Single-pulse nuclear echo signals in magnetically ordered media

An analytical expression for the amplitude of a single-pulse nuclear echo signal generated in magnetically ordered materials is obtained taking into account the inhomogeneous broadening of the spectroscopic transition and the inhomogeneous distribution of the gain with an average value of greater than unity. It is shown that, in this signal, summation of the oscillations of nuclear magnetic moments with equal amplitudes and phases occurs at each instant of time. The cause of the effective suppression of the nuclear magnetic moment oscillations in the initial portion of the free precession signal is revealed analytically. The dependence of the amplitude of the one-pulse echo signal on the strength of an external alternating magnetic field, the pulse duration, and the width of the gain distribution is determined. The results obtained are compared with the experimental data for a Co₂MnSi ferromagnetic polycrystalline sample.     

Pulsed nuclear magnetic resonance signals in magnetically ordered materials

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). __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 4, pp. 529–538, July–August, 2008.     

Effect of the Excitation Radiation Coherence on Oscillations of the Photon Echo Intensity

The physical reasons for observing the splitting of optical lines several orders of magnitude smaller than the spectral width of a laser pulse are investigated. A theory of coherent and incoherent photon echo (PE) in an external static magnetic field and in the presence of a pulsed magnetic field, which causes oscillations of the PE intensity, is elaborated. It is shown that the periods of oscillations in the echo intensity, the echo duration, and the dimensions of the regions in the inhomogeneous line, where the excited ions are coherent, do not depend on the degree of coherence of the laser pulse and on the external static magnetic field. As follows from the theory, in the case of the coherent excitation of the echo, the amplitude of the intensity oscillations is independent of the external static magnetic field if the inhomogeneous line is symmetric. It is shown that the amplitude of the oscillations at the incoherent excitation of the echo is equal to the autocorrelation function of the distribution function of the transition frequency along the inhomogeneous line with the argument equal to the Zeeman splitting of the optical line in the external magnetic field. In this case, the experimental values of the oscillation amplitude are in good agreement with the calculated values of the autocorrelation function for the total inhomogeneous line in LuLiF₄:Er³⁺ (⁴I_15/2?F_9/2 transition). In the same way, the autocorrelation function has been obtained for YLiF₄:Er³⁺ on the same transition.     

Influence of Reversible and Irreversible Relaxation on the Single-Pulse Echo Signal

An analytical expression for a signal of the single-pulse echo generated in nonresonant pulse excitation of an inhomogeneously broadened two-level quantum system has been obtained, with the reversible and irreversible relaxation taken into account. It is shown that the rate of decay of the single-pulse echo is determined by the rate of reversible and irreversible transverse relaxation. It has been established that the contribution of the reversible and irreversible relaxations to decay of the single-pulse echo depends on the ratio between the detuning of the pulse-carrying frequency from resonance to the Rabi frequency. The difference between the times of transverse irreversible relaxation measured in manganese ferrite MnFe₂O₄ by the methods of single and two-pulse echo of nuclear magnetic resonance has been explained within the framework of the theoretical expressions obtained.     

Secondary Nuclear Spin Echo Signals in Thin Yttrium Iron Ferrite Garnet Films

The results are presented of experimental and theoretical study of the phenomenon of secondary nuclear spin echo in magnetically ordered materials in which the formation of additional echo signals is due to dynamic hyperfine coupling. Numerical simulation of the effect of the amplitude (ω1) and the durations of the first (t1) and the second (t2) exciting pulses on the echo signals is performed. It is found that the maximum amplitude of the secondary echo is formed under the conditions ω1t1 = 0.5π and ω1t2 ≈ 0.6π. It is shown that secondary echo signals can be observed upon inhomogeneous excitation of the spectral line ω1 ≤ Δω, where Δω is the inhomogeneous spectral line width. At a temperature of T = 4.2 K, additional double-pulse spin 3τ-echo signals from iron nuclei are experimentally observed in an epitaxial yttrium ferrite garnet film enriched with 57Fe magnetic isotope to 96%. The experimentally observed phase relationships between the primary and secondary echo signals, as well as the dependence of the echo signal amplitude on the amplitude and duration of the exciting pulses, are in good agreement with the results of numerical simulation of the dynamics of nuclear magnetization with regard to the dynamic hyperfine coupling. It is shown that the secondary echo exhibits the effect of spectral line narrowing, and the amplitude of the secondary echo is proportional to the nuclear magnetic resonance (NMR) enhancement factor in magnets, η. In the case of 57Fe NMR in an yttrium iron garnet (YIG) film, the amplitude of the 3τ-echo is two to three orders of magnitude smaller than the amplitude of the primary 2τ-echo, which corresponds to η ≈ 440. The detection of weak secondary echo signals proves to be possible due to the use of a phase-coherent NMR spectrometer with digital quadrature detection at the carrier frequency and signal accumulation.     

Single-Pulse Echo and Its Secondary Signals in Two-Level Spin Systems

The dependences of the amplitudes of single- and two-pulse spin echoes and their secondary signals in NMR (protons of glycerin in an inhomogeneous magnetic field) in the exciting-pulse repetition period T _r have been compared. The difference in origin of the primary and secondary signals of a single-pulse echo in a two-level spin system has been confirmed. It is shown that only a primary single-pulse echo observed when T _r > T ₁ (T ₁ is the spin lattice relaxation time) results from single-pulse excitation. The secondary single-pulse echo signals are observed for T _r < T ₁ and are due to the multiphase formation mechanism. The results obtained for magnetically ordered substances are analyzed. Based on these data, it was inferred earlier that primary and secondary single-pulse echo signals were formed by one and the same multiphase mechanism.     

Nuclear magnetic resonance in inhomogeneous magnetic fields

The response of the spin system has been investigated by numerical simulations in the case of a nuclear magnetic resonance (NMR) experiment performed in inhomogeneous static and radiofrequency fields. The particular case of the NMR-MOUSE was considered. The static field and the component of the radiofrequency field perpendicular to the static field were evaluated as well as the spatial distribution of the maximum NMR signal detected by the surface coil. The NMR response to various pulse sequences was evaluated numerically for the case of an ensemble of isolated spins (1/2). The behavior of the echo train in Carr-Purcell-like pulse sequences used for measurements of transverse relaxation and self-diffusion was simulated and compared with the experiment. The echo train is shown to behave qualitatively differently depending on the particular phase schemes used in these pulse sequences. Different echo trains are obtained, because of the different superposition of Hahn and stimulated echoes forming mixed echoes as a result of the spatial distribution of pulse flip angles. The superposition of Hahn and stimulated echoes originating from different spatial regions leads to distortions of the mixed echoes in intensity, shape, and phase. The volume selection produced by Carr-Purcell-like pulse sequences is also investigated for the NMR-MOUSE. The developed numerical simulation procedure is useful for understanding a variety of experiments performed with the NMR-MOUSE and for improving its performance. Copyright 2000 Academic Press.     

Self-oscillations of electronic and nuclear polarization during optical excitation of an Si/CaF2 nanostructure in a transverse magnetic field

We examine theoretically low-frequency and high-frequency self-oscillations of electronic and nuclear polarization in an Si/CaF₂ nanostructure in a transverse magnetic field. We show that the low-frequency self-oscillations are stable in zero field, and the analogous high-frequency oscillations are stable beyond the region of the maximum on the Hanle curve. The frequency of the low-frequency oscillations is 0.001–0.500 of the reciprocal nuclear longitudinal relaxation time; the frequency of the high-frequency oscillations is 10⁸–10⁹ Hz, and their amplitude reaches 50% of the initial electronic spin polarization. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 3, pp. 363–369, May–June, 2006.     

Selective saturation in strongly inhomogeneous magnetic fields

The possibility to produce selective saturation by nuclear magnetic resonance (NMR) sequences of low-power radio-frequency pulses in strongly inhomogeneous magnetic fields is explored. The saturation of parts of the sensitive volume is produced by a particular pulse sequence with reduced amplitude distribution and the spectrum of the recorded signal is compared with the simulated spectrum. The spectra of the recorded free induction decays and echo signals are in good agreement with the simulated spectra of the pulse sequence, which demonstrates the effect of the selective saturation. The results obtained are an important step towards the development of new mobile and lowpower NMR equipments operating with inhomogeneous magnetic fields.     

EPR Free Induction Decay Coherence Observed after a Single Pulse in Saturation Recovery Experiments for Samples with Resolved Multiline CW Spectra

An electron paramagnetic resonance (EPR) spin-coherence signal has been observed following a single pulse for rapidly tumbling radicals with well-resolved nuclear hyperfine splitting in fluid solution when B ₁ is large enough to excite multiple hyperfine lines. This signal, which has the shape of a spin echo, arises from constructive interference of overlapping free induction decays (FIDs) from the hyperfine lines. It has been observed for 2,6-di-t-butyl-1,4-benzosemiquinone, 2,5-di-t-butyl-1,4-benzosemiquinone, 2,3,5,6-tetramethoxy-1,4-benzosemiquinone, 2,4,6-tri-t-butylphenoxyl radical, and 3-carbamoyl-2,2,5,5-tetramethyl-3-pyrrolin-1-yloxy. It occurs at a time after the pulse that is equal to the inverse of the nuclear hyperfine splitting, independent of EPR resonance frequency from 250 MHz to 9.1 GHz. As the length of the pulse is increased, separate coherence signals can be observed that correspond to the beginning and end of the pulse. This coherence is distinct from the "single-pulse echo" signals discussed in the literature. For 2,6-di-t-butyl-1,4-benzosemiquinone, which has two resolved couplings (1.24 and 0.052 G), FID oscillations with a period that corresponds to the larger hyperfine coupling are observed on the coherence signal that arises from the smaller hyperfine coupling. If phase cycling is not perfect, the coherence signal can interfere with measurements of T ₁ by saturation recovery. Authors' address: Gareth R. Eaton, Department of Chemistry and Biochemistry, University of Denver, Denver, CO 80208, USA     

Two-pulse nuclear echo signal in magnetically ordered media

An analytical expression is obtained for the amplitude of a nuclear echo signal generated in magnetically concentrated materials upon resonant excitation of the nuclear subsystem by two pulses with an equal amplitude. It is revealed that, when both the inhomogeneous broadening of the spectroscopic transition and the inhomogeneous gain distribution are taken into account in the theory simultaneously, the spin echo signal can consist of eight satellites symmetrically located around the central peak. The analytical expressions obtained are used to determine relations between the relative amplitudes and the instants of generation of satellites, on the one hand, and microscopic parameters, such as the inhomogeneous half-width of the spectral line, the halfwidth of the gain distribution function, and the average gain, on the other hand. The results of theoretical calculations and the experimental data obtained for the FeV (2 at % V) alloy are in good agreement.     

Dynamics of pulsed saturation in inhomogeneously broadened two-level systems

On the basis of Bloch's equations an analytical expression is obtained for the pulsed saturation signal of a two-level quantum system with allowance for inhomogeneous line broadening. It is shown that in this case the signal drop is exponential over the initial portion and nonexponential for long times. It is found that starting from a certain time, which depends on the field magnitude, relaxation parameters, and inhomogeneous width of the line, a through appears in the line contour, the depth and width of which increases with an increase in pulse duration. At smaller durations of the pulse, when the line is bell-shaped, an exponential decay of the signal indicates saturation of homogeneously broadened line. Comparison of the results obtained in an experiment on pulsed saturation in ruby shows that at large amplitudes of the field and considerable inhomogeneous broadening, one observes a deviation from the Bloch theory manifesting itself as a biexponential drop in the pulsed saturation signal. A conclusion is drawn that the Bloch theory satisfactorily describes the experiment until the effective time of energy transfer to the lattice is smaller than the time of the spectral propagation of excitation. Institute of Solid-State and Semiconductor Physics, Academy of Sciences of Belarus, 17, P. Brovka St., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 197–203, March–April, 1997.     

The nuclear spin-echo signals under combined action of magnetic field and RF pulses

The effect of a pulse magnetic field on formation of the single-pulse echo signal in some magnetic materials has been studied. The signals of nuclear-spin echo formed by the combined action of radio frequency and magnetic pulses have been observed. The duration of the magnetic pulse was only limited by the length of the radio frequency pulse. The echo signal formed by the two magnetic pulses, the edges of a long magnetic pulse, and other situations that allowed us to reproduce the analogue of multipulse action, were observed as well.     

Multiquantum triple-pulse spin-echo signals from quadrupole nuclei in magnetically ordered substances

We analyze theoretically the formation of NMR pulse responses from a quadrupole spin system in which the inhomogeneous broadening of a spectral line is due to both magnetic and electric quadrupole interactions. We derive formulas for the moments of formation of multiquantum echo signals in the case of three exciting pulses. For the first time we detected in experiments multiquantum spin-echo signals from copper nuclei in ferromagnetic copper sulfochromite in the cases of double-pulse and triple-pulse excitations. We find that there is good agreement between the calculated and experimentally observed moments of echo signal formation. Zh. éksp. Teor. Fiz. 115, 2106–2112 (June 1999)     

Photon Echo from Localized Excitons in Semiconductor Nanostructures

An overview on photon echo spectroscopy under resonant excitation of the exciton complexes in semiconductor nanostructures is presented. The use of four-wave-mixing technique with the pulsed excitation and heterodyne detection allowed us to measure the coherent response of the system with the picosecond time resolution. It is shown that, for resonant selective pulsed excitation of the localized exciton complexes, the coherent signal is represented by the photon echoes due to the inhomogeneous broadening of the optical transitions. In case of resonant excitation of the trions or donor-bound excitons, the Zeeman splitting of the resident electron ground state levels under the applied transverse magnetic field results in quantum beats of photon echo amplitude at the Larmor precession frequency. Application of magnetic field makes it possible to transfer coherently the optical excitation into the spin ensemble of the resident electrons and to observe a long-lived photon echo signal. The described technique can be used as a high-resolution spectroscopy of the energy splittings in the ground state of the system. Next, we consider the Rabi oscillations and their damping under excitation with intensive optical pulses for the excitons complexes with a different degree of localization. It is shown that damping of the echo signal with increase of the excitation pulse intensity is strongly manifested for excitons, while on trions and donor-bound excitons this effect is substantially weaker.     

Gamma detected NMRON spin echo profiles for equal turn angle pulses-zero skin effect

The theoretical profiles for both principal (τ₂=τ₁) and harmonic (τ₂=1/2τ₁, 2τ₁) spin echoes in gamma detected triple pulse NMRON experiments are systematically calculated for a wide range of the parameter for inhomogeneous broadening using analytic expressions derived from physical ensemble rotation considerations, specific to a pure Zeeman Hamiltonian. In the absence of skin effects, and assuming equal turn angle pulses, these calculations provide the optimum turn angle conditions for maximum spin echo amplitude.     

Evolution of the ESR spectrum at the metal-insulator transition in quasi-one-dimensional systems

The evolution of ESR spectra in metals containing both conduction electrons and localized paramagnetic centers with inhomogeneous broadening of the magnetic resonance is treated theoretically. It is shown that such a spectrum can be effectively narrowed when a relaxation bottleneck is present for an arbitrary distribution of inhomogeneous broadening. The temperature dependence of the ESR spectrum in the polymeric phase of RbC₆₀ is investigated experimentally in the region of the metal-insulator transition. Application of the calculations to the experimental data demonstrates good agreement with the physical model if it is assumed that the given material is a quasi-one-dimensional system. Zh. éksp. Teor. Fiz. 113, 1048–1057 (March 1998)     

Ultrasound and vortex oscillations in high-temperature superconductors

An HTSC powder sample with grain (particle) diameter of 20–50 μm placed in a dc magnetic field B ₀ and cooled to a temperature below the superconducting transition temperature was exposed to the radiofrequency (rf) pulsed magnetic field B _∼ (B _∼ ⊥ B ₀) at a carrier frequency of 30.7 MHz. Stable echo signals were recorded which followed different rf-pulse trains. This phenomenon has the following mechanism. The rf magnetic field stimulates fluxoid oscillations on the HTSC grain surface, which are transformed into lattice oscillations through the pinning centers and induce a propagating sound wave. The second-order nonlinearity with respect to the gradient of the crystal lattice deviation from the equilibrium position taken into account in the sound wave equation yields the dependence of the crystal lattice natural frequency on the amplitude and length of the pulses which excite these oscillations. This dependence is responsible for the emergence of echo signals.     

Radiative detection of NMR studies of domain nuclei in enriched ferromagnetic iron

Combined host (∼95 at% enriched stable ⁵⁷Fe) and very dilute impurity (∼0.01 at% radioactive ⁶⁰Co) NMR signals have been obtained on the one sample of polycrystalline Fe foil utilising perturbations to the gamma anisotropy from in situ thermally oriented ⁶⁰Co nuclei for both resonances. The NMR-TDNO signals on the ⁵⁷Fe sites have been followed down to applied magnetic fields well below the host magnetic saturation and exhibited two distinct components; a strong, narrow homogeneous signal, superimposed over a broader inhomogeneous signal. The impurity ⁶⁰Co⁵⁷Fe inhomogeneous resonance has been studied with three pulse NMRON and the irreversible decay of the nuclear spin echo measured as a function of applied magnetic field. This revised version was published online in August 2006 with corrections to the Cover Date.