Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines

Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines

In the framework of the Mims transformation matrix method the equations for the nuclear magnetizations are obtained which describe the dynamics of nuclear spin-systems with strong Larmor and Rabi inhomogeneous broadenings of the NMR line in conditions of their nonequilibrium which were earlier ob...

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Hauptverfasser: Chigvinadze, J.G., Mamniashvili, G.I., Sharimanov, Yu.G.
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Veröffentlicht: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2004
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Низкотемпеpатуpный магнетизм
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spelling irk-123456789-1200492017-06-11T03:03:32Z Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines Chigvinadze, J.G. Mamniashvili, G.I. Sharimanov, Yu.G. Низкотемпеpатуpный магнетизм In the framework of the Mims transformation matrix method the equations for the nuclear magnetizations are obtained which describe the dynamics of nuclear spin-systems with strong Larmor and Rabi inhomogeneous broadenings of the NMR line in conditions of their nonequilibrium which were earlier obtained by the statistical tensors method. As an example, the properties of the proton single-pulse echo and its secondary signals in a test material (silicone oil) coated on the surface of high-Tc superconducting-oxide powders and in metallic hydride are presented. 2004 Article Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines / J.G. Chigvinadze, G.I. Mamniashvili, Yu.G. Sharimanov // Физика низких температур. — 2004. — Т. 30, № 10. — С. 1065–1070. — Бібліогр.: 11 назв. — англ. 0132-6414 PACS: 74.60.–w, 74.60.Ge http://dspace.nbuv.gov.ua/handle/123456789/120049 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
topic Низкотемпеpатуpный магнетизм
Низкотемпеpатуpный магнетизм
spellingShingle Низкотемпеpатуpный магнетизм
Низкотемпеpатуpный магнетизм
Chigvinadze, J.G.
Mamniashvili, G.I.
Sharimanov, Yu.G.
Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines
Физика низких температур
description In the framework of the Mims transformation matrix method the equations for the nuclear magnetizations are obtained which describe the dynamics of nuclear spin-systems with strong Larmor and Rabi inhomogeneous broadenings of the NMR line in conditions of their nonequilibrium which were earlier obtained by the statistical tensors method. As an example, the properties of the proton single-pulse echo and its secondary signals in a test material (silicone oil) coated on the surface of high-Tc superconducting-oxide powders and in metallic hydride are presented.
format Article
author Chigvinadze, J.G.
Mamniashvili, G.I.
Sharimanov, Yu.G.
author_facet Chigvinadze, J.G.
Mamniashvili, G.I.
Sharimanov, Yu.G.
author_sort Chigvinadze, J.G.
title Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines
title_short Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines
title_full Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines
title_fullStr Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines
title_full_unstemmed Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines
title_sort single-pulse and secondary echoes in systems with a large inhomogeneous broadening of nmr lines
publisher Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
publishDate 2004
topic_facet Низкотемпеpатуpный магнетизм
url http://dspace.nbuv.gov.ua/handle/123456789/120049
citation_txt Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines / J.G. Chigvinadze, G.I. Mamniashvili, Yu.G. Sharimanov // Физика низких температур. — 2004. — Т. 30, № 10. — С. 1065–1070. — Бібліогр.: 11 назв. — англ.
series Физика низких температур
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AT mamniashviligi singlepulseandsecondaryechoesinsystemswithalargeinhomogeneousbroadeningofnmrlines
AT sharimanovyug singlepulseandsecondaryechoesinsystemswithalargeinhomogeneousbroadeningofnmrlines
first_indexed 2025-07-08T17:09:16Z
last_indexed 2025-07-08T17:09:16Z
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fulltext Fizika Nizkikh Temperatur, 2004, v. 30, No. 10, p. 1065–1070 Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov E. Andronikashvili Institute of Physics of Georgian Academy of Sciences 6 Tamarashvili Str., Tbilisi 380077, Georgia E-mail: jaba@physics.iberiapac.ge Received February 11, 2003, revised February 10, 2004 In the framework of the Mims transformation matrix method the equations for the nuclear magnetizations are obtained which describe the dynamics of nuclear spin-systems with strong Lar- mor and Rabi inhomogeneous broadenings of the NMR line in conditions of their nonequilibrium which were earlier obtained by the statistical tensors method. As an example, the properties of the proton single-pulse echo and its secondary signals in a test material (silicone oil) coated on the surface of high-Tc superconducting-oxide powders and in metallic hydride are presented. PACS: 74.60.–w, 74.60.Ge The single-pulse echo (SPE) is a resonance re- sponse of the inhomogeneously broadened nuclear spin system to the application of a solitary radiofrequency (rf) pulse arising at a time approximately equal to the pulse duration � after its termination. Though SPE was discovered by Bloom in 1955 for protons in water placed in an inhomogeneous magnetic field, the mech- anism of SPE formation is not yet so clear-cut as for the classical Hahn two-pulse echo (TPE) and it con- tinues to attract researcher’s attention [1]. The point is that the theoretical models based ex- clusively on strong Larmor inhomogeneous broaden- ing (LIB) do not agree with the experimentally ob- served signals but instead result in the formation of oscillatory free-induction decays (OFIDs) [1]. SPE formation mechanisms could be conditionally subdivided into two classes: the first one is so called edge-type mechanisms where rf pulse edges act like rf pulses in the TPE method, such as the distortion mechanism [1] and the mechanism connected with the consideration of spectral densities of sufficiently steep rf pulse edges [2], and the second class includes me- chanisms of an internal nature due to particular nonlinearities in the dynamics of spin systems, for ex- ample, connected with a strong dynamic frequency shift of the NMR frequency or with a nonlinear dy- namics of nuclear spins due to the simulteneous pre- sence of large Larmor and Rabi inhomogeneous broad- enings of the NMR line [1]. In this work we consider in more detail the so-called multipulse mechanism of SPE formation, presented in Ref. 1, for systems with both types of fre- quency inhomogeneities of NMR lines. An important example of such a system is that of nuclei arranged in the domain walls (DW) of multidomain magnets, both in the normal metals, due to the metallic skin ef- fect, and in the normal cores of Abrikosov vortices in type-II superconductors. Earlier in [3] we have inves- tigated the properties of the SPE formation in lithium ferrite. It was established that its properties differ sharply from the SPE properties in hexagonal cobalt, where it is formed by the distortion mechanism. Therefore the conclusion was made on the possible effectiveness of the SPE internal mechanism of forma- tion in lithium ferrite. But its concrete mechanism was not finally established. Later on, the effectiveness of the multipulse mecha- nism of SPE formation was experimentally established in this magnet [4]. Moreover, the secondary echo sig- nals of SPE and the two-pulse echo were also formed by this mechanism. It was shown in [1] that the multipulse mechanism of SPE formation was effective in some multidomain ferromagnets like Fe and FeV. From this point of view further theoretical and experimental investigations of SPE multipulse mechanism formation in systems with large Larmor and Rabi inhomogeneous broadenings of NMR lines are of practical interest. © J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov, 2004 In Ref. 1, using the formalism of statistical tensors, a theoretical investigation of the SPE and its second- ary echo-signal formation mechanism was carried out, allowing for both large Larmor and Rabi inhomo- geneous broadenings of the NMR line when the repe- tition period of the rf pulses T obeys the inequality T3 << T2 < T < T1, where T1 is the spin—lattice relaxation time, T2 is the transverse irreversible re- laxation time, and T3 characterizes the transverse reversible relaxation time (T3 � 1/�, were � is the half-width at half-maximum of the inhomogeneously broadened line), therefore a spin system was in a nonequilibrium state before the application of the ex- citing rf pulse, and only a longitudinal component of the nuclear magnetization was important before the rf pulse. It was shown that a dephasing of the nuclear spin system was accumulated during n-time pulse excitations and restored within a time interval elapsing from the trailing edge of the last «counting» [(n + 1)th] pulse in the multipulse train. This resulted in the SPE formation and also its secondary signals at times which were multiples of the rf pulse duration af- ter termination of the «counting» rf pulse. Let us show further a simple classical derivation of the equations describing the nuclear spin-system dy- namics in the investigated case, in the framework of the usual classical approach by solving Bloch equa- tions or by the equivalent Mim’s transformation ma- trix method [5]. We will use the last one as the most visual from the experimental point of view. Let us consider the case when a local static field Hn is directed along Z axis, and a rf field is along the X axis of the rotating coordinate system (RCS) [5,6]. The modulus of Heff in the RCS could be expressed by: H a x n j n eff � � � � 1 2 1 2 1 2 2 � � � � � � . (1) Here x /j� �� �1, where �� � �j j� � 0 isochromate frequency a /� � � (or a /� � �1 1), where � is the rf field gain factor and � its mean value; � ��1 1� APPL is a mean value of rf amplitude in frequency units; � ��1 1� APPL is Rabi frequency of applied rf field and � n is the nuclear gyromagnetic ratio. In addition, let us introduce the following designations [1] for the mean value of the pulse area y t� �1� , where �t is the rf pulse duration, b � � �1 is a characteristic of the time interval following a pulsed excitation and is measured from the trailing edge of the rf pulse; �0 designates the center of the resonance line, and � j is the frequency of jth isochromate. The transformation matrix describing the rotation of the magnetization vector around Heff is [6]: m m m mx y z� ( ; ; ) ( ) ( ) ( ) R S C C S C C S S S C C � � � � � � � � � � � � � � � � � � � � 2 2 1 1 –C S C C –S S� � � � �S C + S C2 2 � � � � � � � , (2) C� � �, ,S C , and S� stand for cos , ,� � �sin cos , and sin �, and � �� �tg 1 1( )� �/ j is the angle between the effective field Heff and Z axis; � is the angle by which the magnetization turns about the effective field Heff during the pulse time �t: � �� nH teff , where Heff is given by (1). Let us consider first the case of single-pulse excita- tion. Let X m /mj xj� ; Y m /mj yj� ; Z m /mj zj� , and � � ( ; ; )X Y Zj j j , where m is the equilibrium nuclear magnetization and at the equilibrium �eq 0 1� ( ; ; )0 . It before the excitation by rf pulse a nuclear spin system was at equilibrium conditions, and therefore �eq 0 1� ( ; ; )0 , then the result of rf pulse action is pre- sented by � �� ( ) .R eq At the termination of rf pulse isochromates precess freely around the Z axis; this is described by the ma- trix: R C � � � � �� � � � � � � � � � � –S S C 0 0 0 0 1 , where � � �� � j is the angle of rotation of the iso- chromate around the Z axis, and � is the time elapsing from the trailing edge of a pulse. Therefore, we have finally: � �� � � � � � � � � � � � � �1 1 1� � � � � �( )( ) ( ) ( )R R C S C C S S S S S C C C Seq S C S C � � � � 2 2� � � � � �� � � � � �� , (3) or in the adopted designations: m m bx ax a x y a x bx a a x y x � � � �� � � � � � � � � cos cos sin sin 2 2 2 2 2 2 1 a x2 2� , m m bx ax a x y a x bx a a x y y � � � �� � � � � � � � � sin cos cos sin 2 2 2 2 2 2 1 a x2 2� , m m a a x y a xz � � � � �� � � � � �1 1 2 2 2 2 2cos . (4) 1066 Fizika Nizkikh Temperatur, 2004, v. 30, No. 10 J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov Expressions (4) coincide with the corresponding ones obtained in [1] for the case of single-pulse excita- tion, and similar expressions [7] obtained by solving the system of Bloch equations for inhomogeneously broadened Hahn systems. Let us find now the effect of n-time rf excitation in the framework of model [1], when before the next rf pulse of a train only the longitudinal component of nuclear magnetization remains. It is not difficult to prove by successive matrix multiplication that expres- sion for nuclear magnetization before the final «count- ing» (n+1)th pulse is: � �� � �n nC S C� �( )2 2 eq , where �eq 0 1� ( ; ; )0 . Then the result of excitation by the «counting» pulse and following free precession of magnetization is described by the expressions � �� � � � � � � � � � � � n n n R R C S C C S C C S S S S S � � � � � � � 1 2 2 1 ( )( ) ( ) ( ) � � � � � � � � � C C C S S C S C ( ) ,1 2 2 � � � � � � � �� � � � � �� (5) which is similar to the one for single-pulse excitation but allowing for a new initial condition. It follows from previous expressions (5) in ac- cepted designations: m m a a x y a x bx ax a x n � � � � � � � � � � � � � � � � � � 1 1 2 2 2 2 2 2 cos cos � � �� � � � � � � � � � � � � � x y a x bx a a x y a x 2 2 2 2 2 2 2 1 cos sin sin , m m a a x y a x bx ax a y n � � � � � � � � � � � � � � � � � � 1 1 2 2 2 2 2 2 cos sin � � �� � � � � � � � � � � � � � x y a x bx a a x y a x 2 2 2 2 2 2 2 1 cos cos sin . (6) These expressions coincide with the ones obtained in [1] using the formalism of statistical tensors. The nth degree multiplier has a simple physical meaning of a longitudinal nuclear magnetization created by n pre- liminary pulses of a multipulse train reflecting the spin system’s memory of the excitation. The expres- sions for the SPE and its secondary echo signal ampli- tudes using similar expressions for nuclear magnetiza- tion vectors were already obtained in [1]. It is easy to prove that above considered approach could be imme- diately applied to the case of periodic two-pulse exci- tation, which is of interest for description of second- ary echo signals in the investigated systems. Let us know also [1] that the effect of SPE and its secondary echo signals formation is present for a large LIB in isolation but is stronger in the simultaneous presence of both frequency inhomogeneities, as in the case of multidomain ferromagnets and type II super- conductors. Let us illustrate some of the above-mentioned de- pendences on concrete examples of practical interest. Experimental results were obtained on a Bruker «Minispec p20» NMR spectrometer provided with a «Kawasaki Electronica» digital signal averager at room and liquid nitrogen temperatures. Figure 1 shows the averager record of SPE and its secondary signals from protons in a liquid solution of MnCl2 (water was doped by Mn++ paramagnetic im- purities by adding a paramagnetic solution of MnCl2 in order to obtain a suitable length of the spin—lattice relaxation time T1 for the data collection) under peri- odic excitation by a pulse train with a period T = 4 ms. The longitudinal and transverse relaxation times are, respectively, T1 = 86 ms and T2 = 72 ms at room tem- perature (T = 300 K). The standard inversion—recov- ery and spin-echo train pulse sequences were employed in this work for the T1 and T2 determinations, respec- tively. In Fig. 2 the dependence of the peak intensities (curve 2) of the SPE (curve 1) and its secondary echo signal on the rf pulse repetition period T at room tem- peratures a liquid solution of MnCl2 are presented. Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines Fizika Nizkikh Temperatur, 2004, v. 30, No. 10 1067 20 �s Time, ms A ,a rb .u n its Fig. 1. Single-pulse echo and its secondary signals in a liquid solution of MnCl2 at room temperature. � = 20 �s, T = 4 ms, T1 = 86 ms, T2 = 72 ms. The optimal inhomogeneous width of the NMR line for the observation of echo signals was achieved by using an additional iron plate placed in the magnet’s clearance as in Ref. 8. Let us consider in more detail the SPE signal for- mation for the example of protons in a test material (silicone oil (SO), Silicon KF96) coated on the sur- face of a powdered sample of the high-Tc superconduc- tor (HTSC) YBCO-(SO + YBCO), which is an object similar the one used in Ref. 8 to study the effect of inhomogeneous broadening of NMR lines due to the formation of an Abrikosov vortex lattice in a HTSC. Figure 3 shows the SPE record of investigated sam- ple (SO + YBCO) at room temperature, and in Fig. 4 its peak intensity dependence on the rf pulse period T at room temperature (a), and at liquid nitrogen tem- perature (T = 77 K) (b). We note that at the given maximal rf pulse length of the spectrometer (20 �s) for the observation of the SPE signal one should introduce an artificial external magnetic field inhomogeneity (with the help of an ad- ditional iron plate [8]) to allow for condition (1)). At the same time at T = 77 K (b), the SPE signal is ob- served in an homogeneous magnetic field, but the inhomogeneity of the NMR line is caused by the effect of the Abrikosov vortex lattice (AVL) formation. The character of the dependence on the repetition period T points on a comparatively large role of the multipulse mechanism in the SPE formation at low temperatures. The SO concentration in the sample under investi- gation was chosen as small as possible for enhance- ment of the vortex lattice effect [9]. For comparision, in Fig. 5,a a record of the TPE and its secondary echo signals is presented for an SO + YBCO sample with a larger concentration of coating material to obtain more intense signals, while Fig. 4,b shows the peak intensity dependences of the TPE (curve 1) and its secondary signal (curve 2) on 1068 Fizika Nizkikh Temperatur, 2004, v. 30, No. 10 J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov 20 40 60 80 1000 20 40 60 80 100 2 1 H 2 O + Mn Cl 2 T, ms A ,a rb .u n its Fig. 2. Dependence of the SPE (1) and its secondary echo signal’s peak intensities (2) on the rf pulse repetition pe- riod T at room temperatures in a liquid solution of MnCl2. 20 s� Time, s� A , a rb . u n its Fig. 3. SPE in silicone oil (SO) mixed with YBCO pow- der (SO + YBCO) at room temperature. T = 500 ms, T2 = = 150 ms, T1 = 350 ms. 0 200 400 600 800 1000 T, ms 10 20 30 40 50 A ,a rb .u n its A ,a rb . u n its 0 50 100 150 200 250 10 20 30 40 T, ms a b Fig. 4. Dependence of SPE peak intensities on the period T of the single-pulse train at room temperature (a) and at liquid nitrogen temperature (b) in SO + YBCO. the period T of the two-pulse train at room tempera- ture. It is seen that dependences of the SPE and second- ary TPE signals on T have a similar character, reflect- ing the significant contribution of the multipulse mechanism in the SPE intensity. It is known that sec- ondary TPE signals are formed by the multipulse mechanism in proton-containing systems [10]. Vanadium hydride (VH0.68) could be considered as one more example of a system possessing both types of inhomogeneities. In this case the inhomogeneities are the result of the metallic skin effect. Figure 6 shows the dependence of the SPE signal peak intensity on T at room temperature. In this case its intensity is prac- tically unchanged with increase of T showing that the contribution of the distortion mechanism is signi- ficant in this material, as it is in some metallic ferromagnets [1]. Analysis of the results obtained shows that the SPE could be useful not only for a simple determination of the characteristic relaxation parameters of inhomo- geneously broadened spin systems, but could provide an interesting approach to the study of AVL dynamics using the SPE signal due to the effect of magnetic field inhomogeneity caused by the AVL formation. This allows one to use the SPE effect for the study of AVL stimulated dynamics using pulsed and low fre- quency magnetic fields [11]. In conclusion, in the framework of a simple classi- cal approach using Mim’s transformation matrix method, the equations for the nuclear magnetizations are obtained which describe the dynamics of nuclear spin systems with strong Larmor and Rabi inhomogeneous broadenings of NMR lines in condi- tions of their unequilibrium. Properties of the proton single-pulse echo and its secondary signals in a test material (silicone oil) coated on the surface of high-Tc superconducting-ox- ide powders and in metallic hydride are presented. In addition, it is shown experimentally that the sin- gle-pulse echo effect gives an opportunity to obtain valuable information on the inhomogeneous NMR broadening, reflecting the character of the micro- scopic distribution of magnetic field in such systems as superconductors, hydrides of metals, and so on. This work was supported by the International Sci- ence and Technology Centre through Project G-389. 1. L.N. Shakhmuratova and D.K. Fowler, Phys. Rev. A55, 2955 (1997). 2. B.P. Smoliakov and E.P. Khaimovich, Zh. Eksp. Teor. Fiz. 76, 1303 (1979). 3. A.M. Akhalkatsi and G.I. Mamniashvili, Fiz. Met. Metalloved. 81, 79 (1996). 4. A.M. Akhalkatsi and G.I. Mamniashvili, Phys. Lett. A291, 34 (2001). 5. T.O. Gegechkori and G.I. Mamniashvili, Proc. TSU. 38, 11 (2001). Single-pulse and secondary echoes in systems with a large inhomogeneous broadening of NMR lines Fizika Nizkikh Temperatur, 2004, v. 30, No. 10 1069 0 50 100 150 200 250 25 50 75 100 125 150 T, ms A ,a rb .u n its Fig. 6. The dependence of the SPE peak intensity on the period T of the single-pulse train in vanadium hydride VH0.68 . � = 20 �s, T = 300 K. 0 200 400 600 800 1000 0.2 0.4 0.6 0.8 1.0 T, ms Time, s� 300 s� A , a rb . u n its A , a rb . u n its a 2 1 b Fig. 5. Two-pulse echo (TPE) and its secondary signals in SO + YBCO (a). Dependences of TPE (1), and its sec- ondary signal peak intensities (2) on the period T of the two-pulse train (b). The marks show the time position of the rf pulses for T = 300 K. 6. W.B. Mims, K. Nassau, and J.D. McGee, Phys. Rev. 123, 2059 (1961). 7. V.P. Chekmarev, M.I. Kurkin et al., Zh. Eksp. Teor. Fiz. 76, 1675 (1979). 8. Y. Maniwa, T. Mituhashi et al., Physica C175, 401 (1991). 9. M. Kumimoto, T. Endo et al., Phys. Rev. A25, 2235 (1982). 10. B.F. Alekseev and V.D. Gadaev, Pis’ma Zh. Eksp. Teor. Fiz. 22, 357 (1975). 11. J.G. Chigvinadze and G.I. Mamniashvili, Fiz. Nizk. Temp. 24, 946 (1998) [Low Temp. Phys. 24, 712 (1998)]. 1070 Fizika Nizkikh Temperatur, 2004, v. 30, No. 10 J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov

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