field

Knowledge of the vibrational properties of nanoparticles is of fundamental interest since it is a signature of their morphology, and it can be utilized to characterize their physical properties. In addition, the vibration characteristics of the nanoparticles coupled with surrounding media and subjected to magnetic field are of recent interest. This paper develops an analytical approach to study the radial breathing-mode frequency of elastically confined spherical nanoparticles subjected to magnetic field. Based on Maxwell's equations, the nonlocal differential equation of radial motion is derived in terms of radial displacement and Lorentz's force. Bessel functions are used to obtain a frequency equation. The model is justified by a good agreement between the results given by the present model and available experimental and atomic simulation data. Furthermore, the model is used to elucidate the effect of nanoparticle size, the magnetic field and the stiffness of the elastic medium on the radial breathing-mode frequencies of several nanoparticles. Our results reveal that the effects of the magnetic field and the elastic medium are significant for nanoparticle with small size.     

The dielectric constant of polarizable fluids from the renormalized perturbation theory

A perturbation theoretical equation for the dielectric constant of polarizable dipolar fluids is proposed. For the fluctuation of the dipole moment, namely for the Kirkwood g-factor, a formula is given on the basis of Wertheim's renormalized perturbation theory. Using this formula, a series expansion for ?(p) is suggested on the basis of the Kirkwood equation, which gives an implicit function for ? as a function of ¶. The same series expansion can be derived from the Clausius-Mosotti equation—thus it proves to be independent of the boundary conditions. The resulting equation gives excellent results for the dielectric constant of the polarizable Stockmayer fluid producing good agreement with computer simulation data. The series expansion gives better results than the Kirkwood equation itself.     

Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

The effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly-trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.     

Single-site theory for the random Hubbard alloy

A new theory for the random system with electron correlation is presented, which is an extension of the Hubbard's theory for the random system and also an extension of the CPA for the interacting electron system. The equation of motion for the Green function is solved by the same decoupling method used by Hubbard. The self-consistent relations for the Green function, the self-energy and the effective occupation number are derived. It is predicted in the binary alloy system that tails or satellites of the state density are produced by the combined effect of the randomness and electron correlation. The origin of the tail is the inelastic scattering of the electron byA — B atomic pairs, whose electronic configuration is changed during the scattering. Numerical calculations are reported for a simple model.     

Phase diagram of hard colloidal platelets: a theoretical account

We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory and employing the Parsons–Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard–Jones–Devonshire cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian approximation we are able to show that the nematic–columnar transition is universal and independent of particle shape. The predicted phase diagram is in qualitative agreement with simulation results.     

Influence of a narrow conduction band on a Heisenberg spin system

We consider an idealized model, represented by a Heisenberg spin system, which is influenced by a narrow conduction band via ans-d-exchange interaction. By calculating and decoupling the equation of motion of double-time Green's functions by RPA, we derive the magnon dispersion law. The result is a separation of the spectrum into two magnon bands of different shape, similar to the band structure found by Hubbard in his system. We discuss our result by variation of the system parameters, as there are interactions, polarization, temperature, and external field.     

High-order MR shimming: a simulation study of the effectiveness of competing methods, using an established susceptibility model of the human head

The first step in the process of shimming a magnetic field is to characterize it by obtaining a field map and decomposing that map into a convenient set of basis functions. The strength of each member of the set is then calculated. Finally, a set of correction elements which generate fields corresponding to the same spatial distribution as the basis functions is energized so that the sum of their fields and the error fields is substantially zero. The basis functions used typically are solutions to Laplace’s equation and have been shown to be very effective when the region of interest is substantially free space. This paper addresses issues associated with shimming the magnetic field in a region in which there is a distribution of materials with different susceptibilities and which therefore is not free space. In such a region, Laplace’s equation is no longer valid and in principle cannot be used to describe the magnetic field there. It is demonstrated that in spite of this, the same set of basis functions suffices for analyzing the field and the same set of elements suffices for correcting the field. The motivation for this study stems from the need to improve the magnetic field homogeneity when biological specimens are being imaged by magnetic resonance. In particular, this paper describes a study carried out by various simulated shimming strategies to improve the uniformity of the magnetic field over a multitissue model of susceptibility of the human head. The topics of magnetic susceptibility, the effect of shimming on MR images, shimming hardware and shimming methods are briefly reviewed. Two slices of the human head model were selected for detailed study, both offset inferior to the origin and including the base of the brain and the anterior sinus. The results of the study include comparisons between the strategies of global shimming, local slice-selective shimming and combinations of the two; the effects of shimming to various orders of spherical harmonics; and the effects of rotation and displacement of the head with respect to the shim frame of reference.     

Total angular momentum and atomic magnetic moments

A new calculation of the magnetic moment of an atom is suggested on the basis of the hypothesis that the total angular momentum of one electron is the same in a complex atom situated in a solid as in a hydrogen-like atom described in Dirac's theory. The latter is first revisited and the quantum states thus defined are compared with those of Schrödinger's theory. Then, the experimental basis of the notion of spin is recalled and compared to the subshell division of the p, d and f shells in Dirac's theory.Using this division in subshells a calculation of the magnetic moment is applied to the heavy rare earth metals, iron, cobalt, nickel and the chromium compounds and compared with experimental data. This leads us to a discussion of the Pauli exclusion principle and to the choice of a convenient electronic configuration of each magnetic element. Finally these configurations are compared to the theoretical magnetic moments.     

On acoustic radiation by a rigid object in a fluid flow

A problem of sound radiation by an absolutely rigid object, moving with respect to the surrounding fluid, is considered on the basis of the Lighthill's equation for aerodynamic sound. An integral representation of the radiated acoustic field is utilized, where the field is characterized as the sum of three fields, generated by a volume distribution of monopoles and by distributions of monopoles and dipoles on the surface of the rigid object. It is shown that, due to a discontinuity of Lighthill's stress tensor on the rigid boundary, a layer of surface divergence of hydrodynamic stresses on the boundary must be taken into account when evaluating the volume integral over Lighthill's quadrupole sources. When the contribution of the surface divergence is included in the solution of Lighthill's equation, amplitudes of the monopole and dipole sound radiated by the rigid object are shown to depend on the potential components of the normal velocity and the pressure on the rigid surface. The obtained solution is compared with Curle's solution for this problem, which establishes that the sound radiation by a rigid object is determined by the force exerted by the object upon the fluid. Both solutions are applied to two known problems of sound scattering and radiation by a rigid sphere in variable pressure and velocity fields. It is shown that predictions based on the obtained solution are equivalent to the results known from literature, whereas Curle's solution gives predictions contradicting the known results. It is also shown that the Ffowcs Williams and Hawkings equation, which coincides with Curle's equation for an immoveable rigid object, does not lead to the correct predictions as well.     

Magnetostatic Green's functions for the description of spin waves in finite rectangular magnetic dots and stripes

We present derivation of the magnetostatic Green's functions used in calculations of spin-wave spectra of finite-size non-ellipsoidal (rectangular) magnetic elements. The elements (dots) are assumed to be single domain particles having uniform static magnetization. We consider the case of flat dots, when the in-plane dot size is much larger than the dot height (film thickness), and assume the uniform distribution of the variable magnetization along the dot height. The limiting cases of magnetic waveguides with rectangular cross-section and thin magnetic stripes are also considered. The developed method of tensorial Green's functions is used to solve the Maxwell equations in the magnetostatic limit, and to represent the Landau–Lifshitz equation of motion for the magnetization of a magnetic element in a closed integro-differential form.     

Application of the Green's function method to ferrimagnetism

The Green function theory, which has been used hitherto for ferro- and antiferromagnetism, has been extended for the case of a two-sublattice ferrimagnet. Two parametrized Green functions are used corresponding to the two sublattices. The equations of motion are set up and the higher order Green functions are decoupled according toCallen's approximation. The functions are obtained by solving the simultaneous equations. The quasi-particle energies are evaluated from the singularities of the Green functions and the magnetization at low temperatures is found to obey theT ^3/2-law. These results obtained for the energy and magnetization agree well with those obtained by the conventional spin wave method.