Spin density oscillations

The Fe-Mn alloys (2-8-6-7 at. % Mn) have many similarities to the Fe-Al system [36], with the exception that the conduction-electron spin-density oscillations show a phase variation with concentration corresponding to a change in the Fermi radius and band structure (see Figs. 11.5 and 11.6) [32]. In this case the Mn atoms are contributing to the.magnetic structure. 

A very similar application of the modified Bloch equations was based in the work of Adams and Connelly.4 ESR spectra (Figure 5.8) of [Mo P(0 Me)3 2(MeC = CMc)Cp] show the expected triplet (two equivalent 31P nuclei) at 280 K, but only a doublet at 160 K. At intermediate temperatures, the lines broaden. The interpretation is that the alkyne undergoes a pendulum oscillation, which in the extrema diverts spin density from one or the other phosphite. Interestingly, the diamagnetic cation undergoes a similar motion on the NMR time scale, but then the alkyne undergoes a complete rotation. Thus, analysis of the effect leads to a measure of the rate of the oscillation. The... 

For any reservoir in equilibrium the fluctuation-dissipation theorem provides the relation between the symmetrized and antisymmetrized correlators of the noise Sx(x) = Ax(x) coth(w/2T). Yet, the temperature dependence of Sx and Ax may vary depending on the type of the environment. For an oscillator bath, Ax (also called the spectral density Jx(x)) is temperature-independent, so that Sx(x) = Jx(x)coth(x/2T). On the other hand, for a spin bath Sx is temperature-independent and is related to the spins density of states, while Ax([Pg.14]

The spectral density is a measure of the amplitude of the M-quantum component of the nuclear spin interaction oscillating at frequency Mlj0 as a result of molecular motion. 

Direct evidence for a spin density wave transport is the detection of a current oscillating at a frequency that is proportional to the dc current carried collectively. The recent observation of such oscillations the harmonic and subharmonic locking of this oscillation to an external ac source and a motional narrowing of the NMR spectrum in the sliding SDW state have established firm evidence for the existence of a novel collective transport in a SDW condensate. 

A treatment of transport properties in terms of this surface is no more complicated in principle than that in the polyvalent metals, but there is not the simple free-clectron extended-zone scheme that made that case tractable. Friedel oscillations arise from the discontinuity in state occupation at each of these surfaces, just as they did from the Fermi sphere. When in fact there arc rather flat surfaces, as on the octahedra in Fig. 20-6, these oscillations become quite strong and directional. A related effect can occur when two rather flat surfaces are parallel, as in the electron and hole octahedra, in which the system spontaneously develops an oscillatory spin density with a wave number determined by the difference in wave number between the two surfaces, the vector q indicated in Fig. 20-5. This generally accepted explanation of the antiferromagnetism of chromium, based upon nesting of the Fermi surfaces, was first proposed by Lomer (1962). 

However, these very low-frequency oscillations periodic in jB could be successfully explained by the standard model for field induced spin density waves [75, 76], see also Figs. 2.8 and 2.9 in Sect. 2.2.3. Although this effect is strongly related to the quasi-lD band structure and is by itself highly interesting no direct conclusions concerning the FS topology can be extracted from the measurements. 

The magnetic interaction between the ions in the magnetic metals for example, can then be considered as carried by the conduction electrons in the well known Rudermann-Kittel-Kasuya-Yoshida (1 ) interaction. The physical origin of this interaction is a point like polarization of the conduction electrons (CE), at the atomic sites, by the magnetic moments of the f electrons, resulting in an oscillation of the spin density of the CE. The point like approximation is useful because the maxima of the f wave functions are found well inside the atomic core, in radii smaller than 0.7 atomic units. This polarization is carried from ion to ion by the generated polarization oscillation of the conduction electron spins, which has a wave length = 27r/e (C =... 

A feature of peculiar importance in one dimension is that long wavelength charge or spin-density-wave oscillations constructed by the combination of electron-hole pair excitations at low energy form extremely stable excitations... 

In the UHF approximation (Fig. 6 e-h) the situation is somewhat different.In the optimization an extremely broad polaron is obtained which is practically an equidistant chain some sites apart of the two chain ends. This is obviously an artefact of the well known tendency of UHF to produce metallic polyenes as equilibrium structures [39]. In the simulation we observe also the formation of this polaron like structure after roughly 10 fs(Fig. 6f), however this is destroyed after two oscillations. The spin density in UHF (6g) looks very similar to the... 

The spectral density is a measure of the amplitude of the M-quantum component of the nuclear spin interaction oscillating at frequency Mo as a result of molecular motion. Of course, we should also recognize that since H(t) varies randomly in time, otherwise identical spin systems will have different H(t) at any given time t. Thus, we need to perform an average over the ensembles of spin systems making up the total sample. We denote this ensemble average by a bar, and thus we replace CM in Eq. (11) with... 

Fig. 5 Results of two Ehrenfest simulations on benzene cation with fixed nuclei left side) and with nuclei moving right side). The top figures plot the evolution of the Mulliken spin densities as the function of time. The electron and nuclear motions are represented on the bottom moat diagrams (the nuclear geometry in blue and the electronic character in pink). With nuclei fixed, the electronic character of the system between a set of quinoid/antiquinoid structures. With moving nuclei, the oscillations in the electronic character seem damped until the nuclear geometry slowly catches the electronic character...

---