Pulsed nuclear magnetic resonance signals in magnetically ordered materials

Abstract

We have obtained an analytical expression for nuclear precession and nuclear echo signals generated in magnetically ordered materials upon resonant excitation of the nuclear subsystem by two pulses of identical amplitude but different durations. We show that in a nuclear subsystem with inhomogeneous broadening of the spectroscopic transition and an inhomogeneous gain distribution, the two-pulse precession and echo signals are split into four and nine components respectively. We have analytically established a correlation between the macroscopic parameters of the components of the two-pulse signals (relative amplitudes, signal formation times) and the microscopic parameters of the magnetically ordered media (inhomogeneous half-width of the spectral line, half-width of the gain distribution function, average gain). The theoretically calculated formation times for the components of the nuclear precession and nuclear echo signals agree with the experimental data obtained for the alloy FeNiCo (70% Co).Key words: nuclear magnetic resonance, two-pulse precession and echo signals, magnetically ordered FeNiCo alloys, inhomogeneous broadening of a spectroscopic transition, inhomogeneous gain distribution.Introduction. The procedure of averaging the observable quantity (polarizability, magnetization) along the contour of the inhomogeneously broadened line is traditional in echo spectroscopy [1][2][3]. Also in some cases the need arises for additional averaging connected with the spread in the values of the transition operator matrix elements [2,3]. For example, in an ensemble of two-level resonant systems, the orientations of the transition dipole moments can be different [2]. In this case, the observable quantity must be averaged over the distribution function of the angles between the directions of the external variable electromagnetic field and the transition dipole moment.In ferromagnets and ferrimagnets, which are combined under the general name "magnetically ordered media", besides inhomogeneous broadening of the NMR line we need to take into account the inhomogeneous gain distribution [3,4]. The nature of the gain distribution involves the following. Magnetically ordered media are characterized by a branched domain structure with a certain direction of the magnetic moment in each domain. Due to shielding of the nucleus by the electron shell of the atom, the external variable magnetic field acts on the nucleus through the electronic subsystem via the hyperfine interaction [3,4]. Therefore the amplitude of the NMR signal will be determined to a large extent by the amplitude of the oscillations of the electronic moments. Such a situation is described by introducing the gain, bearing in mind that the amplitude of the external variable magnetic field at the nucleus in a ferromagnet is amplified compared with the case of the direct action of a variable field on the nucleus [4]. In the general case, there is a spread in the gain over the volume of the sample, since the amplitudes of the field are different within the domain...

Resonant excitation of single-pulse nuclear spin echo in magnetically ordered media

“…A theoretical model of the formation of multiple nuclear echo signals after two RF pulses in the ferromagnetic alloy FeNiCo was examined taking into account these sources [11]. Herein the mechanism of formation of the FSE signal is found taking into account inhomogeneous broadening of the spectroscopic transition and the inhomogeneous distribution of the enhancement factor.…”