Determination of the microwave field strength by microwave-induced transitory oscillations in pulsed electron spin resonance

Abstract

The accurate determination of the microwave field strength B1 at the sample position is often a prerequisite for successful ESR experiments. In particular in pulse experiments, such as in extended time excitation (I, 2), the rotation angles induced by the microwave pulses must be set precisely to avoid artifacts. It is however known to the experimentalist that a reliable measurement of B1 is often difficult. A new method is proposed which is suitable for the measurement of B, in pulse experiments and which does not require a special test sample. In continuous-wave ESR, a variety of methods for the measurement of B1 have been proposed. The standard technique is based on the measurement of the shift of the resonator frequency induced by a small perturbing metallic sphere placed inside the resonator. The frequency shift is dependent on BI and on some further measurable parameters such as the loaded quality factor (3,4). Another technique proposed recently considers the magnetization hysteresis of in-phase and out-of-phase ESR spectra (5). Further approaches make use of the &-dependent saturation behavior (6), line broadening (5, 7-9), or signal intensity (10) of ESR transitions of selected test samples. For a determination of absolute B, values, however, all these methods require an additional calibration procedure. A method for absolute measurements, adapted from NMR (11), is based on the slight shift of the sideband signal positions caused by the strong centerband field in a pulse modulation experiment. The measurement requires a test sample with linewidths much smaller than the separation of the sidebands (12, 13). This is again a serious disadvantage, since size, shape, homogeneity, and dielectric property of sample, sample holder, and glassware in the resonator may severely alter the microwave field (14). In pulsed ESR, the absolute B, field strength can be determined from the duration TO of a a/2 pulse, rB1 = a/(2~~), leading to maximum signal, or of a r pulse, -r& = 1r/r0, causing a zero signal. This requires, however, a linewidth that is much smaller than the microwave field strength, 2/Tf 4 ~3~. Related measurements can also be based on Torrey oscillations in the rotating frame (15). In most solid-state work, however, the inhomogeneous linewidth by far exceeds the maximum B, fields available