Spin waves model

As remarked in the introduction, section 1, the temperature dependence of the hyperfine field provides a measurement of the temperature dependence of the magnetization on the microscopic level. This point is illustrated by the data of Sweger et al. (1974) for Hen in Dy metal. In this case, Hen(T) is not well represented by a Brillouin function. Paralleling the bulk magnetization data, the behavior of Hen for T 100 K can be interpreted in terms of a spin-wave model of the form [Niira (I960)],... 

Krylov AI (2001) Size-consistent wave functions for bond-breaking the equation-of-motion spin-flip model. Chem Phys Lett 338 375... 

It would be important to figure out the low energy excitation modes (Nambu-Goldstone modes) built on the ferromagnetic phase. The spin waves are well known in the Heisenberg model [10]. Then, how about our case [32] ... 

From the spin wave (or magnon) model of magnetic systems, the heat capacity versus temperature behavior below the ordering temperature is given192 by the following equation ... 

The group velocity of de Broglie matter waves are seen to be identical with particle velocity. In this instance it is the wave model that seems not to need the particle concept. However, this result has been considered of academic interest only because of the dispersion of wave packets. Still, it cannot be accidental that wave packets have so many properties in common with quantum-mechanical particles and maybe the concept was abandoned prematurely. What it lacks is a mechanism to account for the appearance of mass, charge and spin, but this may not be an insurmountable problem. It is tempting to associate the rapidly oscillating component with the Compton wavelength and relativistic motion within the electronic wave packet. 

Because quantum theory is supposed only to deal with observables it may be, and is, argued as meaningless to enquire into the internal structure of an electron, until it has been observed directly. To treat an electron as a point particle is therefore considered mathematically sufficient. However, an electron has experimentally observed properties such as the Compton wavelength and spin, which can hardly be ascribed to a point particle. The only reasonable account of such properties has, to date, been provided by wave models of the electron. 

Let us consider a more general spin-ladder model, for which the zigzag model (2) is a particular case. So, we consider the cyclic ladder model containing N — 2M spins s = (Fig.4). The proposed form of wave function (4) can be generalized for a ladder model as follows ... 

There is one more spin-i model with an exact ground state of the RVB type [15]. This is the model (9) describing the F-AF transition point. The exact singlet ground state can be expressed by the combinations of the RVB functions (i,j) distributed uniformly over the lattice points (8). The analog of the wave function (8) in the SB terms is ... 

The ground state wave function of the spin ladders can be represented in an alternative form as a product of second-rank spinors associated with the lattice sites and the metric spinors corresponding to bonds between nearest neighbor sites. Two-dimensional spin-1 model is constructed with exact ground state wave function of this type. The ground state of this model is a nondegenerate singlet... 

This model, which gives good results for high values of S, can neither be applied to S A nor to compounds with chain structures. More recently, improvements have been achieved by Ishikawa and Oguchi by including into the spin-wave theory kinematic interactions besides dynamic ones270) for CuF2 H20, S = A, / i(exp) = 0.63 and Xi calc. = 0.64. 

We have measured with great accuracy the reflectivity of electron doped Pr2 sCe, Cu() at various Ce doping levels. An optical conductivity spectral weight analysis shows that a partial gap opens at low temperatures for Ce concentrations up to x = 0.15. A spin density wave model reproduces satisfactorily the data. 

Chubukov A.V., Pines D., and Schmatian J., (2003). A Spin Fluctuation Model for d-wave Superconductivity in The Physics of Conventional and Unconventional Superconductors eds. by Bennemann K.H. and Ketterson J.B., Vol. 1 (Springer-Verlag). 

Those curves that do not approach T = 0°K with zero slope are not realized in nature. The N6el model is a molecular field model, and is subject to the same criticisms as the Weiss field model for ferromagnets. Kaplan (325) has applied spin wave theory to ferri-magnets and worked out a Bloch Tz/2 law, similar to equation 98, for low temperatures. In this approximation M /M% remains constant,... 

The conventional macroscopic Fourier conduction model violates this non-local feature of microscale heat transfer, and alternative approaches are necessary for analysis. The most suitable model to date is the concept of phonon. The thermal energy in a uniform solid material can be jntetpreied as the vibrations of a regular lattice of closely bound atoms inside. These atoms exhibit collective modes of sound waves (phonons) wliich transports energy at tlie speed of sound in a material. Following quantum mechanical principles, phonons exhibit paiticle-like properties of bosons with zero spin (wave-particle duality). Phonons play an important role in many of the physical properties of solids, such as the thermal and the electrical conductivities. In insulating solids, phonons are also (he primary mechanism by which heal conduction takes place. 

Jansen and van der Avoird (1985) have also made spin-wave calculations as described earlier. The RPA equations with the effective spin Hamiltonian (140), averaged over the translations and librations, could be solved analytically for any wave vector q. The optical (q = 0) magnon frequencies emerging from these calculations are 6.3 and 20.9 cm-1, in reasonable agreement with the experimental values 6.4 and 27.5 cm-1. This agreement is very satisfactory if we realize that the spin Hamiltonian has been obtained from first principles, with none of its parameters fitted to the magnetic data. We conclude that the RPA model, both for the lattice modes and the spin waves, when based on a complete crystal Hamiltonian from first principles, yields a realistic description of several properties of solid O2 that were not well understood before. 

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