Nuclear hyperfine parameters

As discussed in Chapter 6, in systems with more than one unpaired electron the ESR spectrum contains features that involve electron-electron coupling parameters analogous to the nuclear hyperfine parameters. In those types of samples the advantages of double resonance are carried out by employing the use of two different microwave frequencies, one fixed and saturating, and one variable frequency that searches for transitions. This technique is known as ELDOR (electron-electron double resonance).38,40,41,44 It has been used much less than ENDOR and usually requires custom-built equipment. 

Although simple /rSR spectra that do not depend on the nuclear terms in the spin Hamiltonian are the easiest to observe, one loses valuable information on the electronic structure. Under certain circumstances it is possible to use conventional /rSR to obtain a limited amount of information on the largest nuclear hyperfine parameters. The trick is to find an intermediate field for which the muon is selectively coupled to only the nuclei with the largest nuclear hyperfine parameters. Then a relatively simple structure is observed that gives approximate nuclear hyperfine parameters. A good example of this is shown in Fig. 3a for one of the /xSR... 

Note that the position of the juLCR depends on the sign of the nuclear hyperfine parameter relative to that of the muon. Using degenerate perturbation theory one can calculate the effects of the level crossing on the... 

The /u-LCR data also show structure from nuclei that are more distant and therefore have smaller nuclear hyperfine parameters (A 100 MHz). This structure is observed for fields applied along (110) and (111) directions for both GaAs (Kiefl, 1986) and GaP. Since these data are not yet under-... 

One of the most interesting and important results of the study was to show how the molecular constants change as the vibrational quantum number v increases. This behaviour is presented in table 8.10. The electron spin-spin and rotational constant values came, initially, from the analysis of the optical electronic spectrum [47], although the values of the spin-spin constants for different vibrational levels were refined by the analysis of the radiofrequency spectrum. The nuclear hyperfine parameters are obtained solely from the magnetic resonance experiments. We will discuss the significance of these constants in the following subsection. 

Thus far, we have established that the nuclear hyperfine parameters of the spin Hamiltonian are desirable for assessing the chemically interesting problem of structure-funetion eorrelation and reaction control. The advanced EMR methods known as ENDOR and ESEEM best recover this information from samples in which the ehemieal agent of interest is paramagnetic, and, in principle, there are methods that enable the spectroscopist to cope with the sometimes pathologieal behavior of spin systems, in other word, coax a spectrum out of a sample. In this section, however, we shall address the question of whether there is neeessary and sufficient information in a single ENDOR or ESEEM spectrum and how to design an experimental approaeh that enables one to fully parameterize the spin Hamiltonian. 

Nuclear hyperfine parameters of important Mossbauer resonances in the actinides and lanthanides. 

Fig. 9.24 Theoretical calculations of nuclear forward scattering for the relaxation rates as indicated for a system with electron spin S = 1/2, hyperfine parameters A y jg fi = 50 T, and AF.q = 2 mm s in an external field of 75 mT applied perpendicular to k and O . The transition probabilities co in ((9.8a) and (9.8b)) are expressed in units of mm s , with 1 mm corresponding to 7.3 10 s. (Taken Ifom [30])...

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

A major advantage of studying pure compounds is that single crystals can be used, and hence e.s.r. parameters, which are generally anisotropic, can be accurately extracted. Furthermore, if the crystal structure is known, and if, as is frequently the case, the paramagnetic centres retain the orientation of the parent species, the directions of the g- and electron-nuclear hyperfine tensor components can be identified relative to the radical frame. 

Fig. 3. (a) Partially resolved nuclear hyperfine structure in the p.SR spectrum for Mu in GaAs in an applied field of 0.3 T. The structure occurs in the line corresponding to 0 = 90° and Ms = —1/2. (b) Theoretical frequency spectrum obtained by exact diagonalization of the spin Hamiltonian using the nuclear hyperfine and electric quadrupole parameters in Table I for the nearest-neighbor Ga and As on the Mu symmetry axis. Both Ga isotopes, 69Ga and 71Ga, were taken into account. From Kiefl et al. (1987). 

The most convincing evidence for the BC model of Mu in III-V materials comes from the nuclear hyperfine structure in GaAs. The hyperfine parameters for the nearest-neighbor Ga and As on the Mu symmetry axis and the corresponding s and p densities are given in Table I. One finds a total spin density on the As(Ga) of 0.45 (0.38) with the ratio of p to 5 density of 23 (4) respectively. The fact that 83% of the spin density is on the two nearest-neighbor nuclei on the Mu symmetry axis agrees with the expectations of the BC model. From the ratios of p to s one can estimate that the As and Ga are displaced 0.65 (17) A and 0.14(6) A, respectively, away from the bond center. The uncertainties of these estimates were calculated from spin polarization effects, which are not known accurately, and they do not reflect any systematic uncertainties in the approximation. These displacements imply an increase in the Ga—As bond of about 32 (7)%, which is similar to calculated lattice distortions for Mu in diamond (Claxton et al., 1986 Estle et al., 1986 Estle et al., 1987) and Si (Estreicher, 1987). 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

---