HALL EFFECT IN SILVER - RARE EARTH AMORPHOUS ALLOYS

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HALL EFFECT IN SILVER - RARE EARTH AMORPHOUS ALLOYS

R. Asomoza, J. Bieri, A. Fert, B. Boucher, J. Ousset

To cite this version:

R. Asomoza, J. Bieri, A. Fert, B. Boucher, J. Ousset. HALL EFFECT IN SILVER - RARE EARTH AMORPHOUS ALLOYS. Journal de Physique Colloques, 1980, 41 (C8), pp.C8-467-C8-469.

�10.1051/jphyscol:19808116�. �jpa-00220212�

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JOURNAL DE PHYSIQUE Colloque C8, s u p p l h e n t au n o 8 , Tome 41, aoLit 1980, pageC8-467

H A L L EFFECT I N S I L V E R

-

RARE EARTH AMORPHOUS ALLOYS

x

**

R. ~somoza', J.B. Bieri+, A. ~ e r t ~ , B. Boucher and J.C. Ousset

+

Laboratoire de Physique des SoZides, B2t. 510, UniversitS Paris Sud, 91405 Orsay Cedex France.

*

C. E. N. -Saclay, B i t e PostaZe n o 2 , 91 190 Gif-sup-Yvette, France.

**

Universi td Pax Z Sabatier, 3107 7 Tou louse, France.

INTRODUCTION

The extraordinary Hall effect (EHE) is well documented in crystalline magnetic alloys. In particular the mechanism of the EHE in noble metals containing rare-earth (RE) impurities has been analy- sed in a detailed manner /I/. Less is known about the EHE in amorphous magnetic alloys. With the aim of comparing the mechanisms of the EHE in amorphous and crystalline alloys, we have investigated the Hall effect of silver-rare-earth amorphous alloys.

We present and discuss the results of these inves- tigations in this communication. Data on the EHE in similar amorphous alloys (rare-earth with gold or copper) have been already described by McGuire and Garnbino /2/.

EXPERIMENTAL

We have measured the Hall effect of Ag50R50 amorphous alloys (R = Pr, Nd, Gd, Tb, Dy or Er)pre- pared by sputtering at the CEN-Saclay. The measurements have been done using a dc technique, between 1.2 K and 50 K and in magnetic fields up to 70 kG.

An exemple of experimental results is shown in Figure 1. Similar curves of Hall resistivity versus applied field have been obtained for all the investigated alloys. The ordinary Hall effect is known to be much weaker than the EHE in amorphous magnetic alloys /2//3/. We have neglected it and we have considered that the measurements directly yield the extraordinary Hall resistivity.

The extraordinary Hall resistivity is expected to be proportional to the magnetization of the RE ions. Thus, in order to compare the EHE in alloys more or less difficult to magnetize, we have zal- culated normalized Hall resistivities in the follo- wing way :

Fig. 1 : Extraordinary Hall resistivity versus magnetic field at several temperatures in the AgS0TbSO amorphous alloy. Note the hysteresis curves at low temperatures.

sat

at

100

p H =pH(H) X - X - 41)

lJ (HI

where p (H) is the Hall resistivity in the field H, H

u

(H) is the magnetization in the same field (measured on the same alloys by Boucher and Pappa/4/ ) ,

vsat

is the magnetization at saturation (calculated for trivalent ions) and c is the concentration of rare-earth in at % (c = 50 in the present work).We have also calculated normalized Hall angles :

where p is the zero field resistivity of the sam- ple. The normalized Hall resistivities and Hall angles (calculated from measurements at 40 kG) are listed in Table 1. Not very different values are obtained by using data at other fields. We show in Figure 2 the variation of

$J?

throughout the RE series for the AgS0Rs0 alloys.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808116

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JOURNAL DE PHYSIQUE c8-468

Sat (the change of sign occurs between Ho and Er). Si- R p~ '~(40) IJ (40) H' 'sat milar variations of the EHE in the series are also

(pRcm) (pQcm) (uB/at) (ukm) (uB/at) (a)

observed in Au and AL containing RE impurities/l/

Gd 183 -0.93 6.7 -1.94 7 -1 -06 Tb 240 -0.50 5.0 -1.80 9 -0.75 DY 340 M.31 4.8 1.29 10 +0.38 Er 194 +0.87 4.9 3.20 9 +1.65 Pr 350 +3.18 0.58 35.1 3.2 +10.03 Nd 304 +5.74 0.92 40.8 3.27 +13.42 Table 1 :Resistivity at 1.2 K, Hall resistivity at 4.2 K and 40 kG, magnetization per ion at 4.2 K and 40 k ~normalized Hall resistivity magnetic ~ , moment at saturation, and normalized Hall angles in Ag50R50 amorphous alloys.

0

: Variation of the normalized Hall angle in the RE series. The black circles are experimental points. The dashed line corresponds to the variation calculated by using Eq. (2) with A,= 0.35x10-~, A = -0.30x10-~ for the heavy RE and A'= 1.83xl0-~,

2

-

² ¹

A =

-

1.58~10 for the light RE.

2

DISCUSSION

It appears

-

by comparing the Figure 2 and the Figure 12 of ref.1

-

that the variation of the EHE through the RE series is similar in AgRe amorphous alloys and in ~g containing RE impurities.

The EHE is positive for light RE, negative for Gd and the heavy RE just after Gd and becomes again positive at the end of the series. The tendency for the EHE to become positive'at the end of the series is however more marked in the Ag-Re amorphous alloys (the change of sign occurs between Tb and Dy)

,

than in the &-Re diluted alloys

and in Au-RE and Cu-RE amorphous alloys / 2 / . his strongly suggests that the EHE has the same origin in the dilute alloys and in the amorphous alloys.

For the dilute alloys, Fert and Friederich /1/ have shown that the variation of the EHE in the RE series can be accounted for by the combination of two mechanisms of skew scattering :

a) The skew scattering by the orbital term

%(2-g)

X.J

-+ of the k-f exchange interaction gives rise to an extraordinary Hall resistivity proportional to (2-g) < J Z > .

b) The second mechanism results from the combination of spin scattering by the spin term

+ +

a(g-1) s . J of the k-f exchange and resonant scattering with spin-orbit split 5d levels. This combination can be also described as giving an effective a (g-1)

1.3.

The resulting contribution to the Hall resistivity is proportional to (9-1) < J Z > .

Can the model of the EHE for Ag containing RE impurities be applied to the EHE of Ag-RE amorphous alloys ? It can be pointed out that, while the skew scattering is the predominant mechanism in dilute alloys, the contribution from the mechanism of side- jump /5/ 1s expected to be important when the elec- tron mean free path is short, in particular in amorphous alloys. However side-jump effects should

-+ -+

arise from both the orbital exchange a(2-g) L.J and

-+ +

the effective interaction %(g-1) L.J, so that the Hall resistivity is still expected to include con- tributions proportional to (2-g) < J Z > and

(g-1) <JZ> respectively. If we consider the Hall angle at saturation, we are expecting :

where the coefficients A t and A2 are predicted to be approximately constant, at least if the heavy and the light RE are considered apart (k-f interaction is generally thought to be somewhat larger for the light RE). For the heavy RE the best fit with the experimental results is obtained with :

F~~ the light RE, we have only two experimental results (Pr, Nd) which suggest higher values of A1 and A2 (by about a factor of 5). The fit shown in Figure 2, is not perfect but the model can account

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for the successive changes of sign between the light RE and Gd and then between Tb and Dy. The variation of the EHE in Au-RE and Cu-Re amorphous alloys can be accounted for in a similar way /2/.

Finally we will compare the magnitude of the EHE in the Ag-Re amorphous alloys and in silver containing RE impurities. In silver with RE impurities, the extraordinary Hall resistivity can be fitted, for H/T ⁺0 with

pH = g J(J+I) c ro [a1 (2-9) + ag(4-~)] (3) with a1 = 0.43 x 10-8 K/G,~* =

-

1.57 x

lo-'

K/G.

Here c ro is the residual resistivity. By extra- polating this result to saturation and to c = 100%, we predict;

pSat H = 3k

*

¹⁰⁰ ^rn _[&I_(2-9)₊_a2(g-l)j (4)

i l ~

which would correspond in an amorphous alloy of resistivity po (we will take p = 200 pRcm) to,

The value found in the amorphous Ag-RE alloys is about five times larger than A'. As it is reaso-

1

nable to suppose that the interaction between con- duction electrons and rare-earth ions is not very different in crystalline and amorphous alloys, this enhancement has to be rather ascribed to the addi- tional side-jump effects. On the other hand, it is more difficult to compare A; and A2 as the invol- ved mechanism is more complicated.

To sum up, we have investigated the extraordinary Hall effect of silver-rare earth amorphous alloys and we find that it varies through the RE series approximately as for RE impurities in silver We can ascribe it to orbital exchange and 5d spin- orbit interactions as in silver c6ntaining rare- earth impurities.

REFERENCES

1) A. Fert and A. Friederich Phys. Rev.

z,

397 (1076).

2) T.R. McGuire, R.J. Gambino J. Appl. Phys.

50,

7653 (1979)

.

3) R. Asomoza, I.A. Campbell, A. Fert, A.Li6nard and J.P. Rebouillat

J. Phys.

F ,

349 (1979).

4) B. Boucher

Phys. Stat. Sol. (a)g, 16 (1977).

B. Boucher, J. Phys. Lettres (Dec. 1976).

C. Pappa, ThGse 3&me Cycle, Paris (1979).

5) L. Berger, Phys. Rev.

s,

4559 (1970)