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Observation of NMR free induction decay signal in nuclear ordered solid 3He
Volume 100A, number 4
PHYSICS LETTERS
23 January 1984
OBSERVATION OF NMR FREE INDUCTION DECAY SIGNAL IN NUCLEAR ORDERED SOLID 3He T. KUSUMOTO, O. ISH1KAWA, T. MIZUSAKI and A. HIRAI Department of Physics, Kyoto Unwersity, Kyoto 606, Japan Received 6 October 1983
We observed the pulsed NMR free induction decay signal at resonance frequency of 920 kHz in nuclear ordered solid 3He. The free induction decay was dependent on the tipping angle and non-exponential. Especially at large tipping angles the free induction signal decayed rapidly These results show that it is necessary to consider the relaxation mechanism in nuclear ordered solid 3He.
The nuclear spin ordering for solid 3He is observed at T = 1.0 mK on the melting curve. NMR measurements are one of the most useful methods for investigating the magnetic properties of nuclear ordered solid 3He [1,2]. Osheroff, Cross and Fisher (OCF) [2] performed a cw-NMR experiment on single crystals of bcc solid 3He and observed the antiferromagnetic resonance spectrum that exhibited large shifts from the Larmor frequency in low magnetic fields. They proposed that the possible magnetic structure of the ordered nuclear spin system in low magnetic fields is of the sequence u p - u p - d o w n - d o w n (uudd) along the [100] direction, which is denoted by the unit vector 1. They also proposed the following coupled equations of motion (OCF equations) for the magnetization S and the order parameter d. The order parameter d corresponds to the sublattice magnetization in the uudd magnetic structure. 3 = d X ( 3 ' H - T2Xo1S),
sx I- x(d.i)(dxi),
(i)
(2)
where ~, is the gyromagnetic ratio, X0 is the transverse susceptibility and d is the unit vector of the direction o f d . They pointed out that the observed cw-NMR spectrum was the solution for OCF equations for small oscillations about equilibrium with X = X0~02/T2, where ~20 is the antiferromagnetic resonance frequency at zero field. 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
In order to further confirm the validity of the OCF equations in the non-linear region and to investigate the nuclear spin relaxation effect in ordered solid 3He, we undertook pulsed NMR experiments in nuclear ordered solid 3He. By the use of pulsed NMR the magnetization could be rotated far away from equilibrium and the non-linear region in eq. (2) could be studied. The OCF equations are very similar to those for the superfluid 3He-A phase except for a change in the sign of the second term in eq. (2) and thus the comparison between both systems is also very interesting [3,4]. In this note, we report the first experiments of pulsed NMR in nuclear ordered solid 3He. Our methods for growing a single crystal were similar to that of OCF. Liquid 3He was first cooled to about 0.6 mK by a nuclear demagnetization refrigerator and then compressed to the melting pressure to form a single crystal of solid 3He. In order to avoid eddy current heating due to the RF field, the main part of the sample cell was made of stycast 1266. The NMR detection coil was of the toroidal type. This was particularly important in calibrating the sensitivity of the NMR system and defining the tipping angle of spins, because a toroidal coil has the same sensitivity in space as long as the solid is formed within the toroidal coil. A heater was put in the toroidal NMR coil and was used to initiate the formation of the solid crystal within it. We observed the cw-NMR resonance spectrum in order to ascertain that a single 201
Volume 100A, number 4
PHYSICS LETTERS
crystal had grown and to determine the angle 0 between the applied magnetic field and the ~ vector for each domain (there were always three magnetic domains even in the very small single crystal). Next we set the applied magnetic field to the resonance field. The free induction signals in ordered solid 3He were measured at a resonance frequency of 920 kHz. RF pulse width was fixed at 24/as and the tipping angle 0p was changed by changing the RF field intensity. Fig. 1 shows the typical results for the tipping angle dependence of the free induction decay signals for the sample with cos20 = 0.134 at T = 0.75 mK. The free induction decay even for small tipping angles was shorter by a factor than that expected by the field inhomogeneity of our magnet. At small tipping angles (0p = 5.6 ° and 7.1 °) the free induction signals decayed nearly linearly in time with a small exponential tail near the end. At 0p = 18 ° and 28 °, the free induction decay signals became neither exponential nor linear in time. At large tipping angles (0p = 71 ° and 103°), the free induction signals decayed very rapidly and were hardly observed due to the dead time of the NMR detection system. Qualitatively this anomalous tipping angle dependence of the free inductmn decay signals was observed for all samples in the range between cos20 = 0 and cos20 ~ 0.5. The free induction decay was very short for samples with cos20 ~> 0.5 even for a very small tipping angle such as 5 ° and we could not get systematic data for the tipping angle dependence of the free induction decay. In fig. 1 the values of 0p are calibrated in the normal Fermi liquid phase. It is important to know whether magnetization was actually tipped in the nuclear ordered phase. In order to estimate the volume of the solid sample, we calibrated the spring constant for the bellows of our compressional cell [5] by using the compressibility of liquid 3He around the mKregion [6]. Therefore knowing the pressure difference across the bellows, we could estimate the amount of sample made in the sample cell. The volume for the sample shown in the figure was estimated to be 0.054 cc. NMR sensitivity was cahbrated against the susceptibilities of normal Fermi liquid [7]. Thus, the signal intensity for a known amount of ordered solid could be calculated for a given tipping angle 0p, assuming that the observed signal for one of the three magnetic domains should correspond to one third of the total signal calcu202
23 January 1984
T : O 75 mK COS2e = 0 134 Op(deg) 1 56 2 71 3 11 4 18 5 28 6 45 7 71 8 113
()
i
Ol
i
02
i
03
i
O~
015
0'6
0'7
0.8 (msec)
Fig 1. Tipping angle dependence of the free induction decay signals for the sample with cos20 = 0.134 at T = 0.75 mK. The tipping angle 0p for each curve is denoted m the figure.
lated by the static susceptibilities measured in the ordered solids [8,9]. The observed signal intensity agreed very well with that calculated for small tipping angles up to about 30 ° within our calibration accuracy (less than 10%). We could not trace the s]gnal intensity for the large tipping angle because of the very short free induction decay. We concluded that the magnetization was tipped as we expected even in the ordered phase at least for tipping angles smaller than 30 ° for the sample shown in the figure. Some experimental results observed in the pulsed NMR measurements should be noted here to describe further properties of the free induction decay signal in the ordered phase. We could not observe any spin echoes except for the solid echoes. The magnettzation recovery time was also measured and seemed to be of the same order of magnitude as the free induction decay even though accurate measurements of the magnetization recovery time could not be taken due to the anomalous free induction signal. The frequency shift of the resonance signal for a large tipping angle was calculated [4] but we could not observe any tipping angle-dependent frequency shift within the accuracy of the frequency determination during the short free mduction decay. The external applied field did not satisfy the condition for the high field limit, (3,H0)2 >> ~22, where the theory is applicable. This may be attributed to the disagreement with the theory.
Volume 100A, number 4
PHYSICS LETTERS
It should be mentioned here that qualitatively similar tipping angle dependence o f the free induction decay signal was also observed in the superfluid 3He-A phase in the same sample cell used for this experiment. In summary, we first observed the free induction decay signal in nuclear ordered solid 3He. The free induction decay depended on the tipping angles, and was non-exponential in time even at small tipping angles. A t large tipping angles the free induction signal decayed very rapidly. There has not been any discussion about the relaxation processes in the nuclear ordered phase. It m a y be necessary to include the relaxation effects in the OCF equations. The uniform mode o f the observed NMR signal m a y not be stable against large spin tipping * 1. The existence of the small magnetic domains in nuclear ordered solid m a y play an important role in the decay o f the free induction signal. ,1 This kind of instability in the superfluid aHe-A phase was discussed by Fomin [ 10] and in nuclear ordered solid aHe independently by Ohml et al. [ 11 ] in connection with this experiment.
23 January 1984
We would like to thank T. Tsuneto, Y. Nagaoka, T. Ohmi, H. Jichu and M. Tsubota for many stimulating discussions.
References [1 ] E.D. Adams, E.A. Schubert, G.E. Haas and D.M. Bakalyar, Phys. Rev. Lett. 44 (1980) 789. [2] D.D. Osheroff, M.C. Cross and D.S. Fisher, Phys. Rev. Lett. 44 (1980) 792. [3] Chia-Ren Hu and T.E. Ham, Phys. Rev. B24 (1981) 2478. [4] H. Namalzawa, Prog. Theor. Phys. 67 (1982) 1989. [5] O.V. Lounasmaa, Experimental principles and methods below 1 K (Academic Press, London, 1974) eh. 4. [6] E.R. Grilly, J. Low Temp. Phys. 4 (1971) 615. [7] J.C. Wheatley, Rev. Mod. Phys. 47 (1975) 415. [8] T.C. Prewitt and J.M. Goodkind, Phys. Rev. Lett. 39 (1977) 1283. [9] T. Hata, S. Yamasaki, S. Taneda, M. Kodama and T. Shigi, J. Magn. Magn. Mater. 31-34 (1983) 737. [10] I.A. Fomin, JETP Lett. 30 (1979) 164. [11] T. Ohm1, M. Tsubota and T. Tsuneto, private communication.
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PHYSICS LETTERS
23 January 1984
OBSERVATION OF NMR FREE INDUCTION DECAY SIGNAL IN NUCLEAR ORDERED SOLID 3He T. KUSUMOTO, O. ISH1KAWA, T. MIZUSAKI and A. HIRAI Department of Physics, Kyoto Unwersity, Kyoto 606, Japan Received 6 October 1983
We observed the pulsed NMR free induction decay signal at resonance frequency of 920 kHz in nuclear ordered solid 3He. The free induction decay was dependent on the tipping angle and non-exponential. Especially at large tipping angles the free induction signal decayed rapidly These results show that it is necessary to consider the relaxation mechanism in nuclear ordered solid 3He.
The nuclear spin ordering for solid 3He is observed at T = 1.0 mK on the melting curve. NMR measurements are one of the most useful methods for investigating the magnetic properties of nuclear ordered solid 3He [1,2]. Osheroff, Cross and Fisher (OCF) [2] performed a cw-NMR experiment on single crystals of bcc solid 3He and observed the antiferromagnetic resonance spectrum that exhibited large shifts from the Larmor frequency in low magnetic fields. They proposed that the possible magnetic structure of the ordered nuclear spin system in low magnetic fields is of the sequence u p - u p - d o w n - d o w n (uudd) along the [100] direction, which is denoted by the unit vector 1. They also proposed the following coupled equations of motion (OCF equations) for the magnetization S and the order parameter d. The order parameter d corresponds to the sublattice magnetization in the uudd magnetic structure. 3 = d X ( 3 ' H - T2Xo1S),
sx I- x(d.i)(dxi),
(i)
(2)
where ~, is the gyromagnetic ratio, X0 is the transverse susceptibility and d is the unit vector of the direction o f d . They pointed out that the observed cw-NMR spectrum was the solution for OCF equations for small oscillations about equilibrium with X = X0~02/T2, where ~20 is the antiferromagnetic resonance frequency at zero field. 0.375-9601/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
In order to further confirm the validity of the OCF equations in the non-linear region and to investigate the nuclear spin relaxation effect in ordered solid 3He, we undertook pulsed NMR experiments in nuclear ordered solid 3He. By the use of pulsed NMR the magnetization could be rotated far away from equilibrium and the non-linear region in eq. (2) could be studied. The OCF equations are very similar to those for the superfluid 3He-A phase except for a change in the sign of the second term in eq. (2) and thus the comparison between both systems is also very interesting [3,4]. In this note, we report the first experiments of pulsed NMR in nuclear ordered solid 3He. Our methods for growing a single crystal were similar to that of OCF. Liquid 3He was first cooled to about 0.6 mK by a nuclear demagnetization refrigerator and then compressed to the melting pressure to form a single crystal of solid 3He. In order to avoid eddy current heating due to the RF field, the main part of the sample cell was made of stycast 1266. The NMR detection coil was of the toroidal type. This was particularly important in calibrating the sensitivity of the NMR system and defining the tipping angle of spins, because a toroidal coil has the same sensitivity in space as long as the solid is formed within the toroidal coil. A heater was put in the toroidal NMR coil and was used to initiate the formation of the solid crystal within it. We observed the cw-NMR resonance spectrum in order to ascertain that a single 201
Volume 100A, number 4
PHYSICS LETTERS
crystal had grown and to determine the angle 0 between the applied magnetic field and the ~ vector for each domain (there were always three magnetic domains even in the very small single crystal). Next we set the applied magnetic field to the resonance field. The free induction signals in ordered solid 3He were measured at a resonance frequency of 920 kHz. RF pulse width was fixed at 24/as and the tipping angle 0p was changed by changing the RF field intensity. Fig. 1 shows the typical results for the tipping angle dependence of the free induction decay signals for the sample with cos20 = 0.134 at T = 0.75 mK. The free induction decay even for small tipping angles was shorter by a factor than that expected by the field inhomogeneity of our magnet. At small tipping angles (0p = 5.6 ° and 7.1 °) the free induction signals decayed nearly linearly in time with a small exponential tail near the end. At 0p = 18 ° and 28 °, the free induction decay signals became neither exponential nor linear in time. At large tipping angles (0p = 71 ° and 103°), the free induction signals decayed very rapidly and were hardly observed due to the dead time of the NMR detection system. Qualitatively this anomalous tipping angle dependence of the free inductmn decay signals was observed for all samples in the range between cos20 = 0 and cos20 ~ 0.5. The free induction decay was very short for samples with cos20 ~> 0.5 even for a very small tipping angle such as 5 ° and we could not get systematic data for the tipping angle dependence of the free induction decay. In fig. 1 the values of 0p are calibrated in the normal Fermi liquid phase. It is important to know whether magnetization was actually tipped in the nuclear ordered phase. In order to estimate the volume of the solid sample, we calibrated the spring constant for the bellows of our compressional cell [5] by using the compressibility of liquid 3He around the mKregion [6]. Therefore knowing the pressure difference across the bellows, we could estimate the amount of sample made in the sample cell. The volume for the sample shown in the figure was estimated to be 0.054 cc. NMR sensitivity was cahbrated against the susceptibilities of normal Fermi liquid [7]. Thus, the signal intensity for a known amount of ordered solid could be calculated for a given tipping angle 0p, assuming that the observed signal for one of the three magnetic domains should correspond to one third of the total signal calcu202
23 January 1984
T : O 75 mK COS2e = 0 134 Op(deg) 1 56 2 71 3 11 4 18 5 28 6 45 7 71 8 113
()
i
Ol
i
02
i
03
i
O~
015
0'6
0'7
0.8 (msec)
Fig 1. Tipping angle dependence of the free induction decay signals for the sample with cos20 = 0.134 at T = 0.75 mK. The tipping angle 0p for each curve is denoted m the figure.
lated by the static susceptibilities measured in the ordered solids [8,9]. The observed signal intensity agreed very well with that calculated for small tipping angles up to about 30 ° within our calibration accuracy (less than 10%). We could not trace the s]gnal intensity for the large tipping angle because of the very short free induction decay. We concluded that the magnetization was tipped as we expected even in the ordered phase at least for tipping angles smaller than 30 ° for the sample shown in the figure. Some experimental results observed in the pulsed NMR measurements should be noted here to describe further properties of the free induction decay signal in the ordered phase. We could not observe any spin echoes except for the solid echoes. The magnettzation recovery time was also measured and seemed to be of the same order of magnitude as the free induction decay even though accurate measurements of the magnetization recovery time could not be taken due to the anomalous free induction signal. The frequency shift of the resonance signal for a large tipping angle was calculated [4] but we could not observe any tipping angle-dependent frequency shift within the accuracy of the frequency determination during the short free mduction decay. The external applied field did not satisfy the condition for the high field limit, (3,H0)2 >> ~22, where the theory is applicable. This may be attributed to the disagreement with the theory.
Volume 100A, number 4
PHYSICS LETTERS
It should be mentioned here that qualitatively similar tipping angle dependence o f the free induction decay signal was also observed in the superfluid 3He-A phase in the same sample cell used for this experiment. In summary, we first observed the free induction decay signal in nuclear ordered solid 3He. The free induction decay depended on the tipping angles, and was non-exponential in time even at small tipping angles. A t large tipping angles the free induction signal decayed very rapidly. There has not been any discussion about the relaxation processes in the nuclear ordered phase. It m a y be necessary to include the relaxation effects in the OCF equations. The uniform mode o f the observed NMR signal m a y not be stable against large spin tipping * 1. The existence of the small magnetic domains in nuclear ordered solid m a y play an important role in the decay o f the free induction signal. ,1 This kind of instability in the superfluid aHe-A phase was discussed by Fomin [ 10] and in nuclear ordered solid aHe independently by Ohml et al. [ 11 ] in connection with this experiment.
23 January 1984
We would like to thank T. Tsuneto, Y. Nagaoka, T. Ohmi, H. Jichu and M. Tsubota for many stimulating discussions.
References [1 ] E.D. Adams, E.A. Schubert, G.E. Haas and D.M. Bakalyar, Phys. Rev. Lett. 44 (1980) 789. [2] D.D. Osheroff, M.C. Cross and D.S. Fisher, Phys. Rev. Lett. 44 (1980) 792. [3] Chia-Ren Hu and T.E. Ham, Phys. Rev. B24 (1981) 2478. [4] H. Namalzawa, Prog. Theor. Phys. 67 (1982) 1989. [5] O.V. Lounasmaa, Experimental principles and methods below 1 K (Academic Press, London, 1974) eh. 4. [6] E.R. Grilly, J. Low Temp. Phys. 4 (1971) 615. [7] J.C. Wheatley, Rev. Mod. Phys. 47 (1975) 415. [8] T.C. Prewitt and J.M. Goodkind, Phys. Rev. Lett. 39 (1977) 1283. [9] T. Hata, S. Yamasaki, S. Taneda, M. Kodama and T. Shigi, J. Magn. Magn. Mater. 31-34 (1983) 737. [10] I.A. Fomin, JETP Lett. 30 (1979) 164. [11] T. Ohm1, M. Tsubota and T. Tsuneto, private communication.
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