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Non-linear effects from the dipolar demagnetising field in 3He at very high magnetic field
Physica B 284}288 (2000) 190}191
Non-linear e!ects from the dipolar demagnetising "eld in He at very high magnetic "eld J.R. Owers-Bradley *, O. Buu , C.J. Mc Gloin , R.M. Bowley , R. KoK nig University of Nottingham, School of Physics and Astronomy, Nottingham NG7 2RD, UK Physikalisches Institut, Universita( t Bayreuth, D 95440 Bayreuth, Germany
Abstract We present NMR measurements in He at 150 mK in a high magnetic "eld leading to non-linear e!ects caused by the dipolar demagnetisation "eld. We report the "rst observation of long-lived free induction decays and provide a theoretical interpretation. 2000 Elsevier Science B.V. All rights reserved. Keywords: Demagnetising "eld; He normal liquid; NMR; Spin dynamics
1. Introduction We present NMR experiments performed in non-degenerate liquid He at high magnetic "eld. Using pulsed NMR methods, we have produced multiple spin echoes and long-lived signals which are signatures of non-linearities present in the spin dynamics. At low temperature, they originate in the Leggett}Rice e!ect [1] which is a consequence of quantum exchange within degenerate Fermi systems. In our experiments, performed at 150 mK, the dominant source of non-linearities is the dipolar demagnetising "eld. The strength of the non-linear term in the equation of spin motion is given by the parameter b"ckM / (DcG) (k being the vacuum permeability, c the gyromagnetic ratio of He, D the spin di!usion coe$cient, G the longitudinal "eld gradient across the sample, and M the equilibrium magnetisation per unit of vol ume) [2]. Einzel et al. [2] have observed multiple spinechoes with low-"eld experiments (below 80 mT, corresponding to b+0.1). In our experiments, performed at high "eld, the dipolar "eld is much stronger (b+10), resulting in the appearance of new phenomena. In par-
* Corresponding author. E-mail address: [email protected] (J.R. Owers-Bradley) Work supported by EPSRC.
ticular, we observe a long-lived free induction decay which is reminiscent of homogeneous precessing domains observed in the Leggett}Rice region [3]. The experiments were performed in pure He at 150 mK at s.v.p. with a 10 T "eld (corresponding to a Larmor frequency of 340 MHz). The sample was contained in a cylindrical epoxy cell of 2.3 mm height and 2.3 mm inner diameter oriented along the applied magnetic "eld.
2. Results and discussion In Fig. 1 we present a series of signals exhibiting multiple echoes. Each signal was recorded during a 9038 ms-903 pulse sequence in the presence of a longitudinal linear "eld gradient G"26 mT/m. For each trace the initial polarization * hence, the parameter b * has been varied by changing the delay time after a 903 saturation pulse. This shows clearly the e!ect of the dipolar "eld: the number of echoes and their amplitude increase with increasing initial magnetisation. Independent spin-echo di!usion measurements indicate that we are out of the Leggett}Rice region: the echo height has a classical q dependence on the pulse separation time q and does not vary with the initial tipping angle. Next, we present the signal following a single tipping pulse (Fig. 2). During these experiments, the polarization "eld was shimmed to achieve the best possible homogeneity. The free induction decay consists of two parts: one
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 3 5 4 - 6
J.R. Owers-Bradley et al. / Physica B 284}288 (2000) 190}191
191
Fig. 1. Multiple echoes recorded after a 903-8 ms-903 pulse sequence in presence of a longitudinal linear "eld gradient of 2.6 G/cm. Each trace corresponds to a di!erent initial polarization (giving a di!erent value of b).
Fig. 2. The free induction decay after a single NMR pulse consists in a short relaxation followed by a long-lived signal. The lifetime of the long ringing down signal strongly depends on the tipping angle h.
with a short time constant, that we ascribe to the usual decoherence of the spins precession due to residual "eld inhomogeneities (the decay time of +3 ms is consistent with the magnet speci"cation). The second part has a much longer time constant (up to 500 ms); it vanishes for large tipping angles. Similar signals have been observed in helium mixtures at high temperature polarised by optical pumping [4]. We interpret this long-lived signal as a coherent precession of the magnetisation throughout the sample; the same phenomenon is known to occur in highly degenerate Fermi systems due to the Leggett}Rice e!ect [3]. Theoretical and numerical investigations of this problem by Jeener [5] showed two main features: (i) due to the dipolar "eld, the NMR line undergoes &spectral clustering'; (ii) non-linearities give rise to an instability at
large tipping angle. Our data agree qualitatively with these conclusions. We are currently performing numerical simulations for our particular geometry to achieve a quantitative agreement with our results.
References [1] A.J. Leggett, J. Phys. C 3 (1970) 448. [2] D. Einzel, G. Eska, Y. Hirayoshi, T. Kopp, R. WoK l#e, Phys. Rev. Lett. 53 (1984) 2312. [3] G. Nunes, C. Jin, A.M. Putnam, D.M. Lee, Phys. Rev. Lett. 65 (1990) 2149. [4] D. Candela, M.E. Hayden, P.J. Nacher, Phys. Rev. Lett. 73 (1994) 2587. [5] J. Jeener, Phys. Rev. Lett. 82 (1999) 1772.
Non-linear e!ects from the dipolar demagnetising "eld in He at very high magnetic "eld J.R. Owers-Bradley *, O. Buu , C.J. Mc Gloin , R.M. Bowley , R. KoK nig University of Nottingham, School of Physics and Astronomy, Nottingham NG7 2RD, UK Physikalisches Institut, Universita( t Bayreuth, D 95440 Bayreuth, Germany
Abstract We present NMR measurements in He at 150 mK in a high magnetic "eld leading to non-linear e!ects caused by the dipolar demagnetisation "eld. We report the "rst observation of long-lived free induction decays and provide a theoretical interpretation. 2000 Elsevier Science B.V. All rights reserved. Keywords: Demagnetising "eld; He normal liquid; NMR; Spin dynamics
1. Introduction We present NMR experiments performed in non-degenerate liquid He at high magnetic "eld. Using pulsed NMR methods, we have produced multiple spin echoes and long-lived signals which are signatures of non-linearities present in the spin dynamics. At low temperature, they originate in the Leggett}Rice e!ect [1] which is a consequence of quantum exchange within degenerate Fermi systems. In our experiments, performed at 150 mK, the dominant source of non-linearities is the dipolar demagnetising "eld. The strength of the non-linear term in the equation of spin motion is given by the parameter b"ckM / (DcG) (k being the vacuum permeability, c the gyromagnetic ratio of He, D the spin di!usion coe$cient, G the longitudinal "eld gradient across the sample, and M the equilibrium magnetisation per unit of vol ume) [2]. Einzel et al. [2] have observed multiple spinechoes with low-"eld experiments (below 80 mT, corresponding to b+0.1). In our experiments, performed at high "eld, the dipolar "eld is much stronger (b+10), resulting in the appearance of new phenomena. In par-
* Corresponding author. E-mail address: [email protected] (J.R. Owers-Bradley) Work supported by EPSRC.
ticular, we observe a long-lived free induction decay which is reminiscent of homogeneous precessing domains observed in the Leggett}Rice region [3]. The experiments were performed in pure He at 150 mK at s.v.p. with a 10 T "eld (corresponding to a Larmor frequency of 340 MHz). The sample was contained in a cylindrical epoxy cell of 2.3 mm height and 2.3 mm inner diameter oriented along the applied magnetic "eld.
2. Results and discussion In Fig. 1 we present a series of signals exhibiting multiple echoes. Each signal was recorded during a 9038 ms-903 pulse sequence in the presence of a longitudinal linear "eld gradient G"26 mT/m. For each trace the initial polarization * hence, the parameter b * has been varied by changing the delay time after a 903 saturation pulse. This shows clearly the e!ect of the dipolar "eld: the number of echoes and their amplitude increase with increasing initial magnetisation. Independent spin-echo di!usion measurements indicate that we are out of the Leggett}Rice region: the echo height has a classical q dependence on the pulse separation time q and does not vary with the initial tipping angle. Next, we present the signal following a single tipping pulse (Fig. 2). During these experiments, the polarization "eld was shimmed to achieve the best possible homogeneity. The free induction decay consists of two parts: one
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 2 3 5 4 - 6
J.R. Owers-Bradley et al. / Physica B 284}288 (2000) 190}191
191
Fig. 1. Multiple echoes recorded after a 903-8 ms-903 pulse sequence in presence of a longitudinal linear "eld gradient of 2.6 G/cm. Each trace corresponds to a di!erent initial polarization (giving a di!erent value of b).
Fig. 2. The free induction decay after a single NMR pulse consists in a short relaxation followed by a long-lived signal. The lifetime of the long ringing down signal strongly depends on the tipping angle h.
with a short time constant, that we ascribe to the usual decoherence of the spins precession due to residual "eld inhomogeneities (the decay time of +3 ms is consistent with the magnet speci"cation). The second part has a much longer time constant (up to 500 ms); it vanishes for large tipping angles. Similar signals have been observed in helium mixtures at high temperature polarised by optical pumping [4]. We interpret this long-lived signal as a coherent precession of the magnetisation throughout the sample; the same phenomenon is known to occur in highly degenerate Fermi systems due to the Leggett}Rice e!ect [3]. Theoretical and numerical investigations of this problem by Jeener [5] showed two main features: (i) due to the dipolar "eld, the NMR line undergoes &spectral clustering'; (ii) non-linearities give rise to an instability at
large tipping angle. Our data agree qualitatively with these conclusions. We are currently performing numerical simulations for our particular geometry to achieve a quantitative agreement with our results.
References [1] A.J. Leggett, J. Phys. C 3 (1970) 448. [2] D. Einzel, G. Eska, Y. Hirayoshi, T. Kopp, R. WoK l#e, Phys. Rev. Lett. 53 (1984) 2312. [3] G. Nunes, C. Jin, A.M. Putnam, D.M. Lee, Phys. Rev. Lett. 65 (1990) 2149. [4] D. Candela, M.E. Hayden, P.J. Nacher, Phys. Rev. Lett. 73 (1994) 2587. [5] J. Jeener, Phys. Rev. Lett. 82 (1999) 1772.