3He NUCLEAR MAGNETIC RELAXATION BEHAVIOURS IN HCP SOLID 3He WITH 4He IMPURITIES

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3He NUCLEAR MAGNETIC RELAXATION BEHAVIOURS IN HCP SOLID 3He WITH 4He

IMPURITIES

S. Maegawa, T. Mizusaki, Y. Hirayochi, T. Kusumoto, A. Hirai

To cite this version:

S. Maegawa, T. Mizusaki, Y. Hirayochi, T. Kusumoto, A. Hirai. 3He NUCLEAR MAGNETIC RE-

LAXATION BEHAVIOURS IN HCP SOLID 3He WITH 4He IMPURITIES. Journal de Physique

Colloques, 1978, 39 (C6), pp.C6-115-C6-116. �10.1051/jphyscol:1978652�. �jpa-00218005�

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JOURNAL DE PHYSIQUE Colloque C6, supplkment au no 8, Tome 39, aozit 1978, page C6-11 j

3 4

He NUCLEAR MAGNETIC

RELAXATION

BEHAVIOURS

IN

^{H C P}SOLID ^{3 ~ e}

WITH

He IMPURITIES S. Maegawa, T. Mizusaki, Y. Hirayochi, T. Kusumoto and A. Hirai

Department of physics, Faculty of Science, Kyoto Uniuersity, Kyoto 606, Japan

~Qsum6.- Les temps de relaxation spin-rLseau ont LtL mesures pour 3 ~ e solide h.~. avec des impuretds 4 ~ e . Trois sortes de processus de relaxation ont LtL observLs 1 basse tempdrature et analyses _P llaide d'un modsle 2 quatre reservoirs.

Abstract.- Spin lattice relaxation times have been measured in hcp solid 3 ~ e with 4 ~ e impurities.

Three kinds of relaxation processes were observed at low temperatures, and were analysed by a four bath model.

We measured the nuclear spin lattice relaxation times in hcp solid 3 ~ e with various amount of 4 ~ e impurities. Experiments were made in the temperature range between 0.4 K and 2 K at the NMR fre- quency of 3 MHz. Our data were taken for samples with the molar volume of 19.39 2 0.02 cm3/mole, the

concentration of which, x, ranged between 7 x and 1.47 x

Typical data of the temperature dependence of the observed relaxation times for a sample with x = 4.2 x 10-3 are shown in figure I, where various relaxation timer are defined.

1

-

U )

-loZ

-

⁽^phonon)

I

,

I

e 1 I

2 :

^'_ITI-2 l

9 -

w ⁰

1 l

TI I TII-1

I

* o w ;

_, + +

Fig. 1 : Temperature dependences of the spin lattice relaxation times for a sample of molar volume of 19.39 cm3/mole.with x = 4.2 x

In region I (exchange plateau region), the relaxation times were independent on the temperature and were not influenced by the existence of 'He impurities. In region 11, the magnetization recovery, measured by the two pulse (90"-90°) method, is des- cribed by the sum of two exponential functions ;

In region 111, the relaxation times,

T ~ ~ l - ~ and TIII-2, were measured by the two pulse method and the magnetization recovery for T

111-2 was found to be non-exponential/l,Z/. We obtained T

111-1 and TIII-2 by fitting the.magnetization recovery to the following equation ;

.

^,..

We found that there exists one more relaxation mechanism for the spin system to achieve a complete thermal equilibrium with the lattice. We measured this relaxation time, TIII-? by the multi-pulse saturation method /2,3/. By this method we can also obtain the sum of the energy constants, ks, of all baths that are weakly coupled to the lattice with the relaxation time T

111-3 '

Such relaxation behaviours were investiga- ted for samples with various 4 ~ e concentrations, The values of TI, TII-], TIII-I

,

TIII-2, R, R' and k were temperature independent except for the transient regions. TIII-2 was strongly dependent on the 4 ~ e concentration ;

.c

x - ~

T11~-2 with n = 3 '1. 4

From the fact that there are three k i d s of relaxation times, we assumed a four bath model as shown in the inset of figure I. By this model, th, observed relaxation times, R, R ' and ks may be rg lated to the intrinsic relaxation times and the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1978652

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energy constants as follows.

k.

k./k =

kz+'k+kY

(9)

S

z kz

By using above equations, we can deduce the intrinsic relaxation times, TZX and Tn, and the energy constants, kX/kZ and %/kZ, from our experimental data. The x-dependences of kX/kZ and ky/kZ are formulated in the following :

Eqs.(4),(6) and (8) were confirmed experimentally.

The relaxation times TII-2 and TIII-3 were temperature dependent and were not continuous to each other at the transient region. However, if we compared the intrinsic relaxation times TXL,s, deduced from TII-2 with eq.(5) and from TIII-3 with eq.(7), the- se were connected smoothly to each other. The empi- rical formula for Tn is expressed by

Tn ' I

+

^{1.2 x}

1o6x2*-,

₍₁₂₎

3.5 1 0 4 ~

Now we will compare the above experimental data with the interaction model by Nakajima, Tsune- to and Yamashita /4/. If we regard the X-bath as a sum of the 3 ~ e - 3 ~ e exchange bath and some part of the 4 ~ e - 4 ~ e elastic interaction bath and if we cho- ose 150 MHz for the strenght of the 4 ~ e - 4 ~ e interaction, VOX, the theory explains -both the concentration dependence of kX(cf. eq, (10)) and that of T (cf. eq. (12)) satisfactorily.But this value of

XL

VOX seems too small compared with the value of Vo, estimated from other types of experiments /5,6,7/.

Next we will consider the Y-bath. This may be regarded a8 a main part of the 4 ~ e - 4 ~ e interac- tion bath, since ky a x2 (cf. eq. (11)) and

ky

^is

much larger than

%.

The value of about 1000 MHz for the strength of the 4 ~ e - 4 ~ e interaction, Voy, ex-

plains the value of

%.

This value of Voy is of the reasonable order of magnitude, compared with the value estimated from other types of experiments men- tioned above. The 3 ~ e - 4 ~ e exchange interaction is a mechanism which is responsible for bringing the 'He- 4 ~ e elastic interaction system into a thermal equilibrium within itself. When the 4 ~ e concentration increases and the average value of the 4 ~ e - 4 ~ e interaction becomes much bigger than the 3 ~ e - 4 ~ e exchange interaction, the 4 ~ e - 4 ~ e interaction may not be regarded as a good bath. This fact seems to be closely related with the experimental result that the relaxation behaviour corresponding to TIIIq2 is non-exponential, although a quantitative analysis of this non-exponential recovery is very difficult at present. It is also not clear how to separate the 4 ~ e - 4 ~ e interaction system to the X-bath and the Y-bath.

References

/I/ Giffard,R.P., Truscott, W.S. and Hatton, J., J. Low Temp. Phys.

5

^(1971)153

. / 2 / Bernier,M. and Deville,G., J.LowTemp.Phys.

16 (1974) 349

-

/3/ Garwin,R.L. and Reich,H.A., Phys.Rev.Letters 12 (1 964) ?54

-

/4/ Nakajima,K., Tsuneto,T. and Yamasbita,Y., J.Phys.Soc. Japan

21

(1974) 1241

/5/ Hirayoshi ,Y., Mizusaki ,T., Maegawa, S. and Hirai, A,, J.Low Temp.Phys.

30

(1978) 137

161 Bertman,B., Fairbank,H.A., Guyer,R.A., and White,C.W., Phys.Rev.

142

^(1966)79

171 Bernier,M., the Proc. of the 13th International Conference on Low Temp. Phys. (Colorado)p.79

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