Dipolar magnetic hyperfine interaction

The magnetic dipolar and hyperfine interactions of the nucleus with the electronic moments can be expressed by ... 

The first three terms are present for both para- and ortho-H2 they represent the electron spin-rotation, electron spin-spin dipolar and spin orbit interactions respectively. The fourth term in (8.187) represents the magnetic hyperfine interactions, which we will come to a little later. We deal first, however, with the terms that do not involve nuclear spin interactions. 

There are three separate contributions to the total magnetic hyperfine interaction, namely, the Fermi contact term, the orbital hyperfine term, and the electron spin-nuclear spin dipolar term ... 

The magnetic hyperfine interaction is represented by the sum of two terms, representing the Fermi contact interaction, and 3Qiip representing the electron spin-nuclear spin dipolar interaction. They are written as follows ... 

The axial component of the magnetic hyperfine interaction for the 2 n 3/2 component is designated //3/2 in terms of the original Frosch and Foley constants [25] h n is equal to a + (1 /2)(b + c), and in terms of our preferred hyperfine constants it is a + (l/2)(fa + 21), the latter constants describing the orbital, Fermi contact and dipolar hyperfine interactions separately. Specifically, our constants are given by,... 

We come now to the magnetic hyperfine interaction, which involves the sum of three terms representing the Fermi contact, orbital and dipolar interactions ... 

It is well-known that the hyperfine interaction for a given nucleus A consists of three contributions (a) the isotropic Fermi contact term, (b) the spin-dipolar interaction, and (c) the spin-orbit correction. One finds for the three parts of the magnetic hyperfine coupling (HFC), the following expressions [3, 9] ... 

In summary, NMR techniques based upon chemical shifts and dipolar or scalar couplings of spin-1/2 nuclei can provide structural information about bonding environments in semiconductor alloys, and more specifically the extent to which substitutions are completely random, partially or fully-ordered, or even bimodal. Semiconductor alloys containing magnetic ions, typically transition metal ions, have also been studied by spin-1/2 NMR here the often-large frequency shifts are due to the electron hyperfine interaction, and so examples of such studies will be discussed in Sect. 3.5. For alloys containing only quadrupolar nuclei as NMR probes, such as many of the III-V compounds, the nuclear quadrupole interaction will play an important and often dominant role, and can be used to investigate alloy disorder (Sect. 3.8). 

Combines sensitivity of EPR and high resolution of NMR to probe ligand super-hyperfine interactions For paramagnetic proteins enhanced chemical shift resolution, contact and dipolar shifts, spin delocalization, magnetic coupling from temperature dependence of shifts Identification of ligands coordinated to a metal centre... 

The dipolar hyperfine interaction is a through-space interaction of the electron and nuclear spin magnetic moments. As such, it is similar to the nuclear spin-nuclear spin dipolar interaction discussed earlier in connection with the H2 molecule in its ground electronic state. We shall meet the dipolar hyperfine interaction in many examples described later, so at the risk of seeming somewhat pedantic and repetitive, we here... 

Freund, Herbst, Mariella and Klemperer [112] expressed their magnetic hyperfine constants in the form originally given by Frosch and Foley [117]. As discussed elsewhere in this book, particularly in chapters 9, 10 and 11, we prefer to separate the different physical interactions, particularly the Fermi contact and dipolar interactions, in our effective Hamiltonian. This separation is usually made by other authors even when the effective Hamiltonian is expressed in terms of Frosch and Foley constants, because it is the natural route if the molecular physics of a problem is to be understood. Nevertheless since so many authors, particularly of the earlier papers, use the magnetic hyperfine theory presented by Frosch and Foley, we present in appendix 8.5 a detailed comparison of their effective Hamiltonian with that adopted in this book. The merit of the Frosch and Foley parameters is that they form the linear combination of parameters which is best determined (i.e. with least correlation) for a molecule which conforms to Hund s case (a) coupling. The values of the constants determined experimentally from the 7 LiO spectrum were therefore, in our notation (in MHz) ... 

The constant b therefore contains contributions from two quite different magnetic interactions, the Fermi contact and the electron-nuclear dipolar interactions. Interpretation of the magnitudes of these constants in terms of electronic structure theory always involves the separate assessment of these different effects, so that we prefer to use an effective Hamiltonian which separates them at the outset. Consequently the effective magnetic hyperfine Hamiltonian used throughout this book is... 

The magnetic hyperfine terms are now familiar, representing the Fermi contact interaction and axial dipolar interaction ... 

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