Nuclear spin, electron quadrupole interaction

It is usual in magnetic solids for the main influence on the Mdssbauer spectrum to be felt through the interactions [1] and [2]. That is, the nucleus senses its own atom and the state of the solid via the effect of the solid on that atom. The interactions of class [1] are (i) the magnetic hypeifine interaction between the atomic spin S and the nuclear spin /, (ii) the interaction between the nuclear quadrupole moment Q (which is proportional to the deviation from a spherical distribution of nuclear charge) and the electric field gradient (EFG) produced by the electronic charge distribution of the atom, and (iii) the electrostatic interaction of the... 

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 ... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

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). 

To resolve hf and nuclear quadrupole interactions which are not accessible in the EPR spectra, George Feher introduced in 1956 a double resonance technique, in which the spin system is simultaneously irradiated by a microwave (MW) and a radio frequency (rf) field3. This electron nuclear double resonance (ENDOR) spectroscopy has widely been applied in physics, chemistry and biology during the last 25 years. Several monographs2,4 and review articles7 11 dealing with experimental and theoretical aspects of ENDOR have been published. 

The main NMR interactions in solution of interest to chemists are the chemical shift relative to some stated standard (6), the indirect coupling constant (7) and the relaxation times T1 (spin-lattice) T2 (spin-spin related to the line width) and T p, the relaxation time in the rotating frame. In the case of solids and oriented samples both the direct dipole-dipole and the electric quadrupole interactions assume greater importance. We shall confine our attention in this chapter to diamagnetic compounds so that we may neglect nuclear interactions with electron spins. 

ESEEM is a pulsed EPR technique which is complementary to both conventional EPR and ENDOR spectroscopy(74.75). In the ESEEM experiment, one selects a field (effective g value) in the EPR spectrum and through a sequence of microwave pulses generates a spin echo whose intensity is monitored as a function of the delay time between the pulses. This resulting echo envelope decay pattern is amplitude modulated due to the magnetic interaction of nuclear spins that are coupled to the electron spin. Cosine Fourier transformation of this envelope yields an ENDOR-like spectrum from which nuclear hyperfine and quadrupole splittings can be determined. 

The nuclear spins give rise to additional terms in the Breit-Pauli Hamiltonian due to the interaction of the electrons with the magnetic moment of the nuclei and the electrostatic interaction with the electric quadrupole interaction of the nuclei. The magnetic interaction term of the spins with the nuclei is of the same type as the spin-spin interaction and following Abragam and Pryce (61) can be written as... 

The interaction between the nuclear electric quadrupole moment and the electrons of the molecule couples the nuclear spin I to the rotational angular momentum J, giving a resultant total angular momentum F, of... 

Molecular nitrogen, N2, is one of the most extensively studied diatomic molecules and optical spectroscopy has provided a wealth of information about its ground and excited electronic states. Molecular beam magnetic resonance studies of N2 in its ground state have yielded information about 14N nuclear spin dipolar and quadrupole interactions. Similar studies of N2 in its electronically excited A 3LU state were described in two very extensive papers by Freund, Miller, De Santis and Lurio [43] (paper I) and De Santis, Lurio, Miller and Freund [44] (paper II). We will describe their results and analysis in detail, but first note in passing that, strictly speaking, the lowest excited triplet state should be labelled the a state the label A has been used by all concerned in the past, so we will continue to do so. 

We now come to the nuclear electric quadrupole interaction, and draw upon the results derived earlier for D2 in its ground state. The present problem is marginally more complicated because of presence of electron spin. We note first that if the quadrupole interaction is given by (8.249), i.e. 

The spin Hamiltonian used to model the deuterium ligand hyperfine interaction consisted of nuclear Zeeman, electron-nuclear hyperfine and nuclear quadrupole terms. 

DPPH = 2,2-diphenyl-1-picrylhydrazyl ENDOR= electron-nuclear double resonance EPR = electron paramagnetic resonance ESE = electron spin echoes ESEEM = electron spin echo envelope modulation EFT = fast fourier transformations FWHM = fidl width at half maximum HYSCORE = hyperfine sublevel correlation nqi = nuclear quadrupole interaction TauD = taurme/aKG dioxygenase TWTA = traveling wave tube amphfier ZFS = zero field sphtting. 

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