INDIRECT MEASUREMENTS OF THE IMPURITY ELECTRON SPIN RELAXATION TIME BY NUCLEAR SPIN LATTICE RELAXATION IN CdMn ALLOYS

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INDIRECT MEASUREMENTS OF THE IMPURITY ELECTRON SPIN RELAXATION TIME BY

NUCLEAR SPIN LATTICE RELAXATION IN CdMn ALLOYS

P. Bernier, H. Launois, H. Alloul

To cite this version:

P. Bernier, H. Launois, H. Alloul. INDIRECT MEASUREMENTS OF THE IMPURITY ELECTRON SPIN RELAXATION TIME BY NUCLEAR SPIN LATTICE RELAXATION IN CdMn ALLOYS.

Journal de Physique Colloques, 1971, 32 (C1), pp.C1-513-C1-515. �10.1051/jphyscol:19711171�. �jpa-

00213993�

JOURNAL DE PHYSIQUE Coltoque C I , supplt!ment au no 2-3, Tome 32, Fkurier-Mars 1971, page C 1 - 513

INDIRECT MEASUREMENTS OF THE IMPURITY ELECTRON SPIN RELAXATION TIME BY NUCLEAR SPIN LATTICE RELAXATION

IN CdMn ALLOYS

P. BERNIER, H. LAUNOIS

Laboratoire de Physique des Solides (*). FacultC des Sciences, 91, Orsay, France and H. ALLOUL (**)

I. S. S. P., University of Tokyo, Tokyo, Japan

R6sum6. - Nous prksentons des mesures du temps de relaxation spin-reseau des spins nuclkaires du Cd dans des alliages de CdMn, pour des champs de 1,4 a 30 kG, et aux tempkratures de l'Hklium liquide. La contribution des impuretb magnktiques est separke en deux parties, d'apr6s sa dkpendance en champ et tempkrature. Notre analyse attribue I'une A une relaxation dipolaire et I'autre a une relaxation scalaire. Un taux de relaxation klectronique d'impuretk d'environ 2 x 1 0 9 s-1 en est dkduit.

Abstract. - Measurements of Cd nuclear spin lattice relaxation time in CdMn alloys are presented in magnetic fields ranging from 1.4 to 30 kG, and at liquid Helium temperatures. The magnetic impurities contribution is separated into two parts from its field and temperature dependences. Our analysis attributes one to a dipolar relaxation, and the other to a scalar relaxation. An impurity electronic relaxation rate of about 2 x 109 s-1 is deduced from both.

In most pure metals, the nuclear spin lattice relaxa- tion is caused by the hyperfine interaction between the nuclei and the conduction electrons. This interac- tion yields the well known Korringa law : a relaxa- tion rate proportional to the temperature and inde- pendent of magnetic field. In this communication, we present an experimental study of the additional nuclear relaxation due to localized electronic spins S in a metal to which paramagnetic impurities have been added. The additional couplings for nuclear relaxa- tion we shall consider in the interpretation of the results are the dipolar and indirect RKKY interactions between nuclei and impurity spins. The former gives rise to a relaxation process well known in insulators.

The latter could introduce two distinct processes : (i) a scalar relaxation (we call it BGS [I]) experi- mentally observed [2] in CuMn at very low fields ; this scalar relaxation involves a real excitation of the impurity ;

(ii) another mechanism (we call it GH [3]) invol- ving a virtual excitation of the impurity which was suggested to explain the high field data on CuMn [4].

The nuclear relaxation studied in this paper is that of Cd113 in CdMn alloys. The impurity contribution can be separated into two parts on the basis of the temperature and field dependences. Our analysis attributes one term to the scalar relaxation and the other to the dipolar relaxation.

The experiments were performed in fields ranging from 1.4 to 30 kG and at liquid Helium temperatures.

This is well above the Kondo temperature, which is lower than 0.1 OK in this system [5], [6]. The bulk samples used by Alloul et al. [6] were filed in an argon atmosphere, and kept in liquid nitrogen. The magnetic impurity concentration of the powders were deter-

(*) Laboratoire associk au C. N. R. S.

(**) Permanent address : Physique des Solides, Facult6 des Sciences, 91-Orsay, France.

mined by susceptibility measurements [7]. The Cd113 TI was deduced from the exponential recovery of the spin echo amplitude after a standard

- ( n n) pulse

2'

2'

sequence.

The difference A(T,)-' between the measured and pure Cd relaxation rates is plotted on figure (1) ver- sus T / H for a sample with 200 ppm of Mn. In the high field range (a) defined by kT < ^p, H, the expe- rimental points fit a unique curve : d(T1)-' is an increasing function of T/H, which seems t o saturate

A ( T , )-I

-

(9)

(5) ^---

$1

C_d

-

200 at ppm

/.'

FIG. 1. - Magnetic impurities cont~ibution to the host nuclear relaxation rate versus T/H. We have separated the figure in two parts ^(a) and (6) from the T and H dependence of the curve.

for kT -

^H. In the low field (or high temperature) range (b), an additional term appears, and distinct isothermal curves occur : A(TJW1 is no longer des- cribed by a T / H function. The low field experimental points (range (b)), are plotted in figure 2 versus H'2 where it is seen that the isotherms are linear functions of In the bottom of this figure, we show the slope of the three different isotherms.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711171

C 1 - ⁵¹⁴ P. BERNIER, H. LAUNOIS AND H. ALLOUL

FIG, 2. -Plot of all the points of range (6) in figure 1 ver- sus

Isothermal curves are linear. In the bottom we have plotted the slope P of each isothermal curve versus T.

The errors are big enough to prevent a clear conclu- sion about its temperature dependence.

Similar results were obtained on a less concentrated alloy [7] (140 ppm).

These data can be discussed in connexion with a global presentation of the effects due to the RKKY interaction [8], giving the following results :

where the subscript K represents the Korringa relaxa- tion, o, the electronic resonance frequency, z the electronic relaxation time of the localized moments, and G(ro) and F(ro) spatial integrals around the impu- rities. The distance r, is defined as follows : all the nuclei separated from the closest impurity by r > ro have a common spin temperature, and are observed in the NMR experiments. The nuclei located closer to an impurity (r < ro) are submitted to high local fields due to RKKY oscillations and do not contribute to the nuclear signal. Furthermore they do not affect the relaxation of the observable nuclei through spin diffusion. This is shown experimentally as the reco- very is exponential in time and no frequency depen- dence characteristic of spin diffusion is observed.

In the following estimates, ro corresponds to a magne- tic wipe out number of about 100, and is assumed temperature and field independent. This is valid when the NMR linewidth is dominated by magnetic effects (high H J O . For low fields a more careful study would be required.

The electronic relaxation rate z-I of magnetic impurities deduced in ESR experiments [9] is the summ of a Korringa term proportional to T, which may be affected by bottleneck effects, and of a tempera- ture independent term, TG1, which is still not unders- tood [9]. For our purposes one also should include

the impurity spin-spin relaxation rate. The tempera- ture dependence of z-' should thus be of the form a T + j3 in expressions (1) and (2). We now discuss each term in more detail.

1. THE BGS TERM. - For low fields expression (1) yields :

Assuming me z % 1, it leads to a T and H dependence of the form (aT + j3) H-2. This is experimentally observed in range (b). We thus conclude that the observed H W 2 term does correspond to the BGS mechanism. For the 200 ppm sample, using a J value of 1 eV, we have estimated the coefficient of 1/H2 z to be 15 x 10-lo (kG)2. Comparison with our data yields z-I - ^{2 x} lo9 s-l. This value must be compa- red with the calculated Korringa value of

As observed in figure 2 the accuracy is not sufficient to establish the temperature variation of z-l.

In the high field range, the BGS term becomes negligible.

2. THE GH TERM. - The field and temperature dependences of relation (2) are given by :

This approaches a maximum value in low fields.

Making a similar estimate as above we find here a rate value of 2 x s-I. This is much too small to correspond to our measurements, in contradic- tion with conclusions of ref. [4].

3. THE DIPOLAR TERM. - AS in insulators, the dipolar relaxation is given by [lo] :

where a,, is the nuclear resonance frequency and H(ro) a spatial summation of r ^-6 around the impurites.

With z of the order of lo-" s, one has o,, z < 1.

With an estimate of H(ro) corresponding to 200 ppm of Mn we find (T,);' - ^{2 x} 10'7. This compared with the saturation value of the term observed in range (a) yields z-I - ^{3 x} lo9 s-l, in good agree- ment with the value deduced from the BGS term.

The field and temperature dependences of the dipolar term need to be calculated in the high field range where a drop of the measured term is observed.

Qualitatively, we expect such a decrease as the impu- rities become saturated.

Within experimental errors, all points fit the same

curve in range (a). This would imply a temperature

independent z value. Is that consistent with the un-

certain temperature variations occurring in range (b) ?

Even if the accuracy could be increased to acertain

the latter, one could explain them by a decrease of

r,, yielding an increase of G(r,). More precise expe-

riments, on systems where the signal to noise ratio is

better, are needed to clarify that point.

INDIRECT MEASUREMENTS OF THE IMPURITY ELECTRON SPIN RELAXATION C 1 - ⁵¹⁵

Our experiments show the possibility of measuring of the electronic relaxation time involved in this the electronic relaxation time of impurities by NMR approach.

measurements performed on the matrix nuclei. This

requires a careful analysis of two nuclear relaxation Acknowledgements. - We like t o thank Pr P. Pin- mechanisms. Several problems remain open concer- cus for being at the origin of this work. We also thank ning the radius r, beyond which nuclei participate t o Pr W. G. Clark, Dr B. Giovannini, Dr. P. Monod, relaxation for given H and T, and the exact definition for very helpful theoretical and technical discussions.

References BENOIT (H.), DE GENNRS (P. G.), SILHOUETTE (D.),

C. R. Acad. Sci., 1963, 256, 3841.

LUMPKIN (0. J.), Phys. Rev., 1967, 164, 324.

GIOVANNINI (B.), HEEGER (A. J.), Solid State Comm., 1969, 7, 287.

LEVINE (R.), Phys. Left., 1969, ^{28 A,} 504.

HEDGCOCK (F. T.), RIZZUTO (C.), Phys. Rev., 1967, 163, 517.

ALLOUL (H.), DELTOUR (R.), CLAD (R.) (to be publi- shed).

171 BERNIER (P.), Thesis, May 1970, Orsay.

[81 GIOVANNINI (B.), PINCUS (P.), GLADSTONE (G.), HEEGER (to be published).

[9] SCHULTZ (S.), SCHANABARGER (M. R.), PLATZMANN (P.), Phys. Rev. Lett., 1967, 19, 749.

MONOD (I?.), SCHULTZ (S.), Phys. Rev., 1968, 173, 645.

[lo] ABRAGAM (A.), The principles of nuclear magnetism,

1961.