FREQUENCY SHIFT OF MICROWAVES ASSOCIATED WITH THE MAGNETOSONIC-ELECTRIC EFFECT IN BISMUTH

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Submitted on 1 Jan 1978

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FREQUENCY SHIFT OF MICROWAVES ASSOCIATED WITH THE

MAGNETOSONIC-ELECTRIC EFFECT IN BISMUTH

T. Morimoto

To cite this version:

T. Morimoto. FREQUENCY SHIFT OF MICROWAVES ASSOCIATED WITH THE

MAGNETOSONIC-ELECTRIC EFFECT IN BISMUTH. Journal de Physique Colloques, 1978, 39

(C6), pp.C6-1119-C6-1120. �10.1051/jphyscol:19786496�. �jpa-00217979�

JOURNAL DE PHYSIQUE Colfoque C6, suppl&ment au no 8, Tome 39, aoct 19'78, page ~ 6 - 1 1 1 9

FREQUENCY S H I F T OF MICROWAVES ASSOCIATED WITH THE MAGNETOSONIC-ELECTRIC EFFECT I N BISMUTH

T. Morimoto

I n s t i t u t e of Atomic Ene~gy, Kyoto University, Kyoto, Japan

~Gsum6.- En accord avec 11interpr6tation du mdcanisme qui engendre des micro-ondes induites par tension continue, on montre la possibilit6 d'une diffusion Brillouin accompagnge d'un dgphasage en frdquence des micro-ondes dans un plasma compens6 de bismuth sous champ magngtique Elevb.

Abstract.- The possibility of a Brillouin scattering accompanied with frequency shift of microwa- ves in a compensated plasma of bismuth under high magnetic fields has been pointed out, in connec- tion with the interpretation of mechanism for generation of microwave-induced dc voltage.

In bismuth crystals athigh magnetic fields at low temperatures, incident microwave can propaga- te as the magnetosonic wave having very short wave- length (see for example, ref. /I/,it is often called as the fast mode of the Alfven wave /2/) when

3,

+ +

where k is the wave vector of microwave and H the magnetic field applied in parallel with the sample surface. Since the magnetosonic wave can be recogni zed as the density wave of electrons and holes, there must be possibility of observing a frequency shift of the incident microwave associated with excitation of longitudinal sound wave. This might be closely re- lated with the origin of the magnetosonic-electric effect observed by Morimoto and Yamamoto / 3 / and independently by Khaikin and Yakubovskii / 4 / , i.e., generation of an oscillatory dc voltage, as shown

+ +

in figure 1 , to the k X H direction when the magneto- - -.

sonic wave is propagating is bismuth crystals.

Fig. 1 : Microwave-induced dc voltage vs magnetic field. h1 and h2 marked by arrows indicate the 1st and 2nd harmonics in the Azbell-Kaner cyclotron resonance due to holes."The sample thickness is 2.10 mm.

voltage, vhich has the same period as that of the geometri'cal resonance of tIie magnetosonic Faye, ta- kes qui'te opposi'te si'gn to that of t& background voltage at lower magnetic fields (H .c. 3 kG), which is supposed to come from the t&ermomagnetic effect, Hence, the sign of the oscillatory dc yoltage i's unlikely expected from the direct drag of electrons and holes by the incident electromagneti'c wave, since the sign of the si'gnal due to the direct drag must be the same as that of the thermomagnetic ef- fect. However, if we assume the excitati'on and the following amplifi'cation of sound wave by. the propa- gating magnetosonic wave, that is equivalent to assume generation of ultrasoni'c wave having negati- ve absorption coefficient and t6e same 'f It as- the magnetosoniewave (see, figure 2), we can underst- and the sign of the microwave-induced dc voltage at high magnetic fields from the sign reversal of the acousto-magneto-electric effect (A M E) due to the

Wnetoscnic wove

v

vs- uJ!msonlc wove

Fig. 2 : Indirect interaction of the magnetosonic wave with particles accompanied with the ultrasonic- wave amplification. As a result the particle has a negative, averaged momentum <Px>, which leads to the sign reversal of the microwave-induced dc vol- tage at high magnetic fields corresponding to the As seen from figure I, the oscillatory dc negative absorption coefficient of the ultrasonic

wave.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786496

ultrasonic wave having negative absorption coeffi- cient (see, reference /5/).

Now, the wavelength A of the magnetosonic wave of frequency f is given by

where no = n = nh is the concentration of electrons and holes atethermal equilibrium, m: and

<

effective masses of electrons and holes, respectively.

According to Yokota and Kobayashi /6/, we assume the interaction of the magnetosonic wave with the longi- tudinal lattice wave through the deformation-poten- tial coupling. The dispersion relation of the cou- pled mode is as follows;

where VA is the Alfven velocity given by H/

J4?rf;r;

(m: + $), vs the sound velocity, p the density,

E* the effective deformation potential constant, w the angular frequency of the wave. Here, (w/k)+

corresponds to the solution fo the Alfven mode, snd (w/k)- to that of the sound-wave mode. This might suggest the possibility of the excitation of longitudinal ultrasonic wave through the deformation- potential coupling, although the coupling is weak.

Therefore, denoting the frequency of the longitudinal sound wave by vs and taking into ac- count the energy and momentum conservation law, we can find the following frequency shift, Af, of the incident microwave ;

This is none other than a Brillouin scattering of microwaves in a compensated plasma under high magne- tic fields.

? / 2

The experimental value of

F

mhTJ

of bismuth for the configuration of k

B

+ -5

axis and H / / bisectrix axis is 1.37 X 10 /3/, so that the value of A for a 24 GHz microwave becomes 8.59 ^X 1 0 - ~ H (gauss) cm. Using this and the appro- priate value of the longitudinal sound velocity 2.6 X 105 cm/s., we can estimate the value of the frequency shift, Af, for a 24 GHz-microwave to be 23.5 MHz at magnetic field of 10 kG. Although, nowa- days, some difficulties are expected for the measu- rement of the frequency shift, this experiment would

offer useful informations on the elementary excita- tions in solids as in the Brillouin scattering ex- periment of light.

The author is indebted to Prof. I. Yokota and Dr. M. Chiba for the valuable discussions.

References

/l/ Spitzer, L., Physics of Fully Ionized Gases (Willey, New York, 1962) Chap. 3.3

/2/ Buchsbaum, S.J., in Plasma Effects in Solids edited by Bok (Dunod, Paris) 1965, p. 3 /3/ Morimoto, T., and Yamamoto, M., 3. Phys. Soc.

Japan, (1971) 1671

/ 4 / Khaikin, M.S. and Yakubovskii, A. Yu., Soviet

Phys. JETP

33

/ 5 / Wang, W.C., Phys. Rev. Letters

2

Japan

2