Magnetic dipole energy

The interaction of the electron spin s magnetic dipole moment with the magnetic dipole moments of nearby nuclear spins provides another contribution to the state energies and the number of energy levels, between which transitions may occur. This gives rise to the hyperfme structure in the EPR spectrum. The so-called hyperfme interaction (HFI) is described by the Hamiltonian... 

Atomic and molecular magnetic dipoles have to obey the angular momentum laws of quantum mechanics, since they are proportional to angular momenta. Each dipole can therefore make just a number of orientations with an applied magnetic induction B. Each allowed orientation corresponds to a different potential energy, and absorption of a photon with suitable energy may cause a change in orientation. 

Figure 2A. Schematic diagram of Mossbauer parameters isomer shift (6), quadrupole splitting (AEq) and magnetic dipole splitting of the nuclear energy states of 57pe leading to various hyperfine splitting in Mossbauer spectra.

Fig. 4.9 Magnetic dipole splitting (nuclear Zeeman effect) in pe and resultant Mossbauer spectrum (schematic). The mean energy of the nuclear states is shifted by the electric monopole interaction which gives rise to the isomer shift 5. Afi. g = Sg/tN and A M,e = refer to the...

It is much more difficult to observe the Mossbauer effect with the 130 keV transition than with the 99 keV transition because of the relatively high transition energy and the low transition probability of 130 keV transition, and thus the small cross section for resonance absorption. Therefore, most of the Mossbauer work with Pt, published so far, has been performed using the 99 keV transition. Unfortunately, its line width is about five times larger than that of the 130 keV transition, and hyperfine interactions in most cases are poorly resolved. However, isomer shifts in the order of one-tenth of the line width and magnetic dipole interaction, which manifests itself only in line broadening, may be extracted reliably from Pt (99 keV) spectra. 

The physical interpretation of the anisotropic principal values is based on the classical magnetic dipole interaction between the electron and nuclear spin angular momenta, and depends on the electron-nuclear distance, rn. Assuming that both spins can be described as point dipoles, the interaction energy is given by Equation (8), where 6 is the angle between the external magnetic field and the direction of rn. 

The classical interaction energy of two magnetic dipoles oriented along the direction of the static magnetic field (Figure 1) is given by... 

There are three possible orientations of the spin in the field and hence three energy levels. The energy of interaction between the magnetic dipole and the field (Bz) is izBz. The separation between neighbouring energy levels is... 

That such a matrix describes a metastable state when H0 Hl can easily be seen and will be discussed in the following section. Since / z is related to the mean magnetic moment and fiD to the mean dipole-dipole energy, this raises the question of the independence of these two invariants of the motion. It may be shown10 by introducing the Fourier transforms of the Iz(j)... 

This constitutes a system with three quasi-invariants the two magnetic moments and the dipole-dipole energy. The corresponding density matrix is... 

However, the energy of the reorientation of magnetic dipole, AE, may be expressed as follows ... 

For absorbers with magnetic dipole transitions, the evanescent magnetic field H leads to absorption of electromagnetic energy. Assuming equal magnetic permeabilities at both sides of the interface, the components of the evanescent field H at z = 0 are... 

Energy transfer probabilities due to multipolar magnetic interactions also behave in a similar way to that previously discussed for multipolar electric interactions. Thus, the transfer probability for a magnetic dipole-dipole interaction also varies with 1 / 7 , and higher order magnetic interactions are only influential at short distances. In any case, the multipolar magnetic interactions are always much less important than the electric ones. 

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