Nuclear spin echo formed by the leading and trailing edges of a pulse

Kuz'min, V. S.; Rutkovskiǐ, I. Z.; Saǐko, A. P.; Tarasevich, A. D.; Fedoruk, G. G.

doi:10.1007/bf00662628

Cited by 5 publications

(7 citation statements)

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“…Until recently, it was assumed that nonresonant excitation leads to a trivial consequence, namely a reduced effect. However, in addition to this fact, under nonresonant excitation conditions in magnetic materials, as shown in [3], an interesting phenomenon has been observed: the appearance of multiple structure in the nuclear spin echo signal. Nonresonant excitation conditions in the theory [4] were described by dividing the parameter Δ into two terms: Δ → (Δ -δ), where Δ corresponds to the spread in the frequencies of the spin packets of the inhomogeneously broadened line, δ = ω n -ω 0 is the detuning from resonance, ω n is the carrier frequency of the electromagnetic field, ω 0 is the central frequency of the quantum transition.…”

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confidence: 95%

Estimate of inhomogeneous line broadening in steady-state magnetic resonance

Kuz'min

Kuźmin

2011

J Appl Spectrosc

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We have established relationships between the experimental and theoretical absorption and dispersion line parameters for steady-state magnetic resonance, allowing us to determine both the field characteristics (amplitude of the a.c. magnetic field) and the relaxation characteristics (longitudinal and transverse relaxation times) of the object under study.Keywords: magnetic resonance spectroscopy, absorption and dispersion line parameters, detuning from resonance, rf field amplitude, relaxation time, inhomogeneous broadening of a spectral line.Introduction. Coherent magnetic spectroscopy of quantum systems are currently widely used in studying the structure and properties of the condensed state of matter. It is subdivided into steady-state and non-steady-state spectroscopy. Steady-state spectroscopy is based on the action of a continuous electromagnetic field on a quantum transition, where the dispersion and absorption signals act as the observable quantities [1, 2]. Non-steady state spectroscopy is based on study of the dynamics of quantum transitions after two-pulse action of coherent electromagnetic radiation on a sample. The observable quantity in this case is the "echo signal" generated at a certain instant of time after the end of the exciting pulse [3]. Among coherent magnetic spectroscopy methods, the most widely used are nuclear magnetic resonance (NMR), electron paramagnetic resonance (EPR), and optical resonance. Most often non-steady-state effects are studied under exact resonance conditions, when the carrier frequency of the pulse matches the central frequency of the quantum transition. Until recently, it was assumed that nonresonant excitation leads to a trivial consequence, namely a reduced effect. However, in addition to this fact, under nonresonant excitation conditions in magnetic materials, as shown in [3], an interesting phenomenon has been observed: the appearance of multiple structure in the nuclear spin echo signal. Nonresonant excitation conditions in the theory [4] were described by dividing the parameter Δ into two terms: Δ → (Δ -δ), where Δ corresponds to the spread in the frequencies of the spin packets of the inhomogeneously broadened line, δ = ω n -ω 0 is the detuning from resonance, ω n is the carrier frequency of the electromagnetic field, ω 0 is the central frequency of the quantum transition.A similar situation also arises in steady-state magnetic resonance, when the dispersion u and absorption υ signals have the form:

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confidence: 95%

Estimate of inhomogeneous line broadening in steady-state magnetic resonance

Kuz'min

Kuźmin

2011

J Appl Spectrosc

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“…In [10], it is shown theoretically and experimentally that the reason for such splitting of the response in magnetically dilute systems is nonresonant excitation conditions. Therefore there is no satellite structure under resonant excitation conditions in magnetically dilute media.…”

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confidence: 98%

Pulsed nuclear magnetic resonance signals in magnetically ordered materials

2008

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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...

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“…The superposition of such magnetic moment oscillations generates a ferromagnetic singlepulse echo signal (FSE) in magnetically ordered media after the RF pulse field is switched off [5,6]. Although the theoretical treatment of this effect has been well studied [7][8][9], the role of the inhomogeneous distribution of the enhancement factor in formation of the FSE signal remains unclear. The proposed mechanism [10] of formation of a single-pulse echo in spin systems cannot be invoked for non-resonant excitation in order to explain the nature of the FSE because experiments indicate that this signal is generated not only under non-resonant but also under resonant excitation conditions [5,6].…”

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“…The free-precession signal (FPS) in magnetically ordered media that is generated after the action of an RF pulse on a system of two-level nuclear spins can be represented through υ-component [9] averaged over the envelope of the inhomogeneously broadened line and the envelope of the inhomogeneous distribution of the enhancement factor:…”

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

Kuz'min

Kolesenko

2009

J Appl Spectrosc

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An analytical expression for a single-pulse nuclear echo signal in magnetically ordered materials has been obtained taking into account inhomogeneous broadening of the spectroscopic transition and non-uniform distribution of the enhancement factor. The signal has been shown to result from superimposing the nuclear magnetic moment oscillations of the same amplitude and phase that arise upon termination of a radio-frequency pulse. The cause for the effective suppression of oscillations of nuclear magnetic moments in the initial phase of the free precession signal has been determined analytically. The single-pulse echo signal amplitude has been found as a function of the external variable magnetic field strength, the exciting pulse duration, the inhomogeneous NMR line broadening, and the distribution width of the enhancement factor. The results have been compared with experimental data observed in a Co 2 MnSi ferromagnetic polycrystalline sample.Keywords: nuclear magnetic resonance, single-pulse ferromagnetic echo signal, Co2MnSi-like ferromagnetic polycrystalline substances, inhomogeneous broadening of spectroscopic transition, inhomogeneous distribution of enhancement factor.Introduction. Inhomogeneous broadening of spectroscopic transitions plays a decisive role in formulating the responses of a quantum system to a pulsed radio-frequency (RF) exciting field in non-steady-state magnetic spectroscopy [1]. The principal sources of inhomogeneous broadening are heterogeneities in the external controlling constant magnetic field, dipole-dipole couplings between spins of different nature, etc.[1]. Besides these sources, static scattering of internal stresses in addition to the presence of point or extended defects leading to inhomogeneous distribution of electric fields within the bulk sample must be considered in the solid state [1]. Therefore, phase inversion of magnetic spin system oscillations in an actual substance can occur through several inhomogeneous broadening mechanisms.Coherent NMR responses in magnetically ordered media are formed not only by inhomogeneous broadening of a spectroscopic transition but also by enhancement of the RF field on nuclei that occurs due to hyperfine coupling between electronic and nuclear subsystems [2,3]. The RF field enhancement factor in nuclei within domains and at their boundaries differs greatly in magnitude because of the presence of the domain structure in ferromagnetics [2, 3]. As a result, magnetic moments of nuclei will have different oscillation frequencies during the action of the variable magnetic field pulse [4]. The superposition of such magnetic moment oscillations generates a ferromagnetic singlepulse echo signal (FSE) in magnetically ordered media after the RF pulse field is switched off [5,6]. Although the theoretical treatment of this effect has been well studied [7][8][9], the role of the inhomogeneous distribution of the enhancement factor in formation of the FSE signal remains unclear. The proposed mechanism [10] of formation of a single-pulse echo in spin sy...

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Nuclear spin echo formed by the leading and trailing edges of a pulse

Cited by 5 publications

References 1 publication

Estimate of inhomogeneous line broadening in steady-state magnetic resonance

Estimate of inhomogeneous line broadening in steady-state magnetic resonance

Pulsed nuclear magnetic resonance signals in magnetically ordered materials

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

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