Knight-shift in NMR

The Knight shift in NMR measures the local magnetic susceptibility around a nucleus. Following the arguments in [15] the reduced Knight shift Ks(TyKs(Tc) for our theory is given by... 

The magnetic moment of a neutral soliton can be seen in the ESR signal and in the static susceptibility as a paramagnetic contribution (unpaired electrons). In the metallic state, when the Peierls transition is suppressed and there is a finite density of states at the Fermi level (no gap), the delocalized electrons will lead to a Pauli paramagnetism, which contributes to the static susceptibility and produces a Knight shift in NMR experiments. Evidence for the motion of solitons can be obtained from NMR-relaxation experiments and from the lineshape of the ESR signal (motional narrowing). 

The main experimental information that usually can be deduced from ESR experiments in metals are the g-shift and the linewidth broadening. Both quantities can be measured as a function of an external parameter, like temperature or pressure. The g-shift corresponds to the Knight-shift in NMR experiments and yields information about the static susceptibility. This review nicely documents how the experimental results on the g-shifts in metals provide direct and detailed information on the band structure. The ESR linewidth in metals is determined by the spin-lattice relaxation time and has to be compared to l/T) as deduced from NMR results. The linewidth is determined by the density of states, but in addition yields detailed information on the low-frequency spectrum of spin fluctuations. This is of high relevance in the field of high-Tc superconductors and heavy-fermion compounds. 

The 71Ga and 14N spectra of several of these films also showed partially-resolved shoulders shifted to higher frequency and having shorter T relaxation times that were attributed to Knight shifts in more heavily unintentionally doped regions of the film. These Knight shifts were observed in other GaN film samples [53] and will be discussed in more detail in Sects. 3.4.3 and 3.4.4, where MAS-NMR was used to improve the resolution in polycrystalline powders of h-GaN. Section 3.3.2 also shows 71Ga and 14N MAS-NMR spectra of GaN. 

Fig. 13 69Ga MAS-NMR spectra of GaN nanopowders labeled by sample codes. Left Knight shift resulting from thermal annealing. Right three different samples produced by GaAs nitridation synthesis containing c-GaN (357 ppm) as well as h-GaN (326 ppm). The broad peak at 470 ppm is assigned to Knight shifts in c-GaN. Reprinted with permission from [234], Copyright 2008 by the American Chemical Society...

E. Pavarini and 1.1. Mazin, NMR relaxation rates and Knight shifts in MgB2. Phys. Rev. 

The pressure dependence of N(EF) has been measured recently through the pressure dependence of the 13C-NMR Knight shift in K3Q0 [94]. In Fig. 25, a plot of In T P) versus K(P) is presented. As shown by this plot, linear behavior is effectively observed, which intersects the y axis at flph = 600 K and = N(EF)V = 0.3 at ambient pressure [94]. Thus the value of Tc appears to be governed by N(EF) and the pressure data suggest that high-frequency intraball phonons are likely to be involved in the superconductivity of fullerenes [20,94]. 

For example, the one-electron models incorrectly predict (even at a qualitative level) the Knight shifts in and NMR spectra of ammoniated electron, and solvated electrons in amines (Sec. 4.1). The same problem arises in the explanation of magnetic (hyperfine) parameters obtained from ESEEM spectra of trapped (hydrated) electrons in low-temperature alkaline ices. The recent resonance Raman spectra of also appear to be incompatible with the one-... 

The way in which this solvent modification occurs is suggested by the pattern of hyperfine constants for (which is one of the few solvated electron species sufficiently stable to obtain its NMR spectrum). The Knight shift of NMR lines is due to the contact Fermi (isotropic) hyperfine interaction of the excess electron with the magnetic nuclei (X) in the solvent molecules it is the measure of spin density, (0) in the r-type atomic orbitals centered on a given nucleus X ... 

Spin-lattice relaxation has been studied by Cu NMR for dilute Cu-Mn and Cu-Cr alloys at temperatures of 0.32-20K while the NMR lines in deformed Cu alloys with Si, A1 and Ga were investigated as a function of plastic deformation. Variations in Cu Knight shifts in Cu-Zn alloys have been reported. Spectra from NMR experiments performed on binary Cu-Au ordered alloys and martensitic ternary Au-Cu-Zn alloys in order to study crystallographic Cu sites microscopically have revealed different distributions of Cu atoms that change appreciably with Cu content. 

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