NMR relaxation times measurements of protons in superconducting powders

Solid State Communications, Vol. 7, pp. 1333—1336, 1969.

Pergamon Press.

Printed in Great Britain

NMR RELAXATION TIMES MEASUREMENTS OF PROTONS IN SUPERCONDUCTING POWDERS E. Ehrenfreund, LB. Goldberg and M. Weger Physics Department, The Hebrew University, Jerusalem, Israel (Received 22 July 1969 by P.G. de Gennes)

T1 measurements in a superconducting hydrated V—Ti ahoy indicate that the main contribution to the proton relaxation rate comes from a ‘purely’ magnetic process. A probable source for this process is a thermal fluctuation of the fluxoids or, less plausible, magnetic impurities.

THE NUCLEAR spin—lattice relaxation time T1 of metallic nuclei in the superconducting state has been investigated intensively. At low temperatures (T << To), and low magnetic fields (H <
consider the fluctuations of a section of a fluxoid of length L2 tied between pinning centers, and neglect the interactions between the fluxoids. Let 6~h~(t) be the transverse fluctuating field. Then 1/T,2~2y,~2f<8h~(O)3h~(t)> eiWnt di ~ 2y

n

2.<~/72> 2

f~k2 ei&Jntdl,

(1)

where k is the wavevector of the fluxoid vibration, t~h 2is the magnetic to theis 2,wherefield ç~due = hc/2e fluxoid the flux (~h2 quantumcb0/2~rA and A is the penetration depth), s (t) is the displacement of the fluxoid, and the <> indicates spatial average. It is assumed that there isno correlation between different

thethis relaxation The relaxation rate due to processisisfast. proportional to the magnetic field, and the temperature dependence is weaker than exponential (approximately T, T ~ T a where a is between 2 and 3). At fields approaching: H 02(T), the relaxation rate may be faster or slower than in the normal state, depending on the temperature and purity of the sample; ~ at relatively high temperatures and for pure samples (small values of K, the Landu—Ginzburg parameter) the relaxation rate is faster than in the normal state, while at low temperatures, and for dirty samples, it is slower. Thermal fluctuation of the fluxoid lattice should give rise to fluctuating magnetic fields, which should also contribute to the nuclear relaxation rate. The order of magnitude of this effect can be estimated as follows. Let us -

modes. This expression neglects interactions between the fluxoids, thus it could perhaps apply for fields H < = coswkt exp(— t/rk) where Tk is the lifetime of the excitation k, and tha~theamplitude 2(O)> k 2 =ofk the vibration is given by 2 L2 mAle T
Gk/w~

1334

NMR RELAXATION TIMES MEASUREMENTS

2kBT/77A2 mA/C, and assuming 2 mA/C.7 For a non-resonant (7i/4m*)k

where G =2yfl

w

=

process, let us assume ~

wk> ~

1.1

5> w,~,then

(1/w~Tk)dk,

Vol.7, No. 18

Measurements of T 1 were performed on fine powders of V 046Ti031H023. The relaxation 5’ times of protons and V were measured as functions temperature andstate. magnetic in the mixed, ofsuperconducting The field, observed

m in

where kmjn is the smallest wavenumber possible, and may be determined by the distance between defects pinning the fluxoids, or particles sizes, etc. If the excitations are helicon-like modes with w = w 2 k2 then, by assuming Tk to be slowly 0A varying near k = kmjn, we get: ~‘-~k 1/ T

1 ~ 2G (k/~ Tk)wk

‘fin

For protons dissolved in typical superconducting alloys at 4°K either of the above processes would contribute a relaxation rate of order 0.2 sec’, if we assume: A = 10~cm; 9sec’; = 6 x lO7sec’ k = 77/L 5cm~ mA/C = 2—3; w0 =‘ eH/m*c = 2 x lO ‘fin 2 =estimate 10 = 10’°sec. Obviously, a crude of this sort cannot be expected to provide anything more than an order of magnitude estimate for this relaxation mechanism. The process of relaxation due to thermal fluctuations distinguishes itself by being due to a ‘pure’ magnetic interaction between the fluctuating currents and the nuclear magnetic moment, which is a long-range interaction, while the previously investigated processes are due to interactions of the nuclear moments with fluctuations of the electronic magnetization at the site of the nucleus or very close to it; ‘fr(0)12 for the Korringa and core-polarization mechanisms and <1/r3>, for relaxation by an orbital process. Thus, it should be relatively more effective for nuclei for which li (0) 2 is small, and the wave function is a pure s-state, which does not contribute to orbital relaxation, Therefore, hydrogen nuclei seem to be particularly suited investigate this alloys process. Thetemperarelaxation time of to protons in Ti—H at low tures follows the Korringa law, T, T = const.8 and the extremely long relaxation time (T, T = 150 sec.°K) indicates a very small effective value of kl’(0)12 at the site of the proton.B Thus, protons should be very sensitive to direct magnetic- interactions with fluctuating magnetic fields.

values are shown in Table 1. It is seen that the relaxation rate of the protons in the superconducting state is relatively faster than that of the metallic nuclei, anti the temperature dependence is much weaker (1/T T a Ta where a~0.5 for protons and 1/T, T ~ 1exp(—A/kBT) for metallic nuclei. See Fig. 1). The relative, normalized, relaxation rate z

i/T,(H’, T)/1/T1(H’, 29°K)

=

1/T,(V ~ T)/ 1/T,(V

~.

(2)

20°K)

-

~ 12

10

io

L

0

~J

6

-

~

i.

-

-5..- 0

-J W

2

• 10MHz -

020. £ 30 I

.2

.6

.1.

Tc

~

.8I

-.2 1.0

(‘K)

FIG. 1. The relative relaxation rate z, defined 5’ in (2), and T 1T of V in V0 46Ti0 31H0 23 is plotted as function of 1/T. The large value of z at low temperatures indicates that most of the relaxation of the protons is due to a direct magnetic The 5’ is characteristic of adependence BCS process ofprocess. relaxation in exponential superconductors. of T, T of V is plotted as a function of temperature for several fields in Fig. 1. The previously observed relaxation processes’ 2 should have yielded z = 1. The large value of z at low temperatures (z ~ 5—10) indicates that mostof the relaxation of the protons is due to a direct magnetic process.

Vol.7, No. 18

NMR RELAXATION TIMES MEASUREMENTS

Table 1. T, of the H’ NMR and V5’ NMR in V 0~Ti~31H023 in the superconducting state 51) (°K) (MHz) (sec) T ii 7’1(sec) (H’) T,(V 20 *

20

3.8

4.1

7, 10, 20 30,45,60

3.0 2.0

by the chromium localized moments. An increase of Te, the relaxation time of the impurities, by state is suggested, and the possibility of 2—3 orders of magnitude in the superconducting relaxation via the conduction electrons (some

0.045

sort of RKKY process)’° is invoked.

15 ±2 15±2

0.20 ±0.05

7, 10, 20 30, 45, 60

19 ±2 19 ±2

0.32 ±0.05

7, 10 20 20, 30, 45

32 ±2

1.0 ±0.2 1.0 ±0.2

The situation here is different. By comparing T, ‘s of very different nuclei (V5’ and H’) it is clear that the process here is ‘purely’ magnetic, and not due to contact interaction with conduction electrons as in RKKY and similar type processes. Also, the temperature dependence of T, isetdifferent fromcase, that T observed by Ducastelle al.9 In our 1

60

30±5

1.43 1.3

5, 10, 20 10 20 45 60

1.22

30

42 ±2

60±5 73±5 92±7 90±15

5

increases with decreasing temperature for all temperatures (approximately 3”2), investigated whereas in Ducastelle’s work, T, T, ~ T more or less constant value at very low reaches temperatures. In order to look for impurity effects, T, of protons in titanium hydrides made

±1

100 ±5

5’ relaxation time is field It isfrequency) seen that independent the V (or up to 20 kG, which is the greatest field investigated. The H’ relaxation time shows a slight frequency dependence at low temperatures. Also it is seen that the temperature dependence of the proton relaxation rate is much weaker than that of the V 51 *

1335

of the same titanium material, was investigated thoroughly.8 No deviation from the T 1 T = const. behaviour was observed at low temperatures, although T, there is considerably longer. The mixed titanium—vanadium hydrides possess a larger density of states and thus the formation of localized moments in them is even less likely than in the titanium hydrides. In conclusion, the measurements of T, in V—Ti—H system in the superconducting state

Normal state.

indicate that the proton relaxation mechanism is A relaxation process which is caused by magnetic impurities and limited by spin duffusion, could in principle also enhance the relaxation rate of the protons relative to that of the metallic nuclei. Relaxation in superconductors caused by magnetic impurities was observed by Ducastelle et a19 in vanadium-nitride containing chromium. The T, of V5’ at low temperatures (T << T 0) is shorter than could be accounted for by the BCS and core-relaxation mechanisms, and this shortening is attributed to a relaxation

a ‘pure’ magnetic one, and we believe that it can be attributed to a relaxation by thern~al fluctuation of fluxoids. However, there is no conclusive proof that that is indeed the case and the possibility of relaxation by magnetic impurities still remains. Acknowledgements

—

We would like to thank

P. Pincus, C. Caroli, P.G. de Gennes, D.E. MacLaughlin, D. Rossier, D. Zamir and N. Kaplan for helpful discussions.

REFERENCES 1.

HEBEL L.C. and SLICHTER C.P., Phys. Rev. 113, 1504 (1959).

2.

SILBERNAGEL B.G., WEGER M. and WERNICK J.H., Phys Rev. Leti. 17, 384 (1966); FITE W. II and REDFIELD A.G., Phys. Rev. Leti. 17, 381 (1966).

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NMR RELAXATION TIMES MEASUREMENTS

Vol.7, No. 18

5.

CAROL! C., DE GENNES P.G. and MATRICON J., Phys. Lett. 9, 307 (1964). CYROT M., FROIDEVAUX C. and ROSSIER D., Phys. Rev. Leti. 19, 647 (1967). ROSSIER D. and MACLAUGHLIN D.E., Phys. Rev. Leit. 22, 1300 (1969). OKUBO N. and MASUDA Y., Phys. Rev. Leit. 20, 1475 (1968).

6.

See, for example, ABRAGAM A., Nuclear Magnetism, Ch. VIII, Oxford (1961).

7.

DE GENNES P.G. and MATRICON

8.

EHRENFREUND E., WEGER M., KORN C. and ZAMIR D., J. Chem. Phys. 50, 1907 (1969).

9.

DUCASTELLE F., MACLAUGHLIN D.E. and ROSSIER D., Proc. XVth Colloque Ampere, Grenoble, p.379. (1968). YOSIDA K., Phys. Rev. 106, 893 (1957).

3. 4.

10.

J.,

Rev, mod. Phys. 36, 45 (1964).

Des measures de T, dans un alliage hydrate V—T 1 montrent que la contribution principale a la relaxation des protons provient d’un processus ‘purement’ magnétique. La cause de ceprocessus est probablement la fluctuation thermale des fluxoides, ou, ce gui est moms probable, des impuretés magnétiques.