Magnetic hyperfine field interactions

The spin state of a paramagnetic system with total spin S wiU lift its (25 + l)-fold degeneracy under the influence of ligand fields (zero-field interaction) and applied fields (Zeeman interaction). The magnetic hyperfine field sensed by the iron nuclei is different for the 25 + 1 spin states in magnitude and direction. Therefore, the absorption pattern of a particular iron nucleus for the incoming synchrotron radiation and consequently, the coherently scattered forward radiation depends on how the electronic states are occupied at a certain temperature. 

If the nucleus feels both a magnetic field and an electric field gradient, and the electric quadrupole interaction is small, then the excited levels shift as indicated in Fig. 10.20e. The result is that only the inner four lines of the sextet are equidistant. This type of spectrum is measured from bulk Fe2C>3, with a magnetic hyperfine field of 51.5 T and a small quadrupole shift on the absorption peaks of 0.10 mm/s. 

In case of Fe, the resonant absorption of 14.4keV y-rays emitted by a radioactive Co source is measured. The spectra are determined by the hyperfine interactions (isomer shift, quadrupole sphtting, and magnetic hyperfine field) of the Mossbauer nucleus caused by the surrounding electron shell. 

The third term of the nuclear Hamiltonian contains two contributions. The nuclear Zeeman term couples the magnetic moment of the nucleus to the external magnetic field Bo. Furthermore, there is a term that describes the interaction of the nuclear spin with the internal magnetic hyperfine field. For paramagnetic samples this is often done in terms of the hyperfine coupling tensor, which multiplied by the spin... 

Low-spin iron(III) ions have an electron hole in the t2g orbitals. Therefore, these centers have S = 1/2 and spin-orbit interaction contribntes considerably to the magnetic hyperfine field. Low-spin iron(III) componnds in solution always show a rather complicated magnetic Mossbauer pattern at temperatures around 4.2 K and low external fields, which means that the relaxation rate of these centers is lower than the nnclear precession rate of 10 s. Sometimes a magnetic sphtting is observed even at 77 K. Therefore, in order to pin down 8 and A g, it is advisory to measure between 100 and... 

Mossbauer spectroscopy has also been used to elucidate the magnetic structure in several amorphous alloys of Dy and 3d metals (Arrese-Boggiano et al., 1976 Chappert, 1979). In these cases, too, several of the Mossbauer lines were found to be broadened if compared to crystalline materials of about the same composition. Results for Dy-Fe alloys are reproduced in fig. 87. Arrese-Boggiano et al. first derived the distribution in magnetic hyperfine fields from the widths of those lines that are not affected by the quadrupole interaction (see fig. 85). The results were used subsequently in the determination of the distribution of the quadrupole interaction from the width of the remaining lines. The magnetic structures proposed by these authors correspond to Dy moments essentially distributed over all directions within a hemisphere (see also section 6.2.1). 

The hyperfme parameters result from shifts in, or the removal of, the degeneracy of the nuclear energy levels s through the electric and magnetic interactions between the nucleus and its surrounding electronic environment. The expressions for the hyperfine parameters, the isomer shift, the quadrupole interaction, and the magnetic hyperfine field always contain two contributions, a nuclear contribution that is fixed for a given nuclide, and an electronic contribution that varies from compound to compound. 

The magnetic hyperfine field is composed of three contributions the Fermi contact, the dipolar, and the orbital contributions. The Fermi contact term, which in most iron-containing materials is dominant, results from the interaction between the nuclear magnetic moment and the unpaired electron spin density at the nucleus. The dipolar and orbital terms represent the dipolar interaction between the nuclear magnetic moment and the electronic spin and orbital moments of their... 

Interaction between the nucleus and the orbital magnetic moment of the 3d electrons. For example, the magnetic hyperfine fields for Fe in Fe-, Co- and Ni-host at OK is —342, - -312 and +283 kOe respectively, while it is 622, 340 and 185 kOe in FeF3, FeF2 and FeS04 host materials. Contribution from the dipole interaction with the moment of the electron spin. 

Fig. 4.4. Mossbauer spectra of RbFeF4 taken over a range of temperature up to 135 K. The changes in the spectra in the region between 120 and 135 K occur as a result of the changing ratio of the strengths of the electric quadrupole interaction, which is essentially temperature independent, and the magnetic hyperfine field, which decreases quickly as the temperature approaches the Neel temperature of 133 1 K. The broadened lines observed in spectra taken just below the Neel temperature are due to changes in hyperfine field within the range of temperature stability of the apparatus. (Rush, Simopoulos, Thomas Wanklyn, 1976.)...

The translational motions and spin dynamics of conduction electrons in metals produce fluctuating local magnetic hyperfine fields. These couple to the nuclear magnetic moments, inducing transitions between nuclear spin levels and causing nuclear spin relaxation. The translational motions of electrons occur on a very rapid time scale in metals (<10 s), so the frequency spectrum of hyperfine field fluctuations is spread over a wide range of w-values. Only a small fraction of the spectral intensity falls at the relatively low nuclear resonance frequency (ojq 10 s ). Nevertheless, the interaction is so strong that this process is usually the dominant mode of relaxation for nuclei in metallic systems, either solid or liquid. 

Time-dependent phenomena can influence the Mossbauer spectrum whenever they make the position of the Mossbauer nucleus or the properties of the nuclear environment and, hence, the hyperfine interactions change with time. Time-dependent effects can influence both the spectral lineshapes and the values of the Mossbauer hyperfine parameters. The nuclear transitions and the hyperfine interactions have characteristic times, and each type of relaxation phenomenon must be considered in the context of the appropriate time scale. In case of super-paramagnetic relaxation, the magnetic hyperfine interaction fluctuates with time. The magnetic hyperfine field acting at a given Mossbauer... 

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