Magnetism hyperfine

The value of the magnetic hyperfine interaction constant C = 22.00 kHz is supposed to be reliably measured in the molecular beam method [71]. Experimental data for 15N2 are shown in Fig. 1.24, which depicts the density-dependence of T2 = (27tAv1/2)-1 at several temperatures. The fact that the dependences T2(p) are linear until 200 amagat proves that binary estimation of the rotational relaxation rate is valid within these limits and that Eq. (1.124) may be used to estimate cross-section oj from... 

Fig. 3.4 Calibration spectrum of metallic iron and magnetic hyperfine splitting of the nuclear levels. The values of the hyperfine splitting in a-iron are = 1.677 mm >2 = 6.167mms >3 = 10.657 mm s. The center of the calibration spectrum is defined as velocity zero left). The isomer shift of a specific sample with respect to metallic iron is indicated as 5 (right)...

The magnetic hyperfine splitting allows the determination of the effective magnetic field acting on the nucleus, which may be a superposition of an applied... 

Pure nuclear magnetic hyperfine interaction without electric quadrupole interaction is rarely encountered in chemical applications of the Mossbauer effect. Metallic iron is an exception. Quite frequently, a nuclear state is perturbed simultaneously by... 

Fig. 4.13 Combined magnetic hyperfine interaction for Fe with strong electric quadrupole interaction. Top left, electric quadrupole splitting of the ground (g) and excited state (e). Top right first-order perturbation by magnetic dipole interaction arising from a weak field along the main component > 0 of the EFG fq = 0). Bottom the resultant Mossbauer spectrum is shown for a single-crystal type measurement with B fixed perpendicular to the y-rays and B oriented along...

Fig. 4.17 Magnetic hyperfine pattern of a powder sample with randomly distributed internal magnetic field (a), and with (b) an applied magnetic field (0q = 90°), and (c) an applied magnetic field (00 = 0°)...

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

The different magnetic hyperfine coupling of the spins a and b in this example as heuristically derived for the coupled presentation from above can also be expressed by using the hyperfine coupling constants... 

The underlying physics and analysis of Mossbauer spectra have been explained in detail in Chap. 4. In that chapter, the principles of how a spectrum is parameterized in terms of spin-Hamiltonian (SH) parameters and the physical origin of these SH parameters have been clarified. Many Mossbauer studies, mainly for Fe, have been performed and there is a large body of experimental data concerning electric-and magnetic-hyperfine interactions that is accessible through the Mossbauer Effect Database. 

The third prominent interaction in iron Mossbauer spectroscopy is the magnetic hyperfine interaction of the Fe nucleus with a local magnetic field. As explained in detail in Chap. 4, it can be probed by performing the Mossbauer experiment in the presence of an applied external magnetic field. 

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] ... 

A detailed study of the magnetic hyperfine structure in Mossbauer spectra and the performance of DFT methods is available [25]. It is known that DFT typically... 

Fig. 6.2 Theoretical Fe Mossbauer relaxation spectra for longitudinal relaxation with the indicated relaxation times and with a hyperline field that can assume the values 55 T. The symmetry direction of the axially symmetric EFG is assumed parallel to the magnetic hyperfine field. (Reprinted with permission from [9] copyright 1966 by the American Physical Society)...

For fiB 2KV, there is only one energy minimum, i.e. there is no energy barrier between different magnetization directions [57], and the fluctuations of the magnetic hyperfine field can therefore be considered fast compared to Tm- The induced magnetic hyperfine field is then proportional to the induced magnetization. Using... 

The magnetic hyperfine field of iron atoms is usually opposite to the magnetization, and therefore... 

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