Spin waves contribution

Among the most interesting studies of thermal properties of rare-earth iron garnets are the heat capacity measurements at low temperature of Meyer and Harris (65, 139), Their data cover only the range 1.4°-20 °K. Below 5°K. the heat capacity of 4 trium iron garnet can be represented by the sum of the lattice term proportional to and by the spin-wave contribution of 2.15 X //(mole °K.). This last term is in... 

The chief source of all this confusion and apparent indecision lies in our inability to ascribe a definite form to the magnetic spin wave contribution to the heat capacity. A number of theories were introduced in the early 1950 s, for a review of which reference should be made to Mackintosh and Mbller (1972) or, for a review in brief, one may consult Lounasmaa and Sundstrom (1%6). For the sake of completeness, we present in table 5.1 the temperature dependences of the various models. 

There have been attempts to calculate the spin wave contribution to the heat capacity from inelastic neutron scattering data for Tb and Gd (Sedaghat and Cracknell, 1971 Stevens and Krukewich, 1973). The former found the power of T to increase with increasing temperature for gadolinium from n = 1.56 to n = 2.3, but no simple power law above 14 K. The latter investigators found n 1.5 for terbium and gadolinium. Wells et al. (1974) have confirmed that for... 

A spin polaron should move at low temperatures with a fixed wave vector k, like any other pseudoparticle, and be scattered by phonons and magnons. The effective mass is expected to be of the form mey /0, where y l. To obtain this result, we compute the transfer integral when the polaron moves through one atomic distance. The spin will contribute a term proportional to... 

The condition j + j > 1 for a matrix element of a first rank tensor operator implies, e.g., that there is no first-order SOC of singlet wave functions. Two doublet spin wave functions may interact via SOC, but the selection rule /+ / > 2 for i (2)(Eq. [171]) tells us that electronic spin-spin interaction does not contribute to their fine-structure splitting in first order. 

In this, my third contribution, I apply freeon dynamics to problems of interest in chemistry and physics and compare with the results obtained by the spin paradigm. In particular I will apply freeon dynamics to the following "spin phenomena" i) spin exchange, ii) spin superexchange, iii) spin polarization, iii) spin density, iv) high-and low-spin states of the transition-metal ions, v) the periodic table, vi) ferromagnetism, vii) spin waves and viii) high-Tc superconductivity. 

The heat capacity of EuS was measured to test the predictions of spin-wave theory from 1° to 38°K. by McCollum and Callaway (137) and independently from 10° to 35°K. by Moruzzi and Teaney (145). A sharp Neel peak was found at 16.2 °K. Magnetic and lattice contributions to the heat capacities were resolved on the assumption of a dependence for the lattice and a T dependence for the magnetic contribution at temperatures above the Neel point. A plot of CT vs. yields a straight line between 21° and 31 °K. and a Debye temperature of 208 °K. 

To determine the unconditional probability distribution for the spin-wave excitations Psw(n), we must find the effective number of transverse modes which contribute to the Raman processes. We identify two extreme regimes which permit analytic treatment a single mode regime where the number of excitations in the 87Rb cell follows Bose-Einstein (thermal) statistics and a multimode regime where it follows Poisson statistics. We find in both cases that the quantities F and Q depend on two experimental parameters 0 ( number of lost Stokes photons) and v ( noise to signal ratio), which are defined in Tab. 1. 

The latter puzzle may find its solution in a recent investigation of the spectrum of He- by Luther [7]. There it is shown that for A < 2 an increasing number of excitation branches appear below the fermion branch which is present for all values of A < 4. The states which correspond to these branches are to be viewed as bound spin-wave states in the model under consideration. From the equivalence of Hu and the Hamiltonian of the Sine-Gordon theory it can be inferred [7], [8] that the lowest bound magnon branch attains boson character as A approaches zero. In all probability hl represents the contribution... 

All kinds of excitahons, e.g., phonons, excitons, spin waves, may contribute to a(q). Higher-order processes such as mulh-phonon interachons may be in-... 

Renormalization factors grijUt) calculated for A 208 nuclei with HO wave functions ha> = 6.88 MeV) and both the H7B and HBB residual interactions. Results are for the ten possible RO transitions in the model space of Fig. 2. For HO wave functions the qs are given by 1 — gj = qj- — 1. A breakdown into the tensor and central contributions is given. The columns labeled central also contain a small spin-orbit contribution. Note the similarity of the central contributions for the H7B and HBB interactions and that the H7B tensor component is larger than that of the HBB interaction... 

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