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Submitted on 1 Jan 1978
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INCREASE OF THE LINEAR
MAGNETORESISTANCE OF INDIUM BY
ARTIFICAL VOIDS
C. Beers, J. van Dongen, H. van Kempen, P. Wyder
To cite this version:
JOURNAL DE PHYSIQUE Colloque C6, supplPment
au
no 8, Tome 39, aolit 1978, page C6-1126INCREASEOF
THE
LINEAR MAGNETORESISTANCE OF INDIUF?
BY
ARTIFICIAL VOIDS
C.J.Beers, J.C.M.van Dongenx, H.van Kempen and P. WyderResearch I n s t i t u t e for Materials, University of Nijmegen, ToernooiueZd,
Nijmegen, The UetherZands
Rdscm6.- L'augmentation de la magnbto-rbsistance de l'indium due 2 des cavitgs artificielles a Qtb dtudibe. La magn6to-rdsistance lindaire se trouve en effet beaucoup accrue par les ca- vitds, en accord avec les calculs theoriques classiques.
Abstract.-The increase of the magnetoresistance of indium as a result of artificial voids has been studied. The voids increase the linear magnetoresistance drastically in accordance with classical theorical calculations.
The linear magnetoresistance (LMR) of simple metals like potassium, aluminium and indium is still one of the unsolved problems of transport properties in metals. The dependence of the observed LMR on sample handling suggests that extrinsic effects like dislocations, stacking faults, inhomogeneities, etc. might play a role. In this paper we describe experiments in which the influence of macroscopic voids on the LMR is compared with theorical predic- tions of Sampsell and Garland /I/, Stroud and Pan /2/ and van Gelder 131.
The calculations of refs./l/,/2/ and /3/ are based on classical arguments and neglect mean free path effects (local approximation). In the high field limit one finds dAp (B)/dB = af/noe where A p (B) = p (B)
-
p(o) (p(B) : resistivity in a magnetic field B) ; no is the volume density ofthe conduction electrons, e the electron charge, f the volume fraction of the voids and a a numeri- cal constant. For spZrerical voids a = 0.49 ; for cylindrical voids perpendicular to,the direction of the current
a.=
1.0 when the cylindrical axis is perpendicular to B] 92 and a = 0 when the axis is parallel1 to.
We have studied the influence of voids experi- mentally by measuring the LMR of indium wires with and without cylindrical voids. The experiments were performed at 4.2 K and 2 K and in fields up to 7 T. We used wires with a diameter of 1 mm of 6 N purity
(residual resistance ration, RRR % ~5000) and 4 N purity (RRR % 2000). Af ter mounting and annealing
Present address: Kamerlingl-Onnes Laboratorium, Nieuwsteeg 18, Leiden, The Netherlands
the transverse magnetoresistance (MR) was measured. Then cylindrical holes perpendicular to theaxis of the wires were punched with a glass punch of O.13mm diameter. The transverse MR was measured both with the holes perpendicular to B antl with the holes pa- rallel to B-. In some cases the longitudinal MR was
measured as well. During all manipulations (annea- ling, punching) the wires were carefully kept in the sample holder with all the leads attached, so any change in the MR can be attributed to the pun- ching of the holes.
Figure 1 shows the strong increase in the LMR
caused by the presence of the holes. Subtracting the resisitivity of the wires without holes from the same wires with holes gives the contribution of the holes to the LMR. As figure 2.shows there is a striking difference between the two direc- tions of the cylindrical axes relat'ive to B. This is in perfect agreement with the theorical expec- tations. One can conclude from this strong direc- tional dependence that indeed the holes are produ- cing the increase in LMR and not crystal defects caused by the punching.
The results for all our samples are summari- zed in Table I. There is good quantitative agree- ment between theory and experiment for the 4 N purity samples. For the 6 N purity samples the agreement is less satisfactory. The experimental values are clearly too high. This might be due to mean free path effects which are neglected in the
-
theory. ( & % 0.2mm, so comparable to the dimen- sions of the voids and to the distance betwenn the voids.)
Fig.1 : Transverse magnetoresistivity P as a func- tion of magnetic field B. +: no voids; A: one cy- lindrical hole12 mm; o : one cylindrical hole/mm.
0 1 2 3 L 5 6 7
B IT) Fig.2 : Contribution of the voids to the transver- se magnetoresistivity. and 0 : axes of the cylin- drical holes perpendicular to B for 6 N ( 0 ) and 4 N (O) purity sample. and : the same samples but now with the axes parallel to B.
For a single void one expects the same i n - fluence on the longitudinal as on the transverse MR.However, our experiments show a much smaller in-
crease in the LMR for the longitudinal case Also the increase is notproportional to the void density (Figure 3). This can be explained by a mutual inter- ference of the distortions of the current lines around the voids.
Part of this work has been supported by the "Stichting voor Wetenschappelijk Onderzoek der Mate- rie" (FOM) with financial support from the "Neder-
derzoek" (ZWO)
.
Table I
The measured slopes dAp/dB for eight samples.
void
RRR3 density (10 dAe(gB h/T) (10 dAe4$B h/T) (xIO ) (number/mm) theory experiment
Fig. 3 : Longitudinal magnetoresistivity p as a function of the magnetic field B. A: no voids; o : one cylindrical hole12 mm; : one cylindrical hole/ mm.
References
/l/ Sampsell, J.B. and Garland, J.C., Phys.Rev. B
2
(1976) 583/ 2 / Stroud,D. and Pan, F.P., Phys.Rev. B
13
(1976) 1434.131 Van Gelder, A.P. to be published.
