The possibility of comparatively simple and fast determination of
characteristic relaxation parameters T1, T2 and T3 for nuclear spin-systems
with strong Larmor and Rabi inhomogeneous broadenings of NMR lines using the
secondary echo signal effect was experimentally shown. Resides, this method
gives opportunity to obtain a valuable infomation on the inhomogeneous NMR
broadening which reflects the character of magnetic field microscopic
destribution in such systems, as example, multidomain magnetics and
superconductors.Comment: 12 pages, 5 figure

Akhalkatsi A. M.

Alekseev B. F.

Chekmarev V. P.

Chigvinadze J. G.

G. I. Mamniashvili

Gegechkori T. O.

J. G. Chigvinadze

Kumimoto M.

Maniwa Y.

Shakhmuratova L. N.

Smolyakov B. P.

Yu. G. Sharimanov

English

arXiv

Crossref

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 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

Chigvinadze, J.G.

Mamniashvili, G.I.

Sharimanov, Yu.G.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

Fizika Nizkikh Temperatur, 2004, v. 30, No. 10, p. 1065–1070Single-pulse and secondary echoes in systems with alarge inhomogeneous broadening of NMR linesJ.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. SharimanovE. Andronikashvili Institute of Physics of Georgian Academy of Sciences6 Tamarashvili Str., Tbilisi 380077, GeorgiaE-mail: jaba@physics.iberiapac.geReceived February 11, 2003, revised February 10, 2004In the framework of the Mims transformation matrix method the equations for the nuclearmagnetizations 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 nonequilibriumwhich were earlier obtained by the statistical tensors method. As an example, the properties of theproton single-pulse echo and its secondary signals in a test material (silicone oil) coated on thesurface of high-Tc superconducting-oxide powders and in metallic hydride are presented.PACS: 74.60.–w, 74.60.GeThe single-pulse echo (SPE) is a resonance re-sponse of the inhomogeneously broadened nuclear spinsystem to the application of a solitary radiofrequency(rf) pulse arising at a time approximately equal to thepulse duration  after its termination. Though SPEwas discovered by Bloom in 1955 for protons in waterplaced in an inhomogeneous magnetic field, the mech-anism of SPE formation is not yet so clear-cut as forthe 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 ofoscillatory free-induction decays (OFIDs) [1].SPE formation mechanisms could be conditionallysubdivided into two classes: the first one is so callededge-type mechanisms where rf pulse edges act like rfpulses in the TPE method, such as the distortionmechanism [1] and the mechanism connected with theconsideration of spectral densities of sufficiently steeprf pulse edges [2], and the second class includes me-chanisms of an internal nature due to particularnonlinearities in the dynamics of spin systems, for ex-ample, connected with a strong dynamic frequencyshift 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 theso-called multipulse mechanism of SPE formation,presented in Ref. 1, for systems with both types of fre-quency inhomogeneities of NMR lines. An importantexample of such a system is that of nuclei arranged inthe 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 intype-II superconductors. Earlier in [3] we have inves-tigated the properties of the SPE formation in lithiumferrite. It was established that its properties differsharply from the SPE properties in hexagonal cobalt,where it is formed by the distortion mechanism.Therefore the conclusion was made on the possibleeffectiveness of the SPE internal mechanism of forma-tion in lithium ferrite. But its concrete mechanism wasnot finally established.Later on, the effectiveness of the multipulse mecha-nism of SPE formation was experimentally establishedin this magnet [4]. Moreover, the secondary echo sig-nals of SPE and the two-pulse echo were also formedby this mechanism.It was shown in [1] that the multipulse mechanismof SPE formation was effective in some multidomainferromagnets like Fe and FeV. From this point of viewfurther theoretical and experimental investigations ofSPE multipulse mechanism formation in systems withlarge Larmor and Rabi inhomogeneous broadenings ofNMR lines are of practical interest.© J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov, 2004In 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 inequalityT3 << T2 < T < T1, where T1 is the spin—latticerelaxation time, T2 is the transverse irreversible re-laxation time, and T3 characterizes the transversereversible relaxation time (T3  1/, were  is thehalf-width at half-maximum of the inhomogeneouslybroadened line), therefore a spin system was in anonequilibrium state before the application of the ex-citing rf pulse, and only a longitudinal component ofthe nuclear magnetization was important before the rfpulse. It was shown that a dephasing of the nuclearspin system was accumulated during n-time pulseexcitations and restored within a time intervalelapsing from the trailing edge of the last «counting»[(n + 1)th] pulse in the multipulse train. This resultedin the SPE formation and also its secondary signals attimes which were multiples of the rf pulse duration af-ter termination of the «counting» rf pulse.Let us show further a simple classical derivation ofthe equations describing the nuclear spin-system dy-namics in the investigated case, in the framework ofthe 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 mostvisual from the experimental point of view.Let us consider the case when a local static field Hnis directed along Z axis, and a rf field is along the Xaxis of the rotating coordinate system (RCS) [5,6].The modulus of Heff in the RCS could be expressedby:H a xnjneff    1 212 1 2 2  . (1)Here x /j  1, where   j j  0 isochromatefrequency a /   (or a /  1 1), where  is the rffield gain factor and  its mean value;  1 1APPLis a mean value of rf amplitude in frequency units; 1 1APPL is Rabi frequency of applied rf field and n is the nuclear gyromagnetic ratio. In addition, letus introduce the following designations [1] for themean value of the pulse area y t 1 , where t is therf pulse duration, b   1 is a characteristic of thetime interval following a pulsed excitation and ismeasured from the trailing edge of the rf pulse; 0designates the center of the resonance line, and  j isthe frequency of jth isochromate. The transformationmatrix describing the rotation of the magnetizationvector around Heff is [6]: m m m mx y z ( ; ; )( )( )( )RS C C S C CS SS C C              2 2 11–C SC C –SS    S C + S C2 2	,(2)C  , ,S C , and S stand for cos , ,  sin cos , andsin , and   tg 1 1( ) / j is the angle betweenthe effective field Heff and Z axis;  is the angle bywhich the magnetization turns about the effectivefield Heff during the pulse time t:   nH teff , whereHeff is given by (1).Let us consider first the case of single-pulse excita-tion. LetX m /mj xj ; Y m /mj yj ; Z m /mj zj ,and   ( ; ; )X Y Zj j j ,where m is the equilibrium nuclear magnetization andat the equilibrium eq 0 1 ( ; ; )0 .It before the excitation by rf pulse a nuclear spinsystem was at equilibrium conditions, and thereforeeq 0 1 ( ; ; )0 , then the result of rf pulse action is pre-sented by   ( ) .R eqAt the termination of rf pulse isochromates precessfreely around the Z axis; this is described by the ma-trix:RC~~ ~~ –SS C0 0001,where     j is the angle of rotation of the iso-chromate around the Z axis, and  is the time elapsingfrom the trailing edge of a pulse. Therefore, we havefinally:            111   ( )( )( )( )R RC S C C S S SS S C C C Seq SC S C  2 2,(3)or in the adopted designations:mmbxaxa xy a xbxaa xyx    cos cossin sin2 22 22 21a x2 2 ,mmbxaxa xy a xbxaa xyy   sin coscos sin2 22 22 21a x2 2 ,mmaa xy a xz    1 122 22 2cos .(4)1066 Fizika Nizkikh Temperatur, 2004, v. 30, No. 10J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. SharimanovExpressions (4) coincide with the correspondingones obtained in [1] for the case of single-pulse excita-tion, and similar expressions [7] obtained by solvingthe system of Bloch equations for inhomogeneouslybroadened Hahn systems.Let us find now the effect of n-time rf excitation inthe framework of model [1], when before the next rfpulse of a train only the longitudinal component ofnuclear magnetization remains. It is not difficult toprove by successive matrix multiplication that expres-sion for nuclear magnetization before the final «count-ing» (n+1)th pulse is:   nnC 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 isdescribed by the expressions         n nnR RC S CC S C C S S SS S    12 21( )( )( )( )       C C C S SC S C( ) ,12 2 (5)which is similar to the one for single-pulse excitationbut allowing for a new initial condition.It follows from previous expressions (5) in ac-cepted designations:mmaa xy a xbxaxaxn  	1 122 22 22coscos   	xy a xbxaa xy a x22 22 22 21 cossin sin ,mmaa xy a xbxaxayn  	1 122 22 22cossin   	xy a xbxaa xy a x22 22 22 21 coscos sin .(6)These expressions coincide with the ones obtainedin [1] using the formalism of statistical tensors. Thenth degree multiplier has a simple physical meaning ofa longitudinal nuclear magnetization created by n pre-liminary pulses of a multipulse train reflecting thespin 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 toprove 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 itssecondary echo signals formation is present for a largeLIB in isolation but is stronger in the simultaneouspresence of both frequency inhomogeneities, as in thecase 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 atroom and liquid nitrogen temperatures.Figure 1 shows the averager record of SPE and itssecondary signals from protons in a liquid solution ofMnCl2 (water was doped by Mn++ paramagnetic im-purities by adding a paramagnetic solution of MnCl2in order to obtain a suitable length of the spin—latticerelaxation 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 employedin 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 echosignal 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 linesFizika Nizkikh Temperatur, 2004, v. 30, No. 10 106720 sTime, msA,arb.unitsFig. 1. Single-pulse echo and its secondary signals in aliquid solution of MnCl2 at room temperature.  = 20 s,T = 4 ms, T1 = 86 ms, T2 = 72 ms.The optimal inhomogeneous width of the NMR linefor the observation of echo signals was achieved byusing an additional iron plate placed in the magnet’sclearance 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 objectsimilar the one used in Ref. 8 to study the effect ofinhomogeneous broadening of NMR lines due to theformation 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. 4its peak intensity dependence on the rf pulse period Tat room temperature (a), and at liquid nitrogen tem-perature (T = 77 K) (b).We note that at the given maximal rf pulse lengthof the spectrometer (20 s) for the observation of theSPE signal one should introduce an artificial externalmagnetic field inhomogeneity (with the help of an ad-ditional iron plate [8]) to allow for condition (1)). Atthe same time at T = 77 K (b), the SPE signal is ob-served in an homogeneous magnetic field, but theinhomogeneity of the NMR line is caused by the effectof the Abrikosov vortex lattice (AVL) formation.The character of the dependence on the repetitionperiod T points on a comparatively large role of themultipulse mechanism in the SPE formation at lowtemperatures.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 TPEand its secondary echo signals is presented for anSO + YBCO sample with a larger concentration ofcoating material to obtain more intense signals, whileFig. 4,b shows the peak intensity dependences of theTPE (curve 1) and its secondary signal (curve 2) on1068 Fizika Nizkikh Temperatur, 2004, v. 30, No. 10J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov20 40 60 80 10002040608010021H2O + Mn Cl2T, msA,arb.unitsFig. 2. Dependence of the SPE (1) and its secondary echosignal’s peak intensities (2) on the rf pulse repetition pe-riod T at room temperatures in a liquid solution of MnCl2.20 sTime, sA, arb. unitsFig. 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 1000T, ms1020304050A,arb.unitsA,arb. units0 50 100 150 200 25010203040T, msabFig. 4. Dependence of SPE peak intensities on the periodT of the single-pulse train at room temperature (a) and atliquid 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 multipulsemechanism in the SPE intensity. It is known that sec-ondary TPE signals are formed by the multipulsemechanism in proton-containing systems [10].Vanadium hydride (VH0.68) could be considered asone more example of a system possessing both types ofinhomogeneities. In this case the inhomogeneities arethe result of the metallic skin effect. Figure 6 showsthe dependence of the SPE signal peak intensity on Tat room temperature. In this case its intensity is prac-tically unchanged with increase of T showing thatthe contribution of the distortion mechanism is signi-ficant in this material, as it is in some metallicferromagnets [1].Analysis of the results obtained shows that the SPEcould be useful not only for a simple determination ofthe characteristic relaxation parameters of inhomo-geneously broadened spin systems, but could providean interesting approach to the study of AVL dynamicsusing the SPE signal due to the effect of magneticfield inhomogeneity caused by the AVL formation.This allows one to use the SPE effect for the studyof 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 matrixmethod, the equations for the nuclear magnetizationsare obtained which describe the dynamics of nuclearspin systems with strong Larmor and Rabiinhomogeneous broadenings of NMR lines in condi-tions of their unequilibrium.Properties of the proton single-pulse echo and itssecondary 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 obtainvaluable information on the inhomogeneous NMRbroadening, reflecting the character of the micro-scopic distribution of magnetic field in such systems assuperconductors, 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 linesFizika Nizkikh Temperatur, 2004, v. 30, No. 10 10690 50 100 150 200 250255075100125150T, msA,arb.unitsFig. 6. The dependence of the SPE peak intensity on theperiod T of the single-pulse train in vanadium hydrideVH0.68 .  = 20 s, T = 300 K.0 200 400 600 800 10000.20.40.60.81.0T, msTime, s300 sA, arb. unitsA, arb. unitsa21bFig. 5. Two-pulse echo (TPE) and its secondary signals inSO + YBCO (a). Dependences of TPE (1), and its sec-ondary signal peak intensities (2) on the period T of thetwo-pulse train (b). The marks show the time position ofthe 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. 10J.G. Chigvinadze, G.I. Mamniashvili, and Yu.G. Sharimanov

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Effect of Secondary Echo Signals in Spin-Systems with a Large
  Inhomogeneous Broadening of NMR Line

Effect of Secondary Echo Signals in Spin-Systems with a Large Inhomogeneous Broadening of NMR Line

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Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)