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Submitted on 1 Jan 1978
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MEASUREMENTS OF THE RELAXATION OF THE
LONGITUDINAL MAGNETIZATION IN
SUPERFLUID 3He
R.A Webb
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-31
MEASUREMENTS OF THE RELAXATION OF THE LONGITUDINAL MAGNETIZATION IN SUPERFLUID 3He
R.A Webb
Argonne national Laboratory, Avgonne, Illinois 60439, USA
Résumé.- La technique utilisant un SQUID NMR a été utilisée pour l'étude de la relaxation de l'ai-mantation longitudinale dans l'3He superfluide dans des champs magnétiques de 31, 102, 180, et 306 Oe.
Abstract.- A pulsed SQUID NMR technique has been used for the study of the relaxation of the longi-tudinal magnetization in superfluid 3He in magnetic fields of 31, 102, 180, and 306 Oe.
The phase transition observed in liquid 3He from the normal state to the superfluid state has a profound effect on the relaxation of the longitudi-nal magnetization as measured in pulsed NMR experi-ments /I,2,3/. In particular, for 3He-A, Corruccini and Osheroff /l/ have observed relaxations of the magnetization which are nearly linear in time. Sager et al. Ill have found that very near T , in low magnetic fields, the square of the magnetization
recovers linearly in time as predicted by Leggett and Takagi / 4 / (L-T). In 3He-B, strictly exponential relaxation was observed by Corrucini and Osheroff while near T , Sager et al. observed more
complica-ted non-exponential behavior. In a more recent experiment, /3/,the relaxation phenomena in He has been studied in magnetic fields of 31, 102, 180, and
306 Oe using a pulsed SQUID NMR technique 15/. It is found that the relaxation of the longitudinal magnetization of 3He is very similar in the two phases but the exact nature of the recovery process exhibits a striking dependence on the choice of the initial spin-tipping angle. The adiabatic demagneti-zation cell used for these experiments has been reported elsewhere 15/.
For both 3He-A and 3He-B there is a well de-fined spin-tipping angle, 8 , for which the relaxa-tion process dramatically changes from mainly exponential to non-exponential behavior. Following a rotation of the magnetization by an angle 6, the change in the energy of the spin system is (AE/E )= 2(l-cos 6 ) , where E is the initial energy. Figure 1 shows the temperature and field dependence of 2(l-cos 8 ) for both superfluid phases. The slopes
Based on work performed under the auspices of the U.S. Department of Energy
I ' 1 ' 1 ' 1 ' r n 4.0 - A 3He-A /102 oe 26.1 BAR / 4 * / ^ £ ^ 3 0 6 06 g 0^ f n 1 1 1 1 — ^ 1 1_ ~ 4.0 - , r p . j p
-3.0-
A\nf& ^
-/ -/ »^*306 0e2.0-
/£*/ 2 * °
°0 0.1 0.2 0.3 0.4 (I-T/TC)"2Fig. 1 : Field and temperature dependence of 2 ( 1
-c o s 6c) for which the transition from exponential to
non-exponential relaxation is observed. For 3H e - B ,
D D a n d AA are 21 bar data while 00 and 00 are 23 and 16 bar data respectively. The slopes of the lines drawn through the data are exactly inversely proportional to H .
of the solid lines drawn through the data are exact-ly proportional to the inverse of the static field and in general seem to characterize the overall behavior of the data. Almost no pressure dependence
of 6 w a s observed for either 3He-A or 3He-B has is
c
demonstrated by the 306 O e 3He-B data. A t constant
H , the ratio of the slopes of the lines drawn
through the 3He-A and 3He-B data is (1-cos 0 )f i/
(1-cos 6 ) . » 1.4. These data explain some of the c A
results obtained by Corruccini and Osheroff who in their work used only 90° rotations of the magnetiza-tion. A t melting pressure, for the fields employed in their work, 8 would have been well above 90° in
c
He-B; and exponential relaxation should b e and w a s 4
observed. However, in 3 ~ e - ~ , would have been be- low 90° for fields above 460 Oe in the entire tempe- rature range studied, and strictly non-exponential behavior should be and was observed.
At a constant temperature, the time dependence of the recovery of the magnetization is found to change from exponential behavior, for tipping-angles smaller than €Ic, to nearly linear in time, for tipping-angles slightly greater than €Ic, and then to recoveries that have the square of the magnetiza- tion relaxing linearly in time, for tipping-angles much greater than 8
.
The transition from relaxations that are mainly linear in time to relaxations that are nearly proportional to the square-root of time occurs gradually with increasing tip-angle. For those relaxations that exhibit the theoretical (L-T) square-root time dependence following a 180' pulse, the rate of dissipation of the excess energy in the spin system will be a constant in time and equal to2
/4/ dE/dt = ( - 2 ~ Ho/TF), where TF is the well defined time for full recovery of the magnetization and
x
is the dynamic susceptibility of the liquid 161. A plot of dE/dt as a function of the reduced tempera- ture is shown in figure 2 for all the 180' pulse data obtained in 3 ~ e - ~ and 3 ~ e - ~ that very nearly exhibited the theoretical (L-T).time dependence. In'He-A THEORY
26.1 BAR
Fig. 2 : The temperature dependence of the rate at which the excess energy in the spin system is dis- sipated, following a 180° spin tip, for those rela- xations that very nearly have the theoretically predicted (L-T) time dependence. The solid curves are the theoretically predicted temperature dependences.
with the theoretical predictions, However, in 306Oe, dE/dt was Easter than theoretically predicted while in 31 Oe no (L-T) behavior was ever observed. In 3 ~ e - ~ for I02 and 31 Oe, relaxations that very ne- arly exhibited the theoretically predicted behavior were observed only near Tc. In 18Q Oe, behavior much faster than the existing theory would predict was observed. In 306 Oe, no (L-T) behavior was ever observed. However, in this field, more complicated non-exponential behavior that has tentatively been related with spin-current phenomena was observed /7/.
References
/I/ Corruccini, L.R., and Osheroff, D.D., Phys.Rev. Letters
2
(1975) 564/ 2 / Sager, R.E., Kleinberg, R.L., Warkentin, P.A., and Wheatley, J.C., Phys.Rev.Letters
39
(1977)1343
131 Webb, R.A., to be published in Phys.Rev.Letters 141 Leggett, A.J., and Takagi, S., Ann.Phys. (New
York, in press)
151 Webb, R.A., Rev.Sci.Instr.
