Nuclear frequency spectrum, electron spin echo

Fig. 27a-c. Electron spin echo envelope modulation of Co(acacen), temperature 4K. a) Nuclear modulation pattern of Co(acacen) diluted into a Ni(acacen) 1/2 H20 single crystal. Crystal setting rotation axis I,

Fourier transform of the nuclear modulation pattern (From R. de Beer1 4)) c) Stick spectrum ENDOR frequencies (AmN = 1, 2) calculated from the hfs and quadruple tensors in Ref. 59 dashed lines ms = - 1/2, full lines ms = 1/2... 

Electron spin echo spectroscopy (ESE) monitors the spontaneous generation of microwave energy as a function of the timing of a specific excitation scheme, i.e. two or more short resonant microwave pulses. This is illustrated in Fig. 7. In a typical two-pulse excitation, the initial n/2 pulse places the spin system in a coherent state. Subsequently, the spin packets, each characterized by their own Larmor precession frequency m, start to dephase. A second rx-pulse at time r effectively reverses the time evolution of the spin packet magnetizations, i.e. the spin packets start to rephase, and an emission of microwave energy (the primary echo) occurs at time 2r. The echo ampHtude, as a fvmction of r, constitutes the ESE spectrum and relaxation processes lead to an irreversible loss of phase correlation. The characteristic time for the ampHtude decay is called the phase memory time T. This decay is often accompanied by a modulation of the echo amplitude, which is due to weak electron-nuclear hyperfine interactions. The analysis of the modulation frequencies and ampHtudes forms the basis of the electron spin echo envelope modulation spectroscopy (ESEEM). 

An intensity change of the electron spin echo signal occurs when a RF pulse with a frequency corresponding to a nuclear spin transition is applied. An ENDOR spectrum is obtained by sweeping the RF frequency. Some well-established methods are named after their inventors. Mims-ENDOR [46] is a stimulated echo sequence with a RF pulse inserted between the second and third mw-pulses. The method is particularly used for measurements of small hyperfine couplings. Another pulse technique for performing ENDOR devised by Davies [47] is also commonly employed. The pulse sequence for this method is shown in Fig. 2.26. 

Electron spin echo modulation spectroscopy (Norris et al., 1980 Dikanov Tsvetkov, 1992) is sometimes called FT-ENDOR because the echo modulation time series yields a frequency spectrum that corresponds to transitions among nuclear sublevel (Rowan et al., 1965). The ESEEM technique is often said to be complementary to ENDOR (Tsvetkov Dikanov, 1987) beeause ESEEM tends to yield well-resolved spectra in the low-frequency range (<4 MHz) of the nuclear hyperfine spectrum, where cw-ENDOR is often problematie. The eonverse is likewise true ESEEM tends to be problematic at recording hyperfine frequencies above 10 MHz. 

In Davies ENDOR the first selective m.w. n pulse inverts the polarization of a particular EPR transition (Fig. 15a). During the miKing period a selective r.f. a pulse is applied. If the r.f pulse is resonant with one of the nuclear frequencies (Fig. 15b), the polarization of this transition is inverted, which also alters the polarization of the electron spin echo observer transition (1,3) detected via a primary echo, a/2 - T - % - X - echo. The ENDOR spectrum is thus recorded by monitoring the primary echo intensity as the r.f frequency is incremented stepwise over the desired frequency range. 

Pulsed ENDOR has also become a more common technique. This is achieved by adding a radio frequency pulse within a spin-echo pulse sequence. Then, by detecting the echo intensity while the radio frequency is swept, one can obtain a pulsed ENDOR spectrum which directly reveals electron-nuclear hyperfine frequencies. 

The ESEEM spectrum is substantially better resolved for stimulated echoes than for the two-pulse echo, because it does not contain combination frequencies (sums and differences of the basic resonance frequencies), and the lines are not broadened by fast transverse spin relaxation. Thus stimulated ESEEM is the more preferable for studying electron-nuclear interactions. 

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