Spin wave vector

Here the sum runs over all possible initial states and the operator describes the interaction of the electrons and the radiation field with wave vector q and polarization A. In Eq. (1) it has been assumed that the detector selectively counts photo electrons with energy E, wave vector k, and spin polarization The corresponding final... 

The observed NMR signal, S(k, q), is modulated by the two wave vectors the first, k, is related to the spatial density of the spins and the second, q, is related to a spatial displacement of spins ... 

Following Pauli s exclusion principle, each state corresponding to a given can contain at most two electrons of opposite spin. Therefore, at the absolute zero of temperature aU the states, k, will be occupied within a sphere of radius, kF, the so-called Fermi sphere because these correspond to the states of lowest energy, as can be seen from Fig. 2.9(a). The magnitude of the Fermi wave vector, kF, may be related to the total number of valence electrons N by... 

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... 

Here k is the Fermi wave vector determined from the value of the hole concentration p assuming a spherical Fermi surface, m is the hole effective mass taken as 0.5/no (mo is the free electron mass), is the exchange integral between the holes and the Mn spins, and h is Planck s constant. The transverse and longitudinal magnetic susceptibilities are determined from the magnetotransport data according to x = 3M/dB and xh = M/B. 

Fig. 24. The computed valence band dispersion E(k) computed from the 6 x 6 Luttinger model for the wave vector parallel and perpendicular to the Mn spin magnetization in (Ga,Mn)As. assuming that the spin splitting of the heavy-hole band at the f point is 0.15 eV.

Fig. 34. Schematic valence band diagram of resonant tunneling diode structures, simplified diagram of energy versus wave vector parallel to the interface, and resulting /-V curve by spin-splitting of the valence band of...

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 ... 

Such a low-lying excitation is shown on the right. These elementary excitations are called spin waves. The spin vectors precess on cones and successive spins have a constant angle of phase shift. This is shown in the lower part of the figure showing one wavelength of a spin wave in a chain of spins (a) in perspective projection and (b) viewed from above. 

In (quasi-)one-dimensional systems [22] also SDWs can be found, but in contrast to CDWs they arise due to electron-electron and not to electron-phonon interaction. A SDW can be considered to consist of two CDWs, one for spin-up and another for spin-down electrons (see, e.g., Fig. 5 in [22]). Therefore the spatial modulation of SDWs is characterized by a wave vector Q = 2kp, as for CDWs. 

Pi(t) are the electrical potentials of the leads, the index k is the wave vector, but can be considered as representing an other conserved quantum number, a is the spin index, but can be considered as a generalized channel number, describing e.g. different bands or subbands in semiconductors. Alternatively, the tight-binding model can be used also for the leads, then (186) should be considered as a result of the Fourier transformation. The leads are assumed to be noninteracting and equilibrium. 

Neglecting a spin-analysis of the registered electrons, the energy- and angle-dependent differential cross section describing the ejection of two electrons with wave vectors k3 and Kb can be written as... 

---