VOLUME DEPENDENCE OF THE FERMI SURFACE OF Pd

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VOLUME DEPENDENCE OF THE FERMI SURFACE

OF Pd

W. Venema, H. Skriver, E. Walker, R. Griessen

To cite this version:

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JOURNAL DE PHYSIQUE Coiloque C6, supplPment au no 8 , Tome 39, aoat 1978, page ~6-1099

VOLUME DEPENDENCE O F

THE

FERMI SURFACE OF P d

W.J. venemax, H. ~kriver+, E. walker0 and R. ~ r i e s s e n ~

X Natuurjundig Laboratoriwn, V r i j e Universiteit, Amsterdam, The Netherlands

+ Research EstabZishment RI@, 2800 Roskilde, Denmark

o Ddparternent de Physique de Za Matisre Condensde, Universitd de GenBve, SvitzerZand

Resume.- L'influence de la dilatation du reseau cristallin sur la surface de Fermi du palladium est

titudiee P l'aide de mesures de l'effet de Haas-van Alphen sous des pressions hydrostatiques allant

jusqu'l 3,7 kbar. Les valeurs experimentales sont en bon accord avec les rdsultats d'un calcul de structure de bandes employant la methode LMTO (linear-muffin-tin orbitals) dans l'approximation de la densit6 locale pour l'interaction d'Cchange et de corrslation.

Abstract.- Volume derivatives of extremal cross sections of the Fermi surface of palladium are determined by means of de Haas-van Alphen measurements under pressures up to 3.7 kbar. The experimental pressure derivatives are found to be in good agreement with theoretical values obrained from a self-consistent band structure calculation based on the linear-muffin-tin orbitals (LMTO) method using the local density approximation for exchange and correlation.

INTRODUCTION.- Recently the first de Haas-van Alphen measurements on the interstitial alloy Pd-H repor- ted by Griessen et al. /l/ were used to determine the changes in area A of extremal cross sections of the Fermi surface hole ellipsoids centered at points

X and L of the Brillouin zone. To interprete the

data /l/ it is necessaty to know the volume derivatives or equivalently the hydrostatic pressure dependence of the cross sectional areas, as the in-

terstitial hydrogen induces a large dilation of palladium host lattice. To our knowledge only the pressure dependence of the T-centered electron sheet of the Pd Fermi surface has been investigated so far /2,3/. The purpose of our investigation is to ma- ke a detailed experimental and theoretical analy- sis of the volume dependence of the Fermi surface of Pd.

EXPERIMENT.- The pressure derivatives dlnA/dp of extremal cross sections of the r-electron sheet

and the X and L hole ellipsoyds were determined by

measuring the corresponding de Eaas-van Alphen fre- quencies at zero pressure and at pressures up to 3.7 kbar. The hydrostatic pressure was applied

using the method of isobaric freezing of helium 141.

The extremal cross sections were measured by means

of a large field modulation method / 5 / . An Ag refe-

rence de Haas-van Alphen signal was used as magne- tic field indicator to get accurate, equidistant

points in reciprocal field 1 6 1 .

Table I. The minus sign for the pressure dependen-

ce of the L-pocket is rather unusual ; to our know-

ledge there is only one other orbit -the810001

1

in

Zirconium / 7 / which exhibits a negative pressure

dependence.

CALCULATION.- The energy bands for Pd at several atomic volumes have been calculated by the linear muffin-tin orbitals (LMTO) method /S/. The pressu- re dependent potential parameters were those of

Andersen et al. /g/ obtained self-consistently

using the local density approximation /10/ for exchange and correlation. The two parameters needed to describe the spin-orbit interaction were obtained from standard muffin-tin potentials at the ap- propriate lattice spacings. The calculation further included the so-called "correction terms" which ta- ke account of the interstitial region and improve the R-convergence. Details of the present version

of the M O technique may be found in other refe-

rences /11,12/.

Before considering the calculated pressure derivatives in table I and their relation to experiment one should note that all the orbits (except the Torbit which as a large extremal area on the scale of a free electron Fermi surface) belong to small pockets of the Fermi surface and that the comparison with experiment is thus a strong test of the accuracy of the energy band calculation. On this background the agreement between calculated

The results of the measurements are given in and measured pressure derivatives shown in table I

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is very satisfactory.

A detailed discussion about the pressure behaviour of the L-pocket is given in /3/.

Table I : Hydrostatic pressure dependence of various orbits of the Pd Fermi surface.

he

coordinates of

the orbit center are given in units of 2r/a. The volume derivatives dlnAldlnQ can be obtained by

dividing dlnA/dp by dlnQ/dp =

-

0.52 X 10-~bar-l/14/.

a) Experimental values of Vuillemin and Bryant /2/

b) Determined by summing the uniaxial stress dependences measured by JOSS and Van der Mark 1151 c) This work References

--

Orbit Center r(0,0,0) X(o,o, 1) X(l ,O,o) L(lsl,l) L(l,l,l)

/l/ Griessen, R., Venema, W.J., Jacobs, J.K., Manchester, F.D., and Ribaupierre, Y.de

J. Phys. (1977) L133

/ 2 / Vuillemin, J.J. and Bryant, H.J., Phys. Rev. Letters

2

(1969) 914

/3/ Das, S.G., Koeling, D.B. and Mueller, F.M., Solid St. Commun.

12

(1973) 89

/4/ Schirber, J.E., Cryogenics

10

(1970) 418

direction 10011 1001

I

lool

l

Ioo1

1 1 1 1 1 1

IllA caculation dp

I

mar-1

I

C 0.42 0.42 0.68

-

3.1

-

IllA experiment dP _!mar-l

_]

/5/ Stark, R.W. and Windmiller, L.R., Cryogenics

8

(1968) 272

/6/ Harmans, C.J.P.M., and Lassche, L., J. Phys. (1977) 155

/7/ Schirber, J.E., Phys. Lett. A33 (1970) 172 a

0.40 i 0.04

/8/ Andersen, O.K., Phys. Rev. (1975) 3060

dHvA Frequency ( ~ ~ a u s s l 273.5 5.69 8.87 2.24 1.88

/g/ Andersen, O.K., Madsen, J., Poulsen, U.K., Jepson, 0. and Kollar, J. Physica 86-88B

(1977) 249

/10/ Barth, U.V. and Hedin, L., J. Phys.

2

(1972) 1629

Area

l

a.ul 0.731 0.0152 0.0237 0.0060 0.0050 b 0.35 f 0.05 1.05

+

0.2 0.7 f 0.8

-

/l]/ Skriver, H.L., Phys. Rev. (1976) 5187

/12/ Skriver, H,L., Phys. Rev.

B15

(1977).1894

/13/ Skriver, H.L., Venemci, B.J., Walker, E. and Griessen, R. to be published

C 0.41 t 0.08 1 .OS f 0.07 0.61 f of07

-

1.7 f 0.2 -3.45 f 1.0

b14/ Walker, E., Ortelli, J. and Peter, M., Phys. Lett.

A31

(1970) 240

-

/IS/ Joss, W. andvan der Mark ,W.

,

Proc. Int. Conf. on Physics of Transition Metals