MAGNETOMETER FOR STUDYING THE MAGNETIC PROPERTIES OF WHISKERS

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Submitted on 1 Jan 1978

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MAGNETOMETER FOR STUDYING THE

MAGNETIC PROPERTIES OF WHISKERS

V. Pudalov, S. Semenchinsky

To cite this version:

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JOURNAL DE PHYSIQUE Coilope C6, suppliment au no 8, Tome 39, aolit 1978, page C6-1199

MAGNETOMETER FOR STUDYING THE MAGNETIC PROPERTIES OF WHISKERS

V.M.Pudalov and S.G.Semenchinsky

AZZ-Union Scientific-Research Institute of MetroZogicaZ Sewice, Gosstandart of the USSR, 9, Leninsky prospect, Moscow, 11 7049, U. S.S.R.

R6sum6.- On dLcrit une m6thode d'investigations des oscillations quantiques de moment magn6tique dans les "whiskers". Cette m6thode se distingue du magnetomstre de torsion habituel, car la torsion est d6tect6e par la mesure de l'angle de courbure du "whisker" lui-msme.

Abstract.- The method for investigations of magnetic moment quantum oscillations in whiskers is described. Unlike usual torque magnetometers the torque acting on the sample is measured by detec- ting the angle of bending of the sample itself.

In the experimental studies of electronic properties of metallic whiskers only d . ~ . conductivity measurements were available until now. Other proper-

ties (in particular thermo-dynamic ones) are difficult to be measured because of small dimensions of the samples. The typical dimensions of Zn or Sb whiskers are IxlOxlOO p/I/, hence the magnetic mo ment of the samples is about M - 10-l1 CGS in magnetic fields H

-lo3

Oe. This value is much less than the resolution of usual torque magnetometers /2/, Faraday's magnetometers, inductive bridges and others.

Here, the magnetometer is described, where bending of the sample caused by magnetic moment, is being measured.

1.PRINCIPLE.- The sample (whisker) is placed in a magnetic field H, the angle between the field di- rection and the whisker being 0 <$<90° (figure 1).

One end of the sample is fixed. The magnetic moment M, induced in the sample by a field H, is directed along the sample. As a result a torque is applied to the sample

,

L = d(M:H)/dH, which tends to bend it. According to the elasticity theory a mean angle of thesample bending

where d is the thickness, b- the width, 1- the length of the sample, E

-

Young's modulus, y

-

the factor,of order 1. The angle a can be measured directly and according to (1) the changes in a represent changes in the torque L, and hence in the moment M. It is seen also from (I) that

a,

being measured, increases with reducing of the sample tickness.

4

3) 6,

Fig.] (a) : Low temperature part of the optical system : 1

-

whisker, 2- quartz plate, 3-metallic base, '4

-

mirror ;

(b)

lock-dyiagram

of apparatus.

A moment Lst, of electrostatic compensating changes in the torque L, may be applied to the sample. The changes in the torque L in that case may be calculated as changes in Lst, if the geometry is known.

2.BLOCK DIAGRAM.- Of the experimental system is shown in figure l(b). The whisker 1 (rectangular cross section) is attached to the plate 2 of fused quartz with a conducting epoxy. The plate 2 is mounted on the metallic base 3 so that the sample makes an angle 45' with the vertical. A gap between the sample and thebase 3 is-0.5 mm. The plane of the sample is perpendicular to the mirror plane 4.

A laser beam is reflected by the sample, mirror and through the diaphragm 6 i-eaches a photo- multiplier (P.M.). The deflection of an output beam

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changes the illumination of the diaphragm, which is detected by the P.M. An output signal of the P.M. is first amplified and then fed to a multichan- nel analyzer (M.C.A.). By averaging of the results

df a number of measurements M.C.A. improves a signal to noise ratio. Addresses of channels corres- ponds to a current, supplying a superconducting so- lenoid.

A negative feedback is achieved by applying a voltage U = 0 + I00 V from the high voltage output of a DC-amplifier between the sample and the base 3. Because the angle a does not practically change the torque L and the compensating moment Lst = 11 IJ2 are connected with an equation L + L

St

= Const, where

n

is a geometric factor. The cons- tant in the right part of the last equation is determined from the condition L = 0 at H = 0.

Approximating the sample by a rod over an infinite $lane rl = 12/8h (lr1(2h/a))~, where h is the distan- ce between the sample and the base 3, and a

-

a certain mean transverse dimension. An output voltage of the DC-amplifier is capable to compensate the torque L up to dyn.cm for the sample with dimensions 0.5~10~500 l~

.

The dynamic range of the system described is equal to 80 dB.

3.THICKNESS MEASUREMENTS.- The magnetometer design makes it possible to determine the thickness of the sample by measuring resonant frequencies of its vibrations. For a case of small vibrations of a sample with b,d <<I

where p is the density and k = 3.56 for the lowest resonant frequency. The density and Young's modulus are knwon values, the lenght 1 can be measured with a microscope. Sample vibrations may be excited by electrostatic forces. The accuracy of the deter- mination d is not better than

-

20%

,

as the length of a free part of the sample is difficult to measu- re with an accuracy better than f 10%.

4.AN EXAMPLE OF AN EXPERIMENTAL RECORD.- Of de Haas-van Alphen oscillations in Bi whisker at 4.2 K is shown in figure 2. The record is obtained by sum- ming of 1

d

series scannings. The sample dimensions

are d = 1 , 1 = 600 p. The oscillations are due to electron parts of the Fermi surface, P(H,C,)

=

60'. The amplitude of the angle of bending for ?he oscillations shwon is a

-

rad, variations in the moment M

-lo-".

aig. 2 : Quantum oscillations of d(~-~)/d@ in Bi sample (lxlOx600p).

References