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Spectral investigation of spin echo emission
Solid State Communications, Vol. 87, No. 5, pp. 421-424, 1993. Printed in Great Britain.
SPECTRAL INVESTIGATION
Department
0038-1098/93$6.00+.00 Pergamon Press Ltd
OF SPIN ECHO EMISSION
R. Boscaino of Physical Sciences, University of Cagliari, Via Ospedale 72, I-09100 Cagliari, Italy
F. M. Gelardi Institute of Physics, University of Palermo, Via Archirafi 36, I-90123, Palermo, Italy. (Received 24.9.92 in revised form lZ.l.lPP3, by E. Molinarl)
The spectral content of the echo radiation emitted after a two-pulse sequence is measured in a two-level spin system. The spectral profiles exhibit maxima and zeroes of spectral density depending on the exciting sequence parameters. A calculation based on a vectorial model relates the zeroes to those packets that happen to be transparent to the second (refocusing) pulse. Moreover we report on a new spectral narrowing effect which we tentatively ascribe to the instantaneous diffusion.
information on the echo dynamics of the individual packets. In fact, for a resonant excitation, the spectral density at a given frequency offset l from the spectrum center represents the contribution coming from the packet located at wo+e, where o,=yB is the spin system frequency. At variance to standard methods, the spectral detection of the echo emission does not aim to measuring the relaxation time Tz nor the homogeneous line shape. Rather, it may be used for investigating those situations where the different behavior of various packets is relevant, e.g. when only a part of the line (Atype spins) takes part to the echo generation8, when diffusion mechanisms are effectivegTlo, or when the relaxation times depend on the spectral positio&. In this respect, it can be considered as a complement to the time- and field-domain experiments, where the single packet response is hidden by its convolution over the frequency distribution. To our knowledge, it has not been reported previously. The experiments described below show that, for a resonant excitation, echo spectra occupy a narrow band around the spin frequency o. and are structured with maxima and zeroes of spectral density, whose position and width depend on the exciting sequence, To illustrate these features, we report the results obtained in two samples, chosen for their relatively long relaxation times. Sample no.1 is a system of E’ centers11*12 (S=1/2) in a silica matrix, with Tl=(200+40) ms and T2=(115?15) Ps, at T=4.2 K and B=0.2 T. Sample no.2 is a crystal quartz containing [A104J” defects13,14 (S=1/2), with Tl=(45?10) ms and T2=(64O+6O) us, in
Echo emission is on the basis of widely exploited techniques for investigating the relaxation dynamics in atomic and spin systems1-3. Standard echo-spectroscopy involves time-domain measurementsq For instance, for a two-pulse excitation sequence, the echo intensity I is measured as a function of the interpulse distance t and the decay-kinetics I(r) is used to guess the nature and the strength of the coherence loss mechanisms. Occasionally, the dependence of the echo intensity on the external static field B (magnetic spectrum) has been also consideredsm6, as it manifests the dispersion of the phase-memory time over the inhomogeneous resonance line. In both kinds of experiment (time- and fielddomain) the measured quantity results from the superposition of the radiation fields emitted by the whole distribution of the echo-active centers. In this Communication the echo radiation emitted by an electron spin system is investigated in the frequency-domain. In the experiments described below, a two-level (S=1/2) electron spin system is excited by a two-pulse sequence (fig. 1) and, for Fired values oft, of the pulse areas 81, 82, and of B, we measure the spectral content of the emitted echo signal. Our frequency-domain study is performed by revealing the echo signal directly by means of a microwave Spectrum Analyzer, unlike other methodologies, widely used in nuclear magnetic resonance, based on the Fourier Transform of the free-induction-decay or echo signa17. A worth noting peculiarity of the spectral detection of the echo emission is that it yields 421
SPECTRAL INVESTIGATION
OF SPIN ECHO EMISSION
Vol. 87, No. 5
1.0. (a)
0.8
0.5 0.4 0.2.A
Fig.1.
Schematics of excitation sequence and echo emission. 81 and 82 are the pulse areas, 81,2=XtI,2, where x is the Rabi frequency. t is the interpulse distance.
,
0.2
’
0.0 I -0.4
-0.2
0
0.2
0.4
0.0
I -0.4
-0.2
0
0.2
0.4
frequency offset (MHz)
the same working conditions. Both centers were created by y-irradiation in a 6oCo source at room temperature. In the experimental apparatus the spin system is tuned to the working frequency w,=2ar 5.9 GHz by the static field B and the two-pulse sequence is adjusted to excite the system at the center of the resonance line. For sample no.2, whose ESR spectrum consists of six here refer to the hyperfine lines14, data reported highest-field line; however, essentially similar results were obtained in the other lines of the multiplet. The signal emitted by the system in response to the exciting sequence is firstly gated by a switching diode to isolate the echo signal, then it is amplified by a linear microwave amplifier (gain=40 dB, bandwidth 5.8-6.2 GHz, noise figure 1.8 dB). Finally, it is revealed by a microwave Spectrum Analyzer, tuned to the center frequency w. and scanning typically 1 MHz in 100 s, with a frequency resolution of 10 KHz. Spectra are digitized and stored for off-line processing and analysis. Repetitive operation is required to collect a spectrum; the repetition frequency is kept low enough to allow complete thermal relaxation of the spin system between two successive sequences. A series of four spectra measured in sample no.1 is shown in fig. 2. The first-pulse area and the interpulse distance of the exciting sequence were the same for all the spectra: 01= 120”, t=30 us. Spectra differ from each other for the second-pulse area: 02=100” (a), 82=28O” (b), 82=310” (c), 62=340” (d). For all the spectra, during both pulses, the induced Rabi frequency was x=2n 220 KHz; this was measured by preliminarily revealing the nutational regime I5 induced by a long pulse at the same power level. The values of the pulse areas 81 and 82 were .inferred from the value of x and from the measured pulse lengths (81,2=Xtl,2). As the halfwidth of the resonance line in sample no.1 is u=2n 1.25 MHz, only a fraction of the spins (A spins) are directly involved in the echo generation, for x=~.z 220 kHz . This is evident in the spectrum (a) of fig. 2, where we measure a half-width at half-maximum 6=2rc (0.35-cO.02) MHz. We have verified that echo
Fig.2.
Experimental echo spectra in sample no.1 for x=2.rc 220 kHz, 81=120”, t=30 us, and: e2=iooo (a), e2=2800 (b), e2=3ioo (~1, 82=340” (d). Arrows point the zeroes of spectral density: a(17225) kHz (b), t(129%5) kHz (c), and e(78r5) kHz (d). In the spectrum is dpp=& (d) the peak-to-peak distance (OSOkO.02) MHz.
spectra tend to broaden when x is increased at fixed values of 01, 02 and t. Echo spectra are bell-shaped only for low values of the pulse areas. The sequence of spectra (b)-(d), where the second pulse area 82 is progressively increased by steps of 30”) illustrates the extent to which the spectral profiles are sensitive to the refocusing pulse area. On increasing further 82, spectra become more and more structured, with more and more side maxima; but the observation of distant maxima is severely conditioned by the value of the signal-to-noise ratio. Moreover, we have measured that the spectral profiles as well as their widths do not depend on the interpulse distance t, but for an obvious decay factor. The occurrence of zeroes of spectral density in the spectra (b)-(d) of fig.2 can be explained using a vectorial model. The generic packet located at a frequency offset E from the line center precesses during the second pulse at the frequency j3=(c2+x2)112 and spans an angle @2(c) = fit2, where t2 is the duration of the second pulse. It is just this rotation that causes refocusing; however, for selected values oft, it happens @2(t)=2rur, where n is an integer, which means that the corresponding packets recover at the end of the second pulse exactly their original orientation. Refocusing does not occur for these packets, which can be considered as transparent to the second pulse. They will not take part to the echo emission and a zero of spectral density will appear at their frequency. So, zeroes are expected to
Vol. 87, No. 5
SPECTRAL. INVESTIGATION OF SPIN ECHO EMISSION
occur at •n=‘~[(2Jtn/82)~-1]~n, as obtained by imposing @2(c)=2mr and expressing t2 in terms of the pulse area. The agreement with the experimental spectra is quantitative. For the conditions in which the spectra (b)-(d) of fig.2 were taken, we calculate the position of the first-order (n=l) zero at *178 kHz, ?130 kHz, and +77 kHz; these theoretical values are in fair agreement with the experimental positions: +(172+5) kHz (b), *(129-c5) kHz (c), and +(78?5) kHz (d), respectively. We have calculated an approximate analytical expression of the spectral profile of the echo radiation emitted by an inhomogeneous spin system 16. Here we limit ourselves to report the final expression without deriving it: S(c) = k g(E Cj3/2p3> (1 - cosC’2) [sin 1/?tl + (E2/p2) (1 - cor@l)2]1/2 (1) where the constant k depends on the s in-cavity coupling and g(c)=(l/%)*n (l/o) exp( -e2/20 !?) models the inhomogeneous lineshape. Eq.(l) was calculated by using a vectorial model and neglecting the dephasing interactions. We have found a general qualitative agreement between Eq.(l) and the experimental results as regards the spectral shapes and their dependence on the pulse areas. In particular, in agreement with the above consideration, Eq.(l) yields S(e) = 0 for co& = 1, corresponding to the packets transparent to the second pulse. We note that other minima are expected for &=2n.n, to be related to those packets that are left aligned along the static field (zero in-plane component of the magnetization) at the end of the first pulse. In the experimental conditions of fig.2, these zeroes are expected to fall in the far wings of the spectrum outside the horizontal scale, where the signal is buried below noise. The agreement between Eq.(l) and the experimental spectra is also quantitative in sample no.1, not only as regards the minima, as noted above, but also for the maxima positions. The situation is somewhat different as regards sample no.2, where, even if the experimental spectra reproduce the expected patterns, their structures were found to be located at a distance from the center less than expected from Eq.(l), roughly by a factor 1.5. To illustrate this narrowing effect we report in fig.3 the experimental spectrum measured in sample no.2 for the same two-pulse sequence as for the spectrum (d) of fig. 2 taken in sample no.l. In spite of the close similarity between the two spectral profiles, we note that the peak-to-peak distance between the maxima in fig.3 (sample no.2) is 6pp =2n (0.3420.02) MHz, to be compared with the value of dpp=2n (O.SO+-0.02) MHz measured in the spectrum of fig.2(d) (sample no.l). The difference is well above the experimental uncertainties
frequency
423
offset (MHz)
Fig.3. Experimental spectrum measured in sample no.2 for a two-pulse sequence with x=2n 220 kHz, 81=120”, t=30 ps, 82=340”. The peak-to-peak distance is Spp=2n (0.3420.02) MHz.
and this behavior is typical, in the sense that a similar narrowing has been observed for other sequences and pulse areas. The different behavior of our two sample cannot be ascribed to their different inhomogeneous linewidth (a=2.n 1.25 MHz in sample no.1, a=2n 0.25 MHz in sample no.2). In fact, a numerical calculation of S(c) and 6nl, from Eq.(l) shows that, for a given value of x, the spectral profiles are poorly effected by the value of a, up to x/a = 2.0. In particular, for the experimental conditions of fig.2(d) and fig.3, we calculated Spp= 2~ 0.49 MHz and 6np = 2-z 0.46 MHz, respectively, in spite of the largely different value of CJZwhereas the former value is in fair agreement with the experimental one, the measured 6np in sample no.2 is less than the theoretical one by a factor 1.4. We have not yet found a satisfactory explanation of this effect. Here we limit to remark two main features of the spectral narrowing observed in sample no.2 it is more and more pronounced on increasing 82 whereas it is independent on t, which suggests to relate it to the instantaneous diffusion 4,UO (ID) mechanism. This tentative interpetration is supported by our preliminary observation that the ID plays a more relevant role in the decay kinetics I(t) of the crystalline sample with respect to the amorphous one. In conclusion we have illustrated a novel method for investigating the spin echo effect, which is based on the direct detection of its frequency content and yields informations on the echo dynamics of the individual spin packets. In particular, the experimental study of the 82-dependence of the spectral profiles may reveal the dephasing dynamics during the forced nutation stages. These informations complement those obtainable by the conventional study of the decay kinetics I(t) (or of its Fourier Transform), which depends mainly on the dephasing occurring during the precessional regime. The
424
SPECTRAL. INVESTIGATION
OF SPIN ECHO EMISSION
Vol. 87, No. 5
spectral detection allowed us to evidence an anomalous behaviour in one of the sample examined, which we have tentatively related to the non-uniform action of the ID over the spin frequency distribution. Further experimental work is in progress to test the validity of this interpetration.
Acknowledgments - We wish to thank E. Calderaro for taking care of sample irradiation and G Lapis for technical assistance. Financial support was provided by Italian Ministry of University and Research (national and local funds), Rome, Italy, by the National Institute of the Physics of Matter (INFM), Italy.
1.
The Principles of Nuclear A. Abragam, magnetism, Clarendon, Oxford (1961).
9.
2.
LAllen and J.H.Eberly, Optical Resonance and Two-level Atoms, Wiley, New York (1985).
3.
V.A.Atsarkin, Mag.Res.Rev. 16, 1 (1991).
4.
K_M.Salikhov and Y.D.Tsvetkov, Time domain electron spin resonance, LKevan and R.N. Schwartz Edts, p.231, Wiley, New York (1979).
10.
11.
12. 13.
5.
I.M.Brown, J.Chem.Phys. S&4242 (1973).
6.
I.N.Kurkin andV.I.Shlenkin, Sov.Phys.SolidState 21, 847 (1979). Fourier Transform N.M. R. D. Shaw, Spectroscopy, Elsevier, Amsterdam, 1976.
14.
J.R.Klauder and P.W.Anderson, 912 (1962).
16.
7. 8.
Phys. Rev. 125,
15.
P.Hu and LR.Walker, Phys.Rev. B 18, 1300 (1978). A.M.Raitsimring, KMSalikhov, S.A.Dikanov, and Yu.D.Tsvetkov, Sov.Phys.Solid State 17, 209.5 (1975). R.A.Weeks and C.M.Nelson, J.Am.Ceram.Soc. 43, 389 (1960). D.LGriscom, Phys.Rev. B 20, 1823 (1979). A.LTaylor and G.W.Farnell, CanJPhys. 42,595 (1964). R.H.D.Nuttal and J.kWeil, Can..LPhys. 59, 1696 (1981). R.Boscaino, F.M.Gelardi and G.Messina, Phys. Rev. B 33, 3076 (1986). R. Boscaino and F.M.Gelardi, Phys.Rev. B 46, 14550 (1992).
SPECTRAL INVESTIGATION
Department
0038-1098/93$6.00+.00 Pergamon Press Ltd
OF SPIN ECHO EMISSION
R. Boscaino of Physical Sciences, University of Cagliari, Via Ospedale 72, I-09100 Cagliari, Italy
F. M. Gelardi Institute of Physics, University of Palermo, Via Archirafi 36, I-90123, Palermo, Italy. (Received 24.9.92 in revised form lZ.l.lPP3, by E. Molinarl)
The spectral content of the echo radiation emitted after a two-pulse sequence is measured in a two-level spin system. The spectral profiles exhibit maxima and zeroes of spectral density depending on the exciting sequence parameters. A calculation based on a vectorial model relates the zeroes to those packets that happen to be transparent to the second (refocusing) pulse. Moreover we report on a new spectral narrowing effect which we tentatively ascribe to the instantaneous diffusion.
information on the echo dynamics of the individual packets. In fact, for a resonant excitation, the spectral density at a given frequency offset l from the spectrum center represents the contribution coming from the packet located at wo+e, where o,=yB is the spin system frequency. At variance to standard methods, the spectral detection of the echo emission does not aim to measuring the relaxation time Tz nor the homogeneous line shape. Rather, it may be used for investigating those situations where the different behavior of various packets is relevant, e.g. when only a part of the line (Atype spins) takes part to the echo generation8, when diffusion mechanisms are effectivegTlo, or when the relaxation times depend on the spectral positio&. In this respect, it can be considered as a complement to the time- and field-domain experiments, where the single packet response is hidden by its convolution over the frequency distribution. To our knowledge, it has not been reported previously. The experiments described below show that, for a resonant excitation, echo spectra occupy a narrow band around the spin frequency o. and are structured with maxima and zeroes of spectral density, whose position and width depend on the exciting sequence, To illustrate these features, we report the results obtained in two samples, chosen for their relatively long relaxation times. Sample no.1 is a system of E’ centers11*12 (S=1/2) in a silica matrix, with Tl=(200+40) ms and T2=(115?15) Ps, at T=4.2 K and B=0.2 T. Sample no.2 is a crystal quartz containing [A104J” defects13,14 (S=1/2), with Tl=(45?10) ms and T2=(64O+6O) us, in
Echo emission is on the basis of widely exploited techniques for investigating the relaxation dynamics in atomic and spin systems1-3. Standard echo-spectroscopy involves time-domain measurementsq For instance, for a two-pulse excitation sequence, the echo intensity I is measured as a function of the interpulse distance t and the decay-kinetics I(r) is used to guess the nature and the strength of the coherence loss mechanisms. Occasionally, the dependence of the echo intensity on the external static field B (magnetic spectrum) has been also consideredsm6, as it manifests the dispersion of the phase-memory time over the inhomogeneous resonance line. In both kinds of experiment (time- and fielddomain) the measured quantity results from the superposition of the radiation fields emitted by the whole distribution of the echo-active centers. In this Communication the echo radiation emitted by an electron spin system is investigated in the frequency-domain. In the experiments described below, a two-level (S=1/2) electron spin system is excited by a two-pulse sequence (fig. 1) and, for Fired values oft, of the pulse areas 81, 82, and of B, we measure the spectral content of the emitted echo signal. Our frequency-domain study is performed by revealing the echo signal directly by means of a microwave Spectrum Analyzer, unlike other methodologies, widely used in nuclear magnetic resonance, based on the Fourier Transform of the free-induction-decay or echo signa17. A worth noting peculiarity of the spectral detection of the echo emission is that it yields 421
SPECTRAL INVESTIGATION
OF SPIN ECHO EMISSION
Vol. 87, No. 5
1.0. (a)
0.8
0.5 0.4 0.2.A
Fig.1.
Schematics of excitation sequence and echo emission. 81 and 82 are the pulse areas, 81,2=XtI,2, where x is the Rabi frequency. t is the interpulse distance.
,
0.2
’
0.0 I -0.4
-0.2
0
0.2
0.4
0.0
I -0.4
-0.2
0
0.2
0.4
frequency offset (MHz)
the same working conditions. Both centers were created by y-irradiation in a 6oCo source at room temperature. In the experimental apparatus the spin system is tuned to the working frequency w,=2ar 5.9 GHz by the static field B and the two-pulse sequence is adjusted to excite the system at the center of the resonance line. For sample no.2, whose ESR spectrum consists of six here refer to the hyperfine lines14, data reported highest-field line; however, essentially similar results were obtained in the other lines of the multiplet. The signal emitted by the system in response to the exciting sequence is firstly gated by a switching diode to isolate the echo signal, then it is amplified by a linear microwave amplifier (gain=40 dB, bandwidth 5.8-6.2 GHz, noise figure 1.8 dB). Finally, it is revealed by a microwave Spectrum Analyzer, tuned to the center frequency w. and scanning typically 1 MHz in 100 s, with a frequency resolution of 10 KHz. Spectra are digitized and stored for off-line processing and analysis. Repetitive operation is required to collect a spectrum; the repetition frequency is kept low enough to allow complete thermal relaxation of the spin system between two successive sequences. A series of four spectra measured in sample no.1 is shown in fig. 2. The first-pulse area and the interpulse distance of the exciting sequence were the same for all the spectra: 01= 120”, t=30 us. Spectra differ from each other for the second-pulse area: 02=100” (a), 82=28O” (b), 82=310” (c), 62=340” (d). For all the spectra, during both pulses, the induced Rabi frequency was x=2n 220 KHz; this was measured by preliminarily revealing the nutational regime I5 induced by a long pulse at the same power level. The values of the pulse areas 81 and 82 were .inferred from the value of x and from the measured pulse lengths (81,2=Xtl,2). As the halfwidth of the resonance line in sample no.1 is u=2n 1.25 MHz, only a fraction of the spins (A spins) are directly involved in the echo generation, for x=~.z 220 kHz . This is evident in the spectrum (a) of fig. 2, where we measure a half-width at half-maximum 6=2rc (0.35-cO.02) MHz. We have verified that echo
Fig.2.
Experimental echo spectra in sample no.1 for x=2.rc 220 kHz, 81=120”, t=30 us, and: e2=iooo (a), e2=2800 (b), e2=3ioo (~1, 82=340” (d). Arrows point the zeroes of spectral density: a(17225) kHz (b), t(129%5) kHz (c), and e(78r5) kHz (d). In the spectrum is dpp=& (d) the peak-to-peak distance (OSOkO.02) MHz.
spectra tend to broaden when x is increased at fixed values of 01, 02 and t. Echo spectra are bell-shaped only for low values of the pulse areas. The sequence of spectra (b)-(d), where the second pulse area 82 is progressively increased by steps of 30”) illustrates the extent to which the spectral profiles are sensitive to the refocusing pulse area. On increasing further 82, spectra become more and more structured, with more and more side maxima; but the observation of distant maxima is severely conditioned by the value of the signal-to-noise ratio. Moreover, we have measured that the spectral profiles as well as their widths do not depend on the interpulse distance t, but for an obvious decay factor. The occurrence of zeroes of spectral density in the spectra (b)-(d) of fig.2 can be explained using a vectorial model. The generic packet located at a frequency offset E from the line center precesses during the second pulse at the frequency j3=(c2+x2)112 and spans an angle @2(c) = fit2, where t2 is the duration of the second pulse. It is just this rotation that causes refocusing; however, for selected values oft, it happens @2(t)=2rur, where n is an integer, which means that the corresponding packets recover at the end of the second pulse exactly their original orientation. Refocusing does not occur for these packets, which can be considered as transparent to the second pulse. They will not take part to the echo emission and a zero of spectral density will appear at their frequency. So, zeroes are expected to
Vol. 87, No. 5
SPECTRAL. INVESTIGATION OF SPIN ECHO EMISSION
occur at •n=‘~[(2Jtn/82)~-1]~n, as obtained by imposing @2(c)=2mr and expressing t2 in terms of the pulse area. The agreement with the experimental spectra is quantitative. For the conditions in which the spectra (b)-(d) of fig.2 were taken, we calculate the position of the first-order (n=l) zero at *178 kHz, ?130 kHz, and +77 kHz; these theoretical values are in fair agreement with the experimental positions: +(172+5) kHz (b), *(129-c5) kHz (c), and +(78?5) kHz (d), respectively. We have calculated an approximate analytical expression of the spectral profile of the echo radiation emitted by an inhomogeneous spin system 16. Here we limit ourselves to report the final expression without deriving it: S(c) = k g(E Cj3/2p3> (1 - cosC’2) [sin 1/?tl + (E2/p2) (1 - cor@l)2]1/2 (1) where the constant k depends on the s in-cavity coupling and g(c)=(l/%)*n (l/o) exp( -e2/20 !?) models the inhomogeneous lineshape. Eq.(l) was calculated by using a vectorial model and neglecting the dephasing interactions. We have found a general qualitative agreement between Eq.(l) and the experimental results as regards the spectral shapes and their dependence on the pulse areas. In particular, in agreement with the above consideration, Eq.(l) yields S(e) = 0 for co& = 1, corresponding to the packets transparent to the second pulse. We note that other minima are expected for &=2n.n, to be related to those packets that are left aligned along the static field (zero in-plane component of the magnetization) at the end of the first pulse. In the experimental conditions of fig.2, these zeroes are expected to fall in the far wings of the spectrum outside the horizontal scale, where the signal is buried below noise. The agreement between Eq.(l) and the experimental spectra is also quantitative in sample no.1, not only as regards the minima, as noted above, but also for the maxima positions. The situation is somewhat different as regards sample no.2, where, even if the experimental spectra reproduce the expected patterns, their structures were found to be located at a distance from the center less than expected from Eq.(l), roughly by a factor 1.5. To illustrate this narrowing effect we report in fig.3 the experimental spectrum measured in sample no.2 for the same two-pulse sequence as for the spectrum (d) of fig. 2 taken in sample no.l. In spite of the close similarity between the two spectral profiles, we note that the peak-to-peak distance between the maxima in fig.3 (sample no.2) is 6pp =2n (0.3420.02) MHz, to be compared with the value of dpp=2n (O.SO+-0.02) MHz measured in the spectrum of fig.2(d) (sample no.l). The difference is well above the experimental uncertainties
frequency
423
offset (MHz)
Fig.3. Experimental spectrum measured in sample no.2 for a two-pulse sequence with x=2n 220 kHz, 81=120”, t=30 ps, 82=340”. The peak-to-peak distance is Spp=2n (0.3420.02) MHz.
and this behavior is typical, in the sense that a similar narrowing has been observed for other sequences and pulse areas. The different behavior of our two sample cannot be ascribed to their different inhomogeneous linewidth (a=2.n 1.25 MHz in sample no.1, a=2n 0.25 MHz in sample no.2). In fact, a numerical calculation of S(c) and 6nl, from Eq.(l) shows that, for a given value of x, the spectral profiles are poorly effected by the value of a, up to x/a = 2.0. In particular, for the experimental conditions of fig.2(d) and fig.3, we calculated Spp= 2~ 0.49 MHz and 6np = 2-z 0.46 MHz, respectively, in spite of the largely different value of CJZwhereas the former value is in fair agreement with the experimental one, the measured 6np in sample no.2 is less than the theoretical one by a factor 1.4. We have not yet found a satisfactory explanation of this effect. Here we limit to remark two main features of the spectral narrowing observed in sample no.2 it is more and more pronounced on increasing 82 whereas it is independent on t, which suggests to relate it to the instantaneous diffusion 4,UO (ID) mechanism. This tentative interpetration is supported by our preliminary observation that the ID plays a more relevant role in the decay kinetics I(t) of the crystalline sample with respect to the amorphous one. In conclusion we have illustrated a novel method for investigating the spin echo effect, which is based on the direct detection of its frequency content and yields informations on the echo dynamics of the individual spin packets. In particular, the experimental study of the 82-dependence of the spectral profiles may reveal the dephasing dynamics during the forced nutation stages. These informations complement those obtainable by the conventional study of the decay kinetics I(t) (or of its Fourier Transform), which depends mainly on the dephasing occurring during the precessional regime. The
424
SPECTRAL. INVESTIGATION
OF SPIN ECHO EMISSION
Vol. 87, No. 5
spectral detection allowed us to evidence an anomalous behaviour in one of the sample examined, which we have tentatively related to the non-uniform action of the ID over the spin frequency distribution. Further experimental work is in progress to test the validity of this interpetration.
Acknowledgments - We wish to thank E. Calderaro for taking care of sample irradiation and G Lapis for technical assistance. Financial support was provided by Italian Ministry of University and Research (national and local funds), Rome, Italy, by the National Institute of the Physics of Matter (INFM), Italy.
1.
The Principles of Nuclear A. Abragam, magnetism, Clarendon, Oxford (1961).
9.
2.
LAllen and J.H.Eberly, Optical Resonance and Two-level Atoms, Wiley, New York (1985).
3.
V.A.Atsarkin, Mag.Res.Rev. 16, 1 (1991).
4.
K_M.Salikhov and Y.D.Tsvetkov, Time domain electron spin resonance, LKevan and R.N. Schwartz Edts, p.231, Wiley, New York (1979).
10.
11.
12. 13.
5.
I.M.Brown, J.Chem.Phys. S&4242 (1973).
6.
I.N.Kurkin andV.I.Shlenkin, Sov.Phys.SolidState 21, 847 (1979). Fourier Transform N.M. R. D. Shaw, Spectroscopy, Elsevier, Amsterdam, 1976.
14.
J.R.Klauder and P.W.Anderson, 912 (1962).
16.
7. 8.
Phys. Rev. 125,
15.
P.Hu and LR.Walker, Phys.Rev. B 18, 1300 (1978). A.M.Raitsimring, KMSalikhov, S.A.Dikanov, and Yu.D.Tsvetkov, Sov.Phys.Solid State 17, 209.5 (1975). R.A.Weeks and C.M.Nelson, J.Am.Ceram.Soc. 43, 389 (1960). D.LGriscom, Phys.Rev. B 20, 1823 (1979). A.LTaylor and G.W.Farnell, CanJPhys. 42,595 (1964). R.H.D.Nuttal and J.kWeil, Can..LPhys. 59, 1696 (1981). R.Boscaino, F.M.Gelardi and G.Messina, Phys. Rev. B 33, 3076 (1986). R. Boscaino and F.M.Gelardi, Phys.Rev. B 46, 14550 (1992).