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

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 Co₂MnSi ferromagnetic polycrystalline sample. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 387–394, May–June, 2009.     

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.     

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.     

Multiple nuclear spin echo in thin polycrystalline ferromagnetic films

The formation of multiple nuclear spin echo signals has been studied in thin ferromagnetic polycrystalline films of 3d-metals and their alloys with induced anisotropy at temperatures between 2.2 and 300 K using two-pulse and three-pulse excitation. A method is proposed for the experimental determination of the contributions made by different mechanisms to the formation of spin-echo signals in magnets with strongly inhomogeneous Zeeman and quadrupole interactions. It is shown that in ferromagnets with a high rf field gain at the nucleus, the frequency modulation mechanism has a substantial influence in observations of nuclear spin-echo signals at nuclei with a high magnetic moment, even at liquid-helium temperatures. Fiz. Tverd. Tela (St. Petersburg) 40, 1056–1061 (June 1998)     

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.     

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.     

Observation of a new coherent transient in NMR — Two-pulse nutational stimulated echo in the angular distribution of gamma-radiation from oriented nuclei

A new coherent transient in NMR, the two-pulse nutational stimulated echo is reported for the ferromagnetic system⁵⁰CoFe, observed by monitoring the nuclear spin dynamics as a function of the second pulse duration via anisotropic gamma quanta from thermally oriented radioactive nuclei,⁶⁰Co. The mechanism of echo formation under strong Larmor inhomogeneous broadening and the secondary but important role of inhomogeneity associated with the rf amplitude (Rabi freqeuncy) due to skin-effect are investigated via the method of concatenation of perturbation factors in the statistical tensor formalism. For those experiments performed on time scales short compared with irreversible relaxation the theoretical predictions and subsequent experimental time-domain signals are in excellent accord. Remarkable constancy of amplitude of the new gamma-detected two-pulse echo with increase of interpulse time interval is observed, the longitudinal relaxation being manifest in the off-echo signals. Comparisons are made with NMRON four-pulse stimulated off-echo decay (analogous with conventional NMR three pulse stimulated echo) which is also sensitive to longitudinal relaxation, and with three-pulse on-echo decay (analogous with conventional NMR two-pulse Hahn echo) which measures transverse relaxation.     

X-ray studies of magnetic phase transitions in the intermetallic compounds RMn2Ge2 (R=La, Sm, Gd, Nd, Tb, and Y)

The lattice parameters a and c of the tetragonal intermetallic compounds RMn₂Ge₂ (R=La, Sm, Gd, Nd, Tb, and Y) have been measured by x-ray diffraction in the temperature interval 10–800 K. Anomalies are observed in the temperature dependence of a and c due to phase transitions from the paramagnetic to the magnetically ordered state in the Mn subsystem, transitions between various magnetically ordered phases due to a change in the magnitude and sign of the Mn-Mn exchange interaction, and magnetic transitions caused by ordering of the rare-earth subsystem leading to a rearrangement of the magnetic structure of the Mn subsystem. It is concluded that, along with the lattice parameter a, the lattice parameter c also has an influence on the Mn-Mn exchange interaction. Fiz. Tverd. Tela (St. Petersburg) 41, 2053–2058 (November 1999)     

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)     

Nonresonant echo spectroscopy of inhomogeneously broadened two-level systems

Effects which arise in inhomogeneously broadened systems upon nonresonant excitation are examined theoretically. The effect of such excitation on the signals representing a decaying free polarization and a two-pulse echo is discussed. The onset of echo signals generated in two-pulse retarded nutation during the application of a field is studied. The response can acquire a multicomponent structure. This structure is manifested in the appearance of a single-pulse echo, eight satellites in the two-pulse echo, and four nutation echo signals in the retarded two-pulse nutation. An experimental study of these effects is reported. The possibility of using them to determine relaxation times is analyzed.Institute of Solid-State and Semiconductor Physics, Academy of Sciences of Belarus. Scientific-Research Institute of Problems of Semiconductor Physics, Belarus State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 59–71, July, 1993.     

Multiple structure of two-pulse nuclear spin echo in cobalt films

The conditions for the formation of two-pulse echo signals from ⁵⁹Co nuclei in thin magnetic films at T=4.2 K are investigated. In the framework of the existing mechanisms, numerical simulation of the conditions for the formation of extra 3τ and 4τ echo signals (τ is the time delay between pulses) is carried out. It is shown that the multiple structure of the echo from ⁵⁹Co nuclei at T=4.2 K is due to a mechanism in which an additional hyperfine magnetic field proportional to nuclear magnetization is acting on the nuclear spin system.     

Nonsecular contribution to the decay of spin-echo signals of quadrupolar nuclei in magnetically ordered materials

We analyze the influence of fluctuations of the nonsecular part of the spin Hamiltonian on the decay of ordinary and multiquantum signals of the two-pulse spin echo in a quadrupole spin system with an inhomogeneously broadened spectral line. Expressions are obtained for the rate of decay of an echo in the case of selective excitation of a signal from quadrupole nuclei with arbitrary spin. These expressions are then used to analyze the experimentally observed ordinary and multiquantum echo signals from quadrupole nuclei with spin I=3/2 (⁵³Cr, ⁶³Cu, and ⁶⁵Cu) in ferromagnetic chromium chalcogenide spinels. Zh. éksp. Teor. Fiz. 116, 204–216 (July 1999)     

Formation of the pulsed electron-electron double resonance signal in the case of a finite amplitude of microwave fields

A theoretical study of the effect of microwave (MW) fields of finite amplitude on the process of pulsed electron-electron double resonance (PELDOR) signal formation is carried out. It is shown that the behavior of the experimentally observed values can be described by four vectors of partial magnetizations whose motion is reduced to precession in effective magnetic fields. In the case of strong spin-spin interaction, the PELDOR effect can be observed when a sufficiently powerful MW field is applied at pumping frequency to affect both components of the Pake doublet. The possibility of a “two-frequency” spin echo to appear under the action of two pulses with different carrier frequencies in the system where the inhomogeneous broadening of the electron spin resonance line contour is mainly determined by the dipole-dipole interaction is demonstrated.     

Spin–Spin Interactions and Nuclear Magnetic Relaxation in Magnetic Solids

The influence of the orientational fluctuations of the electronic magnetization, which modulate nuclear spin–spin interactions (Suhl–Nakamura and dipole–dipole), on the spin-lattice relaxation of magnetic nuclei with spin I = 1/2 in the magnetically ordered solids has been investigated. It has been shown that this mechanism of the spin-lattice relaxation is less effective in comparison with the process of spin-lattice relaxation caused by the direct fluctuations of hyperfine fields, which appear when there are the fluctuations of electronic magnetization direction.     

Nuclear spin echo experiments in solid H2

Measurements of the nuclear spin echo decays are reported in solid H₂ after two-pulse and three-pulse sequences. The characteristic times T₂ and τ_E describe the spin-spin interaction and the stimulated echo decay respectively. A sharp increase in τ_E is observed upon cooling into the long-range orientationally ordered phase, and a continuous one during freezing into a quadrupolar glass. However, no significant change is observed for T₂ during either process.     

Electromagnetic excitation of ultrasound in magnetically ordered dielectrics

The electromagnetic excitation of sound in magnetically ordered dielectrics—ferro-and antiferromagnets—is investigated theoretically. It is shown that sound generation in dielectrics by the Lorentz mechanism (displacement current) is much less efficient than in metals. The magnetoelastic mechanism of sound excitation in dielectrics is just as efficient as in metals. In antiferromagnets the amplitude of the excited sound depends on the relaxation parameter in the magnetic subsystem. The sound excitation efficiency increases as the orientational phase transition point or the ferromagnetic resonance frequency is approached. Zh. éksp. Teor. Fiz. 111, 1810–1816 (May 1997)     

The magnetostriction of Invar alloys

The principles of the theory of a phase transition into a magnetically ordered state are formulated for Invar alloys and other similar inhomogeneous ferromagnets, for which the concept of a local Curie temperature distribution corresponding to the experimentally observed broadened temperature interval of the transition into the ferromagnetic state has existed for 10 years. A method is proposed for obtaining information about the local temperature distribution from experimental data on the change in the properties of magnets in response to a change in temperature. For iron-nickel-chromium alloys it is shown how to obtain the temperature dependence of the magnetostrictional susceptibility of the paraprocess from data on the magnetic contribution to the thermal expansion coefficient. This confirms the important role of the local Curie temperature distribution, and it also indicates a need for new analysis of experimental data on temperature-broadened magnetic ordering phase transitions. Zh. éksp. Teor. Fiz. 113, 213–227 (January 1998)     

Antiferromagnetism in hydrated 123 compounds

Copper nuclear quadrupole resonance and zero-field nuclear magnetic resonance (ZFNMR) studies of YBa₂Cu₃O_6.5 show that a magnetic phase appears in underdoped 123 superconductors treated in ambient moist air. The studies give convincing evidence that the “empty” CuO chains play the role of easy water insertion channels. The reaction occurs first in ordered regions of the crystallites. The final product of the reaction is a nonsuperconducting antiferromagnetic compound characterized by at least two types of magnetically ordered copper ions, with ZFNMR spectra in the frequency ranges 46–96 and 96–135 MHz, respectively. Even for powder samples fixed in an epoxy resin, this reaction is found to have partially occurred after a few years. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 10, 739–744 (25 May 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Fine structure of the permittivity spectrum of a fluorite crystal

The experimental curve of the permittivity of fluorite is decomposed, for the first time, into 11 components in the range 10.5–18 eV (90 K) and 18 components in the range 10–35 eV (300 K) by the Argand diagram method. Three parameters are determined for each component: the energy at band maximum, the half-width of the band, and the oscillator strength. A scheme is proposed for the nature of the components of the permittivity of fluorite. Fiz. Tverd. Tela (St. Petersburg) 41, 1614–1615 (September 1999)     

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.