Nuclear Knight shift

The terms in (la) and (lb) both involve sums of single nuclear spin operators Iz. In contrast, the terms in (lc) involve pairwise sums over the products of the nuclear spin operators of two different nuclei, and are thus bilinear in nuclear spin. If the two different nuclei are still of the same isotope and have the same NMR resonant frequency, then the interactions are homonuclear if not, then heteronuclear. The requirements of the former case may not be met if the two nuclei of the same isotope have different frequencies due to different chemical or Knight shifts or different anisotropic interactions, and the resulting frequency difference exceeds the strength of the terms in (lc). In this case, the interactions behave as if they were heteronuclear. The dipolar interaction is proportional to 1/r3, where r is the distance between the two nuclei. Its angular dependence is described below, after discussing the quadrupolar term. 

Let us now consider the metallic regime, following the discussion of [18]. For nuclei coupled to a mobile system of independent electrons by an isotropic exchange interaction of the form A l S, where I is the nuclear spin and S the electron s spin, the Knight shift can be written as... 

For the metallic regime described above, when the Al S interaction is also responsible for the nuclear relaxation, Korringa [192] showed that the Knight shift and Ti are related by... 

In a sample of bulk Pt metal, all of the nuclei have the same interaction with the conduction electrons and thus see the same local field. The resulting NMR line is quite narrow. However, in our samples of small Pt particles, many of the nuclei are near a surface where the state of the conduction electron is disturbed. This tends to reduce the Knight shift for these nuclei. Since the Pt particles in our samples are of many different sizes and shapes, this reduction in the Knight shift is not the same for every nuclear spin near a surface. Thus, we obtain a broad "smear" of Knight shifts resulting in the lineshapes of Figure 5. 

In liquids, if F crosses the mobility edge c, no discontinuity in the Knight shift is expected, because the timescale of the nuclear resonance is long compared with the time in which atomic movement will change the positions of the localized states. If Warren s interpretation of his measurements on liquid tellurium alloys is accepted, there is certainly no discontinuity in K when this happens. 

J. A. Jackson, also of this laboratory, has made room temperature nuclear magnetic resonance studies of the Knight shift of cadmium in slowly cooled CeCd, 45 alloys with different compositions and different histories. All CeCd 4 5 samples tested showed a major peak at almost the same position and shifted from that of metallic cadmium. One sample showed only this peak, while others clearly showed satellite peaks either at larger or at smaller shift. Possibly some samples had small amounts of both satellite peaks, and there was apparently some further difference in the shapes of satellite peaks and of the major peak these latter observations are tenuous, however, since they were near the resolution limit of the apparatus. The differences apparently do not correlate simply with composition however, they may correlate with differences in microphase structures. 

The LDOS description for the metal NMR assumes that variations in Knight shift K and in spin lattice relaxation time Ti among nuclear spin sites are mainly determined by variations in the intensity of electronic... 

All the NMR interaction parameters for zinc metal have been determined from the central and satellite transitions of the Zn spectrum which indicates a value of — 124 ppm for the axial component of the Knight shift. The isotropic component of the Knight shift and the nuclear quadrupole coupling constant have also been determined as a funtion of temperature over the range 149 32 K (Bastow 1996). 

In general the Cooper pairs in conventional superconductors induced by phonons have. -symmetry where the gap opens uniformly on the Fermi surface and the temperature dependence of physical quantities below Tc is exponential. On the other hand, when the attractive force originates from spin or electron charge fluctuations, the Cooper pair has p- or d-wavc symmetry where the gap disappears on lines or points on the Fermi surface and the physical quantities have power-law temperature dependences. The quantities that are measured by NMR and nuclear quadrupole resonance (NQR) are the nuclear spin-lattice relaxation rate, 1 / T, the Knight shift, K, the spin echo decay rate, 1/T2 and the NQR frequency, vq. The most important quantities, K and 1/77 for the determination of the symmetry of the Cooper pairs are reviewed in the following sections. 

NMR has been applied most successfully for high-temperature superconductors, YBa2Cu307-6 [17-21]. The studies involve mainly 63Cu, and 65Cu NMR and nuclear quadrupole resonance of this compound below, above, and at the critical temperature. Nuclear relaxation, Knight shift, and crystal stmcture are often examined at these temperatures. 

Azz is the component of the hyperfine tensor in the Bq direction. Avesr is called the Overhauser shift. It is analogous to the Knight shift Avnmr of tho nuclear-spin resonance frequency v mr in the presence of conduction electrons with a polarisation P. ... 

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