Spin wave scattering

J. B. Torrance, Spin waves, scattering at 4kFr and spin-Peierls fuctuations in an organic metal Tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ), Phys. Rev. B17 3099-3103 (1978). 

Although o)cT is almost invariably too small to yield information about the Fermi surface topology, the modifications to the conduction electrons trajectories produce a modest positive magnetoresistance, which apparently dominates at the lowest temperatures (fig. 6.44). A satisfactory separation of the spin-wave scattering and electron trajectory effects has not yet been achieved. 

Calculations based on the spin wave scattering model (Yamada and Takada, 1973) indicate that, at low temperatures, the magnetoresistance in the perpendicular configuration reflects the competition between the softening of the acoustic spin wave mode (tending to increase the resistivity) and the increase of the optic mode energy gap which tends to decrease the resistivity. 

Spin-wave scattering of the conduction electrons at low temperatures has been studied in particular by Yamada and Takada (1972). Dispersion relations of the type coccq and coccq yield resistivity contributions proportional to and respectively. As is shown in fig. 12, the agreement with the experimental data is fairly good, at least in the case of Gd. 

From the measurements presented in the paper of Buschow and van Daal (1971) it is not clear whether the slope of Ap versus T in the log-log plot changes at low temperatures due to spin-wave scattering. Note that such a change in the coefficient A has been observed for UFe2 and CeFe2 in the low-temperature region. 

A further effect is discussed in Chapter 5, namely that of spin-orbit scattering. This effect preserves the coherence of the two scattered waves but changes the constructive interference into a destructive one. The characteristic time tw is believed to be independent of Ty and inversely proportional to Z4, where Z is the atomic number. An analysis by Fukuyama and Hoshino (1981) shows that Ac depends on and leads to a behaviour as shown in Fig. 1.24. The negative part should be observed only for heavy metals. 

Here k0 is the wave vector of the incident particle, x(K) is its spin wave function, and k is its spin coordinate. The second term in (4.3) is a superposition of products of scattered waves and the wavefunctions of all the possible molecular states that obey the energy conservation law ... 

Interna] and external magnetic fields also play a special role for the observation of light scattering at magnons, as the quanta of spin waves are called - see Fig. 10. 

Longitudinal fluctuations of a Neel-ordered state are usually strongly damped and not included in a spin-wave approximation of its excitation spectrum. Until now similar modes have been only observed in neutron scattering on spin chain systems as broadened maxima [44 46]. The present narrow linewidth is probably related to the small scattering vector involved in light scattering experiments. 

The phase shifts <5, are calculated by standard partial-wave scattering theory. It involves the electron-atom interaction potential of the muffin-tin model. There are a variety of ways to obtain this potential, which consists of electrostatic and exchange parts (spin dependence may be included, especially when the spin polarization of the outgoing electrons is of interest). One usually starts from known atomic wave functions within one muffin-tin sphere and spherically averages contributions to the total charge density or potential from nearby... 

Neutron diffraction/scattering can also probe SRO and low-lying excited states called spin waves, but this discussion lies again outside the scope of this article. 

The amplitude of the neutron wave scattered by a nucleus of a given element varies from one isotope to another and also between the two spin states of the neutron-nucleus system. In addition to coherent scattering (leading to diffraction effects) this variation of scattered amplitude from atom to atom of the same species produces incoherent scattering in which there is no systematic interference between scattered... 

In previous works, Tse (6) used the spin-polarized scattering wave Xa... 

The application of this approach to spin waves was called by Dyson naive and criticized as incorrect and leading to results different from those obtained by him (see (6), the end of 3). We shall show in what follows, however, on the basis of an exact representation of Pauli operators in terms of Bose operators, that the picture described above does take place for Frenkel excitons. This takes place only because the excitation energy A for Frenkel excitons is large compared with the width of the exciton band. As for the spin waves, where the inequality indicated above is not satisfied, the cross-section for the scattering of long-wavelength spin waves by each other can indeed, in agreement with Dyson, differ substantially from a value that follows from the hard sphere approximation (7). 

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