Spin excitation

There are many specific ways to generate equally spaced tags but they are all based on the same principle of manipulating the rf pulses to generate equally spaced bands of rf radiation in the frequency domain. It is well known that under ordinary conditions, meaning normal levels of nuclear spin excitation, the frequency spectrum of the rf excitation pulse(s) is approximately the Fourier transform of the pulses in the time domain. Thus, a single slice can be generated in the... 

A. A. Jones When the specimen is spun, it is mechanically perturbed at 2-3 kHz. This is a frequency not too different from that of the motion. Does the mechanical spinning excite the system and therefore affect the rotating frame relaxation, assuming that one does everything else correctly ... 

Our estimate of the band form should therefore show strong peaks at the extremities due to the (heavy) spin polarons. For these, k is a good quantum number, as long as kR < 1. If this is not so, the polaron concept breaks down and we come into the region investigated by Brinkman and Rice (1970a) where the electron loses energy rapidly to spin excitations and k is a band quantum number. These authors estimate that the bandwidth contracts by about 70%. 

In stark contrast, in the research field of the high temperature superconductivity (HTSC) the role of the lattice has been all but completely neglected by the majority. The conventional view is that it is a purely electronic phenomenon involving spin excitations, and is described, for instance, by the t-J model [2], There are many reasons why the lattice has been dropped from consideration almost from the beginning, such as the near absence of the isotope effect on the critical temperature, Tc, and the linear resistivity. However, the arguments against the lattice involvement are less than perfect [3],... 

These results show evidence for not simple two-magnon nature of the band at -730 cm"1. Perhaps possible effects connected with the interaction between spin excitations and collective motion of charge domain-walls21,37 are necessary to be taken into account. 

As follows from Eq. (10), the frequencies of spin excitations satisfy the equation... 

The dispersion of spin excitations near Q is of special interest, because this region gives the main contribution into the neutron scattering. This... 

Figure 1. The dispersion of spin excitations near Q along the edge of the Brillouin zone. The dispersion was calculated in a 20x20 lattice for x = 0.06 and T = 17 K (filled squares, the solid line is the fit with u>k = [wq + c2(k — Q)2]1/2). Open squares are the experimental dispersion [1] of the maximum in the frequency dependence of the odd x"(qw), q = k — Q, in YBa2Cua06.5 (x 0.075 [13]) at T = 5 K.

With increasing to the dip in the spin excitation damping is shallowed and finally disappears. Besides, on approaching toq the denominator in Eq. (10) will favor the appearance of the commensurate peak at Q. Thus, the low-frequency incommensurate maxima of converge to the commensurate peak at to wq. The dispersion of the maxima in x" above toq is determined by the denominator in Eq. (10) and is close to that shown in Fig. 1. Consequently, the dispersion of the maxima in x" resembles two parabolas converging near the point (Q,cc>q). The upper parabola with branches pointed up reflects the dispersion of spin excitations, while the lower parabola with branches pointed down stems from the momentum dependence of the spin excitation damping. Such kind of the dispersion is indeed observed in cuprates [3, 23]. 

Notice too that in the present argument the (unpaired-electron) spin density should appear primarily on the sites with an excess free-valence sum, especially for those such sites more well separated from opposite-type sites with non-zero free valence. Yet further too if distant sites need to be spin-paired, then there should be a low-lying higher-spin excited state where the spin-pairing is violated. For finite conjugated molecules this further leads to agreement with the spin result of Eq. 

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