NUCLEAR RELAXATION IN METALLIC SMALL PARTICLES

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NUCLEAR RELAXATION IN METALLIC SMALL

PARTICLES

S. Kobayashi

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C 2 , supplbment au no 7 , Tome 38, Juillet 1977, page C2-121

NUCLEAR RELAXATION

IN METALLIC SMALL PARTICLES

S. KOBAYASHI

Department of Physics, Faculty of Science University of Tokyo, Bunkyo-ky, Tokyo, Japan

Resume.

-

La relaxation nuclBaire enkR.M.N. de 6 5 C ~ dans de petites particules de Cu, de diamktres 100, 50, 25 et 15

A,

est mesurBe B 1,4 et 0,66 K. On observe que la relaxation dans les particules de 25 et 15

A

est beaucoup plus 1ente.que celle du metal massif. On conclut que cet accroissement de T1 rBsulte de la quantification des niveaux d'energie Blectroniques dans les petites particules.

Abstract. - N.M.R. relaxation of 6 5N.M.R. in small Cu particles 100 ~ ~

A,

50

A,

25

A

and

15 A in diameters, are measured at 1.4 K and 0.66 K. The relaxation in 25

A

and 15

A

particles is found to be much slower than that of bulk metal. It is concluded that this enhancement of T I

is the result of electron energy level quantization in small particles.

1. Introduction.

-

The temperature-independent Pauli spin susceptibility and the Korringa relation betwekn temperature and N.M.R. spin-lattice relaxation, T I - T = const., in metals are based on the fact that the electron energy levels form a conti- nuum. The average spacing of the electron energy levels is of order of E F / N where N is the number of

electrons in the crystal. When the size of crystal is reduced and EF/N becomes comparable to k~ T, one can expect that these bulk rules are invalidated.

The anomalies of spin susceptibility have been confirmed in several metals through measurements of N.M.R. Knight shift which is directly proportional to the spin susceptibility [I, 2, 3,

41.

The transition probability of the nuclear spin relaxation process in metal is proportional to

S(Em - E m '

+

Eks - Ers,), where m denotes the

nuclear spin state and ks, the electron kinetic and spin states. In small particles, E , is not continuous and at low temperature this delta function scarcely has chance to be unity. Therefore, the relaxation time is expected t o be strongly enhanced. When the temperature

-

is high enough, that is, k , T

s

6

where

S is the mean level spacing of the energy levels, large

number of thermally excited electrons contributes to the process and the relaxation will be normal.

However, measurements of T1 performed so far in Al, Sn [5] and Cu [3] have not indicated any pronounced enhancement of Tt. But it was noticed

that T I in A1 and Sn are strongly modified by superconducting fluctuation at low temperature and that Cu particles prepared by gas evaporation are c o n s i d e r a b l y c o n t a m i n a t e d w i t h magnetic oxides [5].

In this report, we present the results of TI in Cu

particles which are not exposed to the air, being free from oxidation. The results are positive to

support simple considerations for the quantized level effects mentioned above.

2. Experimental methods and results.

-

The samples were prepared by evaporating very small amount of Cu in vacuum. This method had been used by W. D. Knight and D. Yee to prepare Cu particles [4]. When the evaporated quantity is small, small islands are formed on a substrate instead of a continuous film and the volume of the islands is smaller for smaller evaporated amount. To obtain a sufficient number of particles and to protect particles from oxidation, SiO and Cu were successively evaporated on Mylar substrate at room temperature. The thickness and the evaporation rates of SiO and Cu (average) were monitored by thickness gauge of quartz oscillator type, which has the resolution of 1.3

A

for Cu. Thickness of SiO was 100

A

for all samples. The volume of Cu islands is determined by electron micrograph of one layer sample, which was prepared in the same condition of the N.M.R. sample, and by the average thickness of Cu. The shape of island is almost spherical except for # 4.

The samples are listed in table I.

-

t_: average thickness,

d : average of electron microscopic diameter,

Ad: distribution half value width of d, 6: average volume,

-

S : average level spacing.

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C2-122 S. KOBAYASHI

After evaporation the film is cut into 1 cm wide ribbon, rolled into a cylinder shape and sealed in a thin glass tube with 20 torr of He gas. The N.M.R. properties were checked not to change after one months storage at room temperature.

N.M.R. were performed by conventional pulse method, and crossed coil and bridge type steady method at 1.4 K and 0.66 K in 3He cryostat, at

9 MHz. 6 5 C ~ was chosen because the resonance of more abundant isotope 6 3 C ~ is too close to that of 23Na which exists in glass tube

and

3He dewar. Relaxations were measured by detecting the spin echo height after complete saturation by a long pulse train.

Sample # 1 : The N.M.R. relaxation at 0.66 K is

shown in figure 1. It is not single exponential and surprisingly slow as compared with that of bulk. The relaxation at 1.4 K is nearly exponential, having the time constant of 8.6 r 0.3 s. The bulk TI at this temperature is 0.8 s. The steady state N.M.R. could not be observed. The echo height distributes over more than 100 gauss and it is difficult to determine the peak position of the resonance within the error of 10 gauss because of poor signals.

FIG. 1.

-

N.M.R. relaxation in # 1 at 0.66 K. ME^ is nuclear magnetization at thermal equilibrium.

Sample # 2 : The relaxation is exponential. TI is

3.2

+

0.2 s at 1.4 K and 13.2 s 2 0.4 s at 0.66 K. The half value width of echo distribution A H is

150 + 20 gauss. On the other hand, the steady state signal gives the peak shift K which is smaller than the bulk Knight shift K b , and K / K b at 1.4 K is

0.5

*

0.3. The peak to peak width of the derivative signal AH,-, at 1.4 K is more than 10 gauss.

Sample # 3 : The relaxation profile at 1.4 K is

given in figure 2. These are again not exponential, having a very rapid initial decrease, being faster than that of bulk in the measured time range. AHis

100 a 15 gauss. The steady state signal at 1.4 K gives the peak with K / K b = 0.6

+

0.2 and AH,-, is

13

+

3 gauss.

FIG. 2.

-

N.M.R. relaxation in # 3 at 1.4 K.

Sample # 4 : The initial rapid decrease exists in

relaxation. It is found that this relaxation curve dependes on the rotating r.f. magnetic field strength HI. The initial drop is larger for smaller HI. The r e s u l t s a t 1 . 4 K f o r H1 = 20 g a u s s a n d HI = 60 gauss are given in figure 3. A H is

130

+

10 gauss for H I = 20 gauss. K/Kb,,lk at 1.4 K is 1 + 0.01 and at 0.66 K is 0.9 0.01 AH,-, is

16 +- 0.3 gauss at 1.4 K and 17

+

0.3 gauss at

0.66 K.

0.5 1.0 s

3. - N.M.R. relaxation in # 4 at 1.4 K. 0 is for

H I = 20 gauss, and is for H I = 60 gauss.

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NUCLEAR RELAXATION IN METALLIC SMALL PARTICLES C2-123

of magnetic field. In # 2 , # 3 and # 4, small peaks on the wide back ground are observed. The width of the peaks AHp-, are larger than bulk resonance width which comes from dipole interaction of spins and has a value of 6.4 gauss. The peak widths are larger for smaller particles, and in # 4 the peak was not detectable. It is natural to consider that these peaks are 1 /2

-

- 1 /2 transitions broadened by second order quadrupole interaction and that the broad back ground is other transitions.

The facts that the r.f. field is smaller than AH, that the relaxations are not exponential in # 3 and # 4, and that the relaxation in # 4 depends on r.f. field strength indicate that the spectral diffusion takes place. In # 2 and # 1 , the quadrupole broadenings are too large to allow rapid spectral

diffusion. As shown in figure 1 the relaxation in # 1 is also nonexponential, however, this is not due to the diffusion but to the distribution of relaxation time from particle to particle.

The quantum level effect in the static susceptibility appeares when k T <

8.

However the effect on N.M.R. relaxation is expected to happen at higher temperatures because even considerable number of excitation is present, it is still hard to conserve the energy in the relaxation process. Unfortunately, in Cu particles, the quadrupole effect mentioned above prevents to obtain the characteristic temperature for the relaxation anomaly which might help quantitative understanding of the phenomenon.

The author expresses his sincere thanks to Pr. W. Sasaki and Pr. Y. Wada for valuable discussions.

References

[I] TAUPIN, C., J. Phys. & Chem. Sol. 28 (1%7) 41. [2] KOBAYASHI, S., TAKAHASHI, T. & SASAKI, W., J. Phys. Soc.

Japan 31 (1971) 1442.

[3] KOBAYASHI, S., TAKABASHI, T. & SASAKI, W., J. Phys. SOC. Japan 32 (1972) 1234.

[4] YEE, P. and KNIGHT, W. D., Phys. Rev. B 11 (1975) 3261.

[5] KOBAYASHI, S., TAKAHASHI, T. and SASAKI, W., J. Phys.