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Observation of transmission of 45 GHz microwaves through a thin Mo-disk with and without the presence of a magnetic field
Volume 54A, number 3
PHYSICS LETTERS
8 September 1975
O B S E R V A T I O N O F T R A N S M I S S I O N O F 45 G H z M I C R O W A V E S THROUGH A THIN Mo-DISK WITH AND WITHOUT THE PRESENCE OF A MAGNETIC FIELD J. LEBECH, M. SURMA* and K. SAERMARK Physics Laboratory I, The Technical University of Denmark, DK-2800 Lyngby, Denmark Received 11 July 1975 Transmission of microwaves of a frequency of 45 GHz through a high-purity, plane-parallel, single-crystalline molybdenum sample of a thickness of 0.15 mm and 0.27 mm, respectively, has been observed, both in the presence of a magnetic field and without a magnetic field. Azbel-Kaner type cyclotron resonance was seen in the signal transmitted through the sample.
In the present communication we wish to report on an observation made in connexion with a microwave transmission experiment, the purpose of which was to detect time-of-flight-effects and propagation of cyclotron waves in Mo. Similar experiments have earlier been carried out for silver [1, 2]. The new features of the present experiments consist in the observation of a pronounced transmission of the 45 GHz microwaves applied to the sample, both for a magnetic field B = 0 and for B :/: 0, and in the observation of Azbel-Kaner type cyclotron resonance (AKCR) in the transmitted signal. The transmission in zero field was observed both at room temperature and at helium-temperatures. The Mo-samples were of a very high purity (RRR = 40 000) and were in the shape of plane-parallel disks with (110)-planes as surfaces, and the surfaces were carefully etched and polished. Two different sample thicknesses, d = 0.15 mm and d = 0.27 mm, respectively, were used in the experiments. The sample was mounted in the transmission set-up as a common end-wall between two T E l l 2 mm-wave cavities as shown in fig. 1. The signal transmitted through the sample was detected as a video signal at the output of the 45 GHz receiver, and the signal level was measured to be 20 to 30 dB above the noise level of the receiver. The transmitted signal decreased with increasing * On leave from The Institute of Physics, A. Minckiewicz University, Poznan, Poland.
/,5 GHz " Generato r
Re~ver
Sflverpaint
Sampte
Fig. 1. The TE112-mode transmission cavities and sample mounting.
sample thickness and turned out to be slightly dependent on the angle between the Erf-field and the crystal. lographic axes, as observed by a rotation of the sample. The essential point to be noted, however, is that the transmitted signal turned out to be proportional to the sample-area exposed to the incoming rf-field. This was demonstrated repeatedly by covering successively more of the sample surface in the output cavity with silver-paint. A "complete" isolation was obtained when all of the sample surface was covered with silver paint. In zero magnetic field the measurements were performed both at 300 K and 4.2 K, the magnitude of the transmittzd signal being nearly the same in the two cases. In the transmitted signal, high-quality Azbel-Kaner cyclotron resonances may be directly observed as 211
Volume 54A, number 3
PtlYSICS LETTERS
<1 Mo-d= 150p. Erf J.(110)' Transmission Exp.
}It 1
B19
t
B11B10B 9 B8 B7
I
i
I
500 b. Mo-d=272P. Erf.L<110) Reflection Exp.
-~
B,o B6BS ~.
a=l
~ ~ * % t 6 L 7L6 t s
B3
1000
BITI.104
B2
B~
L~
q
C1 H6
5
C. No-d= 1501~ Erf [/110)
Reftection
Exp.
I\ ~,AA,,/l~Jl ~(jl Z,/\"~ 2000
/,000
", /I ,~
",
6000 BIT].10/'
Fig. 2. Recorded trace of cyclotron resonance in transmission
experiment a), and in reflection experiments for different thicknesses of the molybdenum sample b) d = 0.27 mm, and c) d = 0.15 mm. shown in fig. 2. This indicates that the transmitted microwave field excites the output cavity and that the magnetic field derivative of the Mo surface impedance is being measured. However, it is essential to note that it is the E-field transmitted through the sample which is active and not a stray leakage field. This was demonstrated by covering the sample surface in the output cavity fully with silver paint and artificially introducing a very weak leakage field between the two cavities, yielding the same signal level at the 212
8 September 1975
microwave receiver as when tile unpainted sample surface was used. In the last type of measurements mentioned no Azbel-Kaner cyclotron resonances were observed at all. In fig. 2 we show recorder tracings of AKCR signals obtained with the microwave Err-field oriented perpendicular to the ( 110)-crystallographic direction in the sample surface. The AKCR signals in the reflection experiments, fig. 2b,c, for both o f the samples (d = 0.15 mm and d = 0.27 lnmL and the AKCR signals in the transmission experiment, fig. 2a, for the thinner ( d = 0.i 5 into) sample are well resolved, however, the best signal/noise ratio is obtained for the transmission experiment, fig. 2a. In reflection experiments with the microwave k'rtfield oriented parallel to a ( I 10)-direction in the sample surface, AKCR signals were undetectable whereas very well resolved AKCR signals were observed in trhnsmission experiments with the same field configuration. We take this, together with the remarks concerning fig. 2a,b,c as in indication that the microwave transmission to some extent depends on the relative orientation of the Err-field and the crystallographic axes. In table 1 we indicate by the + sign the Erf-field orientations for which well resolved AKCR performance has been observed both in transmission and in reflection experiments. The sign indicates the Erf-field orientations for which no AKCR signals were observed in reflection experiments, but where, however, well resolved AKCR signals were observed in transmission experiments. A theoretical explanation of the observed transparency o f the thin Mo-samples presents o f course a new problem. In this connexion we wish to point out, however, that earlier [2, 3] experiments as well as the present ones [4] show that the electrons interact to
Table 1
d (mm) 0.15 0.27
Transmission
Reflection
Erf ±(110)
Erfll(110}
+ +
+ +
+ sign: AKCR observed sign: AKCR not observed.
Erfll (110)
Erf±(l 10)
+ +
Volume 54A, number 3
PHYSICS LETI'ERS
a significant extent with the E-field in the skin layer at the sample surface in the input cavity to a distance of ~ 30/am. It should, further, also be pointed out that in the limit of vanishing DC magnetic field, B ~ 0 , the phase velocity o f cyclotron waves of the extraordinary type, which is the one relevant to the present experiments, approaches the Fermi-velocity as indicated by recent calculations [5]. With the frequency applied here this means a wavelength of the order o f 3 0 - 4 0 / a m , i.e. the same magnitude as quoted above. Tentatively we therefore suggest that an explanation of the observed transparency of our Mo-samples is to be found in a study o f the general behavior of cyclotron waves in the limit mentioned above. We wish to thank Dr. R. Herrman for placing the
8 September 1975
Mo-crystal at our disposal. We are, further, grateful to The Danish-Polish Exchange Program and to Statens Naturvidenskabelige Forskningsr~d for financial assistance.
References [1] J.O. Henningsen and D.S. Falk, Phys. Rev. Lett. 26 (1971) 1174; D.S. Falk et al., Phys. Rev. B6 (1972) 377. [2] K. Sa~rmark and J. Lebech, Phys. Lett. 39A (1972) 209; K. Saermark and J. Lebech, Phys. Stat. Sol. (b) 65 (1974) 543. [3] A.P. Volodin et al., JETP 38 (1974) 1052. [4] M. Surma, J. Lebech and K. Saermark, Proc. LT-14, 1975. [5 ] To be published.
213
PHYSICS LETTERS
8 September 1975
O B S E R V A T I O N O F T R A N S M I S S I O N O F 45 G H z M I C R O W A V E S THROUGH A THIN Mo-DISK WITH AND WITHOUT THE PRESENCE OF A MAGNETIC FIELD J. LEBECH, M. SURMA* and K. SAERMARK Physics Laboratory I, The Technical University of Denmark, DK-2800 Lyngby, Denmark Received 11 July 1975 Transmission of microwaves of a frequency of 45 GHz through a high-purity, plane-parallel, single-crystalline molybdenum sample of a thickness of 0.15 mm and 0.27 mm, respectively, has been observed, both in the presence of a magnetic field and without a magnetic field. Azbel-Kaner type cyclotron resonance was seen in the signal transmitted through the sample.
In the present communication we wish to report on an observation made in connexion with a microwave transmission experiment, the purpose of which was to detect time-of-flight-effects and propagation of cyclotron waves in Mo. Similar experiments have earlier been carried out for silver [1, 2]. The new features of the present experiments consist in the observation of a pronounced transmission of the 45 GHz microwaves applied to the sample, both for a magnetic field B = 0 and for B :/: 0, and in the observation of Azbel-Kaner type cyclotron resonance (AKCR) in the transmitted signal. The transmission in zero field was observed both at room temperature and at helium-temperatures. The Mo-samples were of a very high purity (RRR = 40 000) and were in the shape of plane-parallel disks with (110)-planes as surfaces, and the surfaces were carefully etched and polished. Two different sample thicknesses, d = 0.15 mm and d = 0.27 mm, respectively, were used in the experiments. The sample was mounted in the transmission set-up as a common end-wall between two T E l l 2 mm-wave cavities as shown in fig. 1. The signal transmitted through the sample was detected as a video signal at the output of the 45 GHz receiver, and the signal level was measured to be 20 to 30 dB above the noise level of the receiver. The transmitted signal decreased with increasing * On leave from The Institute of Physics, A. Minckiewicz University, Poznan, Poland.
/,5 GHz " Generato r
Re~ver
Sflverpaint
Sampte
Fig. 1. The TE112-mode transmission cavities and sample mounting.
sample thickness and turned out to be slightly dependent on the angle between the Erf-field and the crystal. lographic axes, as observed by a rotation of the sample. The essential point to be noted, however, is that the transmitted signal turned out to be proportional to the sample-area exposed to the incoming rf-field. This was demonstrated repeatedly by covering successively more of the sample surface in the output cavity with silver-paint. A "complete" isolation was obtained when all of the sample surface was covered with silver paint. In zero magnetic field the measurements were performed both at 300 K and 4.2 K, the magnitude of the transmittzd signal being nearly the same in the two cases. In the transmitted signal, high-quality Azbel-Kaner cyclotron resonances may be directly observed as 211
Volume 54A, number 3
PtlYSICS LETTERS
<1 Mo-d= 150p. Erf J.(110)' Transmission Exp.
}It 1
B19
t
B11B10B 9 B8 B7
I
i
I
500 b. Mo-d=272P. Erf.L<110) Reflection Exp.
-~
B,o B6BS ~.
a=l
~ ~ * % t 6 L 7L6 t s
B3
1000
BITI.104
B2
B~
L~
q
C1 H6
5
C. No-d= 1501~ Erf [/110)
Reftection
Exp.
I\ ~,AA,,/l~Jl ~(jl Z,/\"~ 2000
/,000
", /I ,~
",
6000 BIT].10/'
Fig. 2. Recorded trace of cyclotron resonance in transmission
experiment a), and in reflection experiments for different thicknesses of the molybdenum sample b) d = 0.27 mm, and c) d = 0.15 mm. shown in fig. 2. This indicates that the transmitted microwave field excites the output cavity and that the magnetic field derivative of the Mo surface impedance is being measured. However, it is essential to note that it is the E-field transmitted through the sample which is active and not a stray leakage field. This was demonstrated by covering the sample surface in the output cavity fully with silver paint and artificially introducing a very weak leakage field between the two cavities, yielding the same signal level at the 212
8 September 1975
microwave receiver as when tile unpainted sample surface was used. In the last type of measurements mentioned no Azbel-Kaner cyclotron resonances were observed at all. In fig. 2 we show recorder tracings of AKCR signals obtained with the microwave Err-field oriented perpendicular to the ( 110)-crystallographic direction in the sample surface. The AKCR signals in the reflection experiments, fig. 2b,c, for both o f the samples (d = 0.15 mm and d = 0.27 lnmL and the AKCR signals in the transmission experiment, fig. 2a, for the thinner ( d = 0.i 5 into) sample are well resolved, however, the best signal/noise ratio is obtained for the transmission experiment, fig. 2a. In reflection experiments with the microwave k'rtfield oriented parallel to a ( I 10)-direction in the sample surface, AKCR signals were undetectable whereas very well resolved AKCR signals were observed in trhnsmission experiments with the same field configuration. We take this, together with the remarks concerning fig. 2a,b,c as in indication that the microwave transmission to some extent depends on the relative orientation of the Err-field and the crystallographic axes. In table 1 we indicate by the + sign the Erf-field orientations for which well resolved AKCR performance has been observed both in transmission and in reflection experiments. The sign indicates the Erf-field orientations for which no AKCR signals were observed in reflection experiments, but where, however, well resolved AKCR signals were observed in transmission experiments. A theoretical explanation of the observed transparency o f the thin Mo-samples presents o f course a new problem. In this connexion we wish to point out, however, that earlier [2, 3] experiments as well as the present ones [4] show that the electrons interact to
Table 1
d (mm) 0.15 0.27
Transmission
Reflection
Erf ±(110)
Erfll(110}
+ +
+ +
+ sign: AKCR observed sign: AKCR not observed.
Erfll (110)
Erf±(l 10)
+ +
Volume 54A, number 3
PHYSICS LETI'ERS
a significant extent with the E-field in the skin layer at the sample surface in the input cavity to a distance of ~ 30/am. It should, further, also be pointed out that in the limit of vanishing DC magnetic field, B ~ 0 , the phase velocity o f cyclotron waves of the extraordinary type, which is the one relevant to the present experiments, approaches the Fermi-velocity as indicated by recent calculations [5]. With the frequency applied here this means a wavelength of the order o f 3 0 - 4 0 / a m , i.e. the same magnitude as quoted above. Tentatively we therefore suggest that an explanation of the observed transparency of our Mo-samples is to be found in a study o f the general behavior of cyclotron waves in the limit mentioned above. We wish to thank Dr. R. Herrman for placing the
8 September 1975
Mo-crystal at our disposal. We are, further, grateful to The Danish-Polish Exchange Program and to Statens Naturvidenskabelige Forskningsr~d for financial assistance.
References [1] J.O. Henningsen and D.S. Falk, Phys. Rev. Lett. 26 (1971) 1174; D.S. Falk et al., Phys. Rev. B6 (1972) 377. [2] K. Sa~rmark and J. Lebech, Phys. Lett. 39A (1972) 209; K. Saermark and J. Lebech, Phys. Stat. Sol. (b) 65 (1974) 543. [3] A.P. Volodin et al., JETP 38 (1974) 1052. [4] M. Surma, J. Lebech and K. Saermark, Proc. LT-14, 1975. [5 ] To be published.
213