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Production and usage of megagauss fields for solid state physics
Journal of Magnetism and Magnetic Materials 11 (1979) 275-283 © North-Holland Publishing Company
PRODUCTION AND USAGE OF MEGAGAUSS FIELDS FOR SOLID STATE PHYSICS N. MIURA, G. KIDO, M. AKIHIRO and S. CHIKAZUMI Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo, Japan Received 1 August 1978
Pulsed high magnetic fields up to 280 T (2.8 MG) with a rise time of several microseconds were produced by the electromagnetic fiux-eompression method. The produced high fields have been successfully applied to various experiments on solid state physics such as infrared cyclotron resonance in a variety of semiconductors, the interband Faraday rotation, the Zeeman splitting in ruby, the exciton absorption spectra in layer-type semiconductors, and the spin-flip transition in ferrimagnetic iron garnets. The temperature of samples was controlled in the range from 20 K to 300 K.
1. Introduction
ing the megagauss fields are subjected to destruction of some part of the magnet system after every generation of the megagauss field. Hence, any solid state experiments in the megagauss fields are more difficult than those in the lower fields. The difficulties stem also from the short duration (an order of microsecond), and the small effectively available area (a f e w m m in diameter). For a measurement of the electrical conductivity, for example, even a small loop in lead wires to the sample would pick up a large spurious voltage which usually exceeds the signal. For a measurement of the magnetization, the flux density of magnetization would be only 0.1 to 1% of that of the field itself. Among the solid state experiments in the megagauss fields optical measurements are the most convenient method, since they do not need any lead wire to the sample. Most of the measurements in the megagauss fields so far reported have been magneto-optical measurements [8] or cyclotron resonance [9]. We have recently succeeded in producing pulsed high magnetic fields up to 280 T by the electromagnetic flux-compression method, and these fields have been conveniently applied to various experiments on solid state physics, such as cyclotron resonance, Faraday rotation, Zeeman splitting, magneto-optical spectra of excitons, metamagnetic magnetizations, and so on. In this paper we present a review on our recent experiments of the generation of the megagauss fields and their application to solid state physics.
Recently, several techniques have been developed for generating pulsed high magnetic fields exceeding 1 MG or 100 T, which we call megagauss fields [ 1 - 7 ] . As is well known, it is very difficult to produce magnetic fields higher than 70 T by any conventional pulse magnets in a non-destructive way, because under such high magnetic fields the Maxwell stress acting on the coil becomes so strong that it inevitably destroys the coil. For this reason, the generation of the megagauss fields requires special techniques different from those for the lower fields. The megagauss fields are usually produced by the flux-compression technique. Fowler et al. first reported in 1960 the generation of fields higher than 10 MG by the explosive driven flux-compression method [ 1]. The principle of this method is based on the conversion of energy of chemical explosives into the magnetic energy by means of an imploding metal ring, called liner. In 1966, Cnare generated the fields up to 200 T by an alternative method, the electromagnetic flux-compression, method, in which the energy stored in a large condenser bank was used instead of the chemical explosives [2]. The megagauss fields were also generated by a very fast discharge of the large current from a capacitor bank into a small one-turn c o t [4,5]. All of the above mentioned techniques for generat275
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N. Miura et al. / Megagaussfields for solid state physics
2. E x p e r i m e n t a l a p p a r a t u s a n d t e c h n i q u e s
2.1. Generation o f megagauss fields
The principle of our method for generating the megagauss field is essentially the same as that developed by Cnare [2]. The coil system for this method is schematically shown in the inset of fig. 1. In a oneturn primary coil, we put a metal ring (liner) usually made from copper. Large pulsed primary current I is supplied to the primary coil by condenser discharge. Then the secondary current i is induced in the liner in the direction opposite to 1, so as to shield the inner area of the liner against the magnetic flux produced by 1. Thus a large difference in the magnetic field is created between the outer and inner surfaces of the liner. As a result, the liner suffers strong Maxwell stress inwards, by which the liner is squeezed rapidly. Thus the 0-pinch or the implosion of the liner occurs. During the process of the 0-pinch, the total magnetic flux in the inner area of the liner tends to be kept almost
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constant. Accordingly, if we inject seed fields in the inner area in advance, the flux of this field is compressed, and finally we obtain a very high field when the diameter of the liner decreases sufficiently. While the liner is in motion, a part of the magnetic flux produced by I diffuses into the inner area of the liner because of the non-zero electrical resistance of the liner. This diffuse-in field adds to the seed field to be compressed. Accordingly, the megagauss fields can be produced even without the injected seed field. The high field in this case is, however, produced only in a very small volume. When we inject the seed field, on the other hand, the maximum field at the turnaround (see description below) becomes lower, but the rise time of the field becomes longer and we eventually obtain higher fields in a certain useful volume. The above mentioned process is described by a combination of equations of the classical electrodynamics and the classical law of motion. The process is rather complicated because of the non-uniform distribution of the magnetic field inside and outside the liner, the time dependence of the self-inductance of the liner, and the mutual inductance between the primary coil and the liner, the diffuse-in of the field into the liner, the temperature rise of the liner and the mechanical work done on the liner, etc. We have solved the equations with a computer program taking into account all the above mentioned effects [10]. An example of the calculated result is shown in fig. 1. All the parameters needed for the calculation were put equal to the values corresponding to the actual experiment. The secondary current i is first in the opposite direction to I, but it changes the sign at some time when the flux-compression starts, and it builds up rapidly as the radius r of the liner becomes smaller. At the same time the magnetic field H also builds up correspondingly. The radius of the liner starts to increase again after taking a minimum, and both i and H take maximum at the minimum point ofr. This phenomenon is called "turn-around". The turnaround takes place because the magnetic field inside the liner becomes so high that the outward Maxwell stress changes the direction of the liner motion. The results of observation for H and r are also plotted in fig. 1 for comparison. The agreement between the theory and experiment is considered to be excellent since we did not use any adjustable parameters in the computation. This computer simulation
N. Miura et al. / Megagauss fields for solid state physics
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mm. Two slots are cut in the plate as shown in fig, 3, and epoxy plates are thrust into the slots for insulation. These slots are important to keep the current path circular and to improve the uniformity of the field distribution avoiding the effect of the feed gap. This type of primary coil can be repeatedly used over 8 to 10 shots. The primary coil is clamped against the strong magnetic force by heat-treated thick steel plates with thick bolts as shown in fig. 3. The distribution of the magnetic field produced by such a massive coil is slightly different from that in a thin oneturn coil, because in the former coil a part of the current flows on both side surfaces. The effect of the side surface current has been taken into account in the computer simulation in fig. 1. The liner has normally a dimension 66 mm in outer diameter, 20 mm in length and 1.0 mm in thickness. It is machined from a copper pipe with a lathe. A phenolic tube with 2 mm thickness is inserted between the primary coil and the liner both for insulation and for vacuum seal as shown in fig. 2. The seed field is produced by a split-type coil in which copper wires are wound on stainless steel bobbins. The walls of the bobbin (6 mm thick) permit the slow injection field to pass through, but cut out the rapid rise of the field produced by the primary current to avoid induction of high voltage in the coil. By these solenoids, magnetic fields up to 3 T with a quarter
278
N. Miura et al. / Megagauss fields for solid state physics
Fig. 4. High speed photographrepresentingthe motion of the liner taken by an image converter camera. Interval between each frame is 2 tzs. Time sequence is from top-right to bottom left.
period of 1.8 ms were produced at.the center of the liner. The normal size of the sample is 2 mm in diameter. The sample is mounted in a thin black glass tube on which a pick-up coil is wound for measuring the field intensity. The temperature of the sample is decreased by flowing cold helium gas in the vicinity of the sample. The temperature is controlled in the range from 20 K to 300 K and measured with a thermocouple. The entire coil system including the collector plates is enclosed in a protecting shield box 1.4 X 1.5 X 1.6 m 3 made of 12 mm thick steel plates when the experiment is performed. The box is effective to conceal the burst and to shield the electromagnetic noise. The motion of the liner is monitored by an image converter camera. Fig. 4 shows an example of framing pictures of the motion of the liner. We see that the shape of the liner keeps the cylindrical symmetry during the squeezing. By the image converter camera, we can also obtain streak pictures from which the continuous decrease of the liner diameter is observed. The experimental curve for r in fig. 1 is obtained from the streak pictures. We have so far succeeded in generating magnetic fields up to 280 T by the above mentioned technique. 2.2. Measurement o f JTeld intensity The magnetic field intensity is measured by integrating the signal induced in a pick-up coil which is wound on the sample. As the pick-up coil is destroyed. together with the sample in every pulse to megagauss, we have to calibrate the field sensitivity of each pick-
up coil before the experiment for measuring the field accurately. We have made an apparatus for calibrating the field sensitivity accurately and easily [ 11 ]. The principle is that high frequency fields (about 60 kHz) with a constant amplitude are generated in a large coil, into which a pick-up coil with unknown field sensitivity is placed coaxially. The induced voltage in the pick-up coil is read with an ac digital voltmeter and is compared with that in a standard coil. The field sensitivity of the standard coil is calibrated by the Faraday rotation measurements in CdS. We measured the Faraday rotation for CdS at 632.8 nm wavelength by using a H e - N e laser, and found that the rotation is linear with respect to the field at least up to 100 T at this wavelength. Therefore, by knowing the exact value of the Verdet constant measured at lower field, the field intensity can be calculated accurately up to the megagauss range [11,12]. The integration of the induced voltage in the pickup coil is carried out by a 2-stage integrator to eliminate spurious voltage due to the stray inductance contained in the capacitor of the integrator [ 11 ]. The output signal from the integrator which is proportional to the field is recorded with a transient recorder (Biomation model 8100). The best time resolution is 10 ns and the maximum voltage resolution is 1 part in 28 or 0.4%. We are using three transient recorders of this model for recording the field intensity and other signals in the megagauss fields simultaneously. The output from the transient recorders can be conveniently fed into a computer to carry out various data processing [12]. 2.3. Measurement o f infrared cyclotron resonance The infrared cyclotron resonance measurements were performed by using pulsed molecular gas lasers operated at several different wavelengths as a radiation source. We used a 2 m long laser cavity operated with CO2 and H20. The pulsed output was obtained at 16.9/am and 28/am from the H20 laser [13]. For the CO~ laser the oscillation line was selected in the range from 9.4/am to 10.9/am by adjusting a grating in the cavity. The duration of the laser pulse was 100 ~ 200/as. The transmitted radiation through the sample was detected by Cu- or Ga-doped Ge cooled by liquid helium. The response time of the detector system including the amplifier was fast
N. Miura et al. / Megagaussfields for solid state physics enough for the present experiments [I 1]. By recording simultaneously the signals of the magnetic field and the transmission, we obtained the absorption coefficient vs. field curve after the data processing in the computer. 2.4. Magneto-optical spectroscopy in the visible region region Since the megagauss fields are transient and the sample is lost every time, it is important to obtain as much information as possible in each shot to the megagauss field. For the magneto-optical measurement in the megagauss fields, a time-resolving spectrometer can be conveniently utilized because it makes possible to obtain two-dimensional information i.e. the field dependence of the optical spectra in one shot. We have made a time-resolving spectrometer by using an image-converter camera (John Hadland Imacon 700 with a special large cathode). Fig. 5 schematically shows the block-diagram of our spectrometer. The image of the optical spectrum is focused on the photo-cathode, from which the photo-electrons are emitted, accelerated and focused on the phosphor screen, thus reproducing the optical image in the image-converter camera. During the flight of electrons, the electron beam is swept perpendicular to the spectrum line, by applying a voltage ramp to one of the pairs of electrodes. Consequently, the image on the phosphor screen is streaked by time, displaying a timeresolved spectrum. This image is then intensified by a
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279
3-stage intensifier and finally fLxed on a •m in the polaroid camera. In order to calibrate the time scale as a function of magnetic field, double short pulse voltage from the time marker generator is applied to the deflector plate to modulate the electron beam perpendicular to the sweep direction. The time marker signal is made visible more clearly by putting two tiny LED's (light emitting diode) at the both side ends on the spectrum line at the exit of the monochromator. Since there is a little time jitter in the rise of the magnetic field every time, the sweep of the image converter camera is started by a trigger pulse from the comparator which compares the field signal with a preset threshold voltage. The calibration of the wavelength scale is made by taking the line spectra of a Hg lamp. 2.5. Measurement o f magnetization In optically transparent magnetic substances we can obtain the information on the magnetization from the Faraday rotation measurements, because the Faraday rotation is related to the sublattice magnetizations. For various iron garnet crystals, we carded out the Faraday rotation measurements by using a YAG laser as a light source at 1.06/am wavelength [14]. It is very difficult to perform the direct magnetization measurements in the megagauss fields, because the magnetic flux of the magnetization is much smaller than that of the magnetic field. Slight failure of the compensation of the field signal will result in an enormours noise on the magnetization signals. Therefore we develop.ed a system for measuring reversible susceptibility by modulating the magnetization with high frequency magnetic field [7]. Using a high power oscillator, alternating field with a frequency 20 to 40 MHz is applied to the sample in a pulsed form with the width of 100/as through the small coil wound on the sample. In advance to every measurement the output from the detecting coil which is wound also on the sample is compensated with an oppositely wound compensating coil. On applying the high magnetic field, the reversible susceptibility is measured by detecting the high frequency component of the signal from the detecting coil. By the above mentioned technique the susceptibility measurement has so far become possible up to 70 T. Further improvement of the technique is being in progress.
280
At. Miura et al. / Megagauss fields for solid state physics
3. Experimental results on solid state physics
ling constants. The bare band edge masses were evaluated for these crystals [17].
3.1. Infrared cyclotron resonance 3.2. Interband Faraday rotation Infrared cyclotron resonance has been observed in a variety of semiconductors in the megagauss fields. Investigation has been made on the non-parabolicity of the conduction band deep away from the band minima, the energy band structure of substances with low mobility carriers, the field dependence of the line-width and the polaron pinning effect. Fig. 6 shows typical examples of the experimental traces of the cyclotron resonance for various crystals. In InSb, two absorption peaks were resolved corresponding to (0+ -* 1÷) and (0- -+ 13 transitions of electrons [15]. In Ge, the field dependence of the line width was investigated and we found that the relaxation time decreases in proportion to the inverse of the square root of the field at high fields, and that it is nearly independent of temperature in the range 130 ~ 300 K [ 16]. In CdS and CdSe, very large effect of the polaron pinning was observed near and above the reststrahlung frequency reflecting the large electron-phonon coupI
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The Zeeman splitting of the R lines in conc. ruby was observed by using the streak spectrometer. Fig. 8 shows an example of the streak spectra for H ± c. The two separate lines Ra and R2 were observed at H = O. They are split into several lines of which three strong ones are observed at high fields in case of H ± c. The absorption lines are plotted as a function of magnetic field in fig. 9. The theoretical lines expected from the low field data are also shown for comparison. For H I c, the lines are expected to show non-linearity due to the Paschen-Back effect [ 19]. The experimental points well agree with the theoretical lines except for a small discrepancy in the central line. As for H / / c , seven lines were resolved, some of which were not resolved in the lower field measurements [ 19]. At high
N. Miura et al. / MegagaussfieMs for solid state physics
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N. Miura et aL / Megagaussfields for solid state physics
282 145
energy region the experimental points deviated from the theoretical lines showing the non-linear dependence on field.
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3.4, Magneto-optical spectra o f excitons
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The magneto-optical spectra o f exciton absorption lines were observed in layer-type semiconductors GaSe and PbI2 [17]. Fig. 10 shows an example o f the streak photographs exhibiting the exciton-absorptions in the megagauss fields. The ground state line was found to shift to shorter wavelength considerably. This line also showed a splitting and broadening at high fields. The shift o f the N = 2 line was much larger than that o f the ground state. The shift in energy o f the ground state was in reasonably good agreement with existing theories of excitons in a magnetic field. In PbI2, the ground state line was found to shift only slightly (5 meV at 100 T) to higher energy even with the megagauss fields. F r o m the amount of the shift, the reduced effective mass o f exciton was evaluated [ 17].
Fig. 10. Streak photograph showing the magneto-optical spectrum of the exciton absorption lines in GaSe. T = 43 K; H//c.
N. Miura et al. / Megagauss fields for solid state physics
phenomena which may occur in the megagauss fields. We are planning to extend the present field intensity o f a few MG to 10 MG (1000 T) in future. F o r this purpose, we are hoping to install a condenser bank with the total energy o f 5 MJ. The fields up to 1000 T would enable us to perform various exciting experiments, which are challenging to theoretically unsolved problems.
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References
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Fig. 11. Faraday rotation in Y3Gao.sFe4.sOI 2 as a function of magnetic field. In the inset is shown the dbect Faraday rotation signal V before the arc-cosine transformation for Y3 GalFe4012- In the both curves, the critical fields for spinflip transition axe indicated by arrows.
3.5. Spin-flip transition in ferrimagnets Faraday rotation was observed for various iron garnets such as YIG, YaGaxFes_xO12, G d l G and ErIG at 1.06/~m wavelength in megagauss fields [20]. It was found that the Faraday rotation in YIG was linear as a function of field up to 140 T. In Y3GaxFes_x O12 with x = 0.5 and x = 1.0 and in G d l G , the s p i n flip transition was observed as a break in the graphs o f rotation vs. field [14]. Examples o f such graphs are displayed in fig. 11. By plotting the critical field for the s p i n - f l i p transition as a function o f temperature, the magnetic phase diagram was constructed and the exchange coefficients o f YIG were evaluated from the diagram. The s p i n - f l i p transition was also observed in GdIG, b y means ot the reversible susceptibility described in section 2.5.
4.Futureprospect The megagauss fields have an extremely large influence on the electronic system. Therefore, they would open up various new possibilities in solid state physics. The most striking thing is to observe drastic non-linear
[1] C.M. Fowler, W.B. Garn and R.S. Caird, J. Appl. Phys. 31 (1960) 588. [2] E.C. Chafe, J. Appl. Phys. 37 (1966) 3812. [3] S.G. Alikhanov, V.G. Belan, A.L Ivachenko, V.N. Kasjuk and G.N. Kichigin, J. Phys. E1 (1968) 543. [4] H.P. Furth, M.A. Levin and R.W. Waniek, Rev. Sci. Inst. 28 (1957) 949. [5] F. Herlach and R. McBroom, J. Phys. E6 (1973) 652. [6] N. Miura, G. Kido, I. Oguro and S. Chikazumi, Prec. Int. Colloq. on Physique sous Magn~tiques Intenses (Greno (Grenoble, CNRS, 1974) p. 345. [7] S. Chikazumi, N. Miura, G. Kido and M. Akihiro, IEEE Trans. Magnetics 14 (1978) 577. [8] C.M. Fowler, Science 180 (1973) 261. Further refs. axe cited in this paper. [9] F. Herlach, J. Davis, R. Schmidt and H. Specter, Phys. Rev. B10 (1974) 682. [10] N. Miura and S. Chikazumi, to be submitted to Jap. J. Appl. Phys. (1978). [11] G. Kido, N. Miura, K. Kawauchi, I. Oguro and S. Chikazumi, J. Phys. E (Sci. Inst.) 9 (1976) 587. [12] N. Miura, G. Kido, K. Suzuki and S. Chikazumi, Prec. Int. Conf. Application of High Magnetic Fields in Semiconductor Physics 0giirzburg, 1976) p. 441. [13] G. Kido and N. Miura, Appl. Phys. Lett. 33 (1978) 321. [14] N. Miura, G. Kido, I. Oguro, K. Kawauchi, S. Chikazumi, LF. Dillon, Jr and L.G. Van Uitert, Physica 86-88B (1977) 1219. [15] N. Miura, G. Kido and S. Chikazumi, Solid State Commun. 18 (1976) 885. [16] N. Miura and G. Kido, Prec. XIII Int. Conf. Phys. Semiconductors (Rome, 1976), ed. F.G. Fumi, p. 1149. [17] N. Miura, G. Kido and S. Chikazumi, to be published in Prec. XIV Int. Conf. Phys. Semiconductors (Edinburgh, 1978). [18] N. Miura, G. Kid0 and S. Chikazumi, Prec. Int. Conf. Application of High Magnetic Fields in Semiconductor Physics (Oxford, 1978) p. 233. [19] K. Aoyagi, A. Misu and S. Sugano, J. Phys. Soc. Japan 18 (1963) 1448. [20] This work was done in collaboration with Dr. J.F. Dillon, Jr. of Bell Laboratories.
PRODUCTION AND USAGE OF MEGAGAUSS FIELDS FOR SOLID STATE PHYSICS N. MIURA, G. KIDO, M. AKIHIRO and S. CHIKAZUMI Institute for Solid State Physics, University of Tokyo, Roppongi, Minato-ku, Tokyo, Japan Received 1 August 1978
Pulsed high magnetic fields up to 280 T (2.8 MG) with a rise time of several microseconds were produced by the electromagnetic fiux-eompression method. The produced high fields have been successfully applied to various experiments on solid state physics such as infrared cyclotron resonance in a variety of semiconductors, the interband Faraday rotation, the Zeeman splitting in ruby, the exciton absorption spectra in layer-type semiconductors, and the spin-flip transition in ferrimagnetic iron garnets. The temperature of samples was controlled in the range from 20 K to 300 K.
1. Introduction
ing the megagauss fields are subjected to destruction of some part of the magnet system after every generation of the megagauss field. Hence, any solid state experiments in the megagauss fields are more difficult than those in the lower fields. The difficulties stem also from the short duration (an order of microsecond), and the small effectively available area (a f e w m m in diameter). For a measurement of the electrical conductivity, for example, even a small loop in lead wires to the sample would pick up a large spurious voltage which usually exceeds the signal. For a measurement of the magnetization, the flux density of magnetization would be only 0.1 to 1% of that of the field itself. Among the solid state experiments in the megagauss fields optical measurements are the most convenient method, since they do not need any lead wire to the sample. Most of the measurements in the megagauss fields so far reported have been magneto-optical measurements [8] or cyclotron resonance [9]. We have recently succeeded in producing pulsed high magnetic fields up to 280 T by the electromagnetic flux-compression method, and these fields have been conveniently applied to various experiments on solid state physics, such as cyclotron resonance, Faraday rotation, Zeeman splitting, magneto-optical spectra of excitons, metamagnetic magnetizations, and so on. In this paper we present a review on our recent experiments of the generation of the megagauss fields and their application to solid state physics.
Recently, several techniques have been developed for generating pulsed high magnetic fields exceeding 1 MG or 100 T, which we call megagauss fields [ 1 - 7 ] . As is well known, it is very difficult to produce magnetic fields higher than 70 T by any conventional pulse magnets in a non-destructive way, because under such high magnetic fields the Maxwell stress acting on the coil becomes so strong that it inevitably destroys the coil. For this reason, the generation of the megagauss fields requires special techniques different from those for the lower fields. The megagauss fields are usually produced by the flux-compression technique. Fowler et al. first reported in 1960 the generation of fields higher than 10 MG by the explosive driven flux-compression method [ 1]. The principle of this method is based on the conversion of energy of chemical explosives into the magnetic energy by means of an imploding metal ring, called liner. In 1966, Cnare generated the fields up to 200 T by an alternative method, the electromagnetic flux-compression, method, in which the energy stored in a large condenser bank was used instead of the chemical explosives [2]. The megagauss fields were also generated by a very fast discharge of the large current from a capacitor bank into a small one-turn c o t [4,5]. All of the above mentioned techniques for generat275
276
N. Miura et al. / Megagaussfields for solid state physics
2. E x p e r i m e n t a l a p p a r a t u s a n d t e c h n i q u e s
2.1. Generation o f megagauss fields
The principle of our method for generating the megagauss field is essentially the same as that developed by Cnare [2]. The coil system for this method is schematically shown in the inset of fig. 1. In a oneturn primary coil, we put a metal ring (liner) usually made from copper. Large pulsed primary current I is supplied to the primary coil by condenser discharge. Then the secondary current i is induced in the liner in the direction opposite to 1, so as to shield the inner area of the liner against the magnetic flux produced by 1. Thus a large difference in the magnetic field is created between the outer and inner surfaces of the liner. As a result, the liner suffers strong Maxwell stress inwards, by which the liner is squeezed rapidly. Thus the 0-pinch or the implosion of the liner occurs. During the process of the 0-pinch, the total magnetic flux in the inner area of the liner tends to be kept almost
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netic flux-compression.
constant. Accordingly, if we inject seed fields in the inner area in advance, the flux of this field is compressed, and finally we obtain a very high field when the diameter of the liner decreases sufficiently. While the liner is in motion, a part of the magnetic flux produced by I diffuses into the inner area of the liner because of the non-zero electrical resistance of the liner. This diffuse-in field adds to the seed field to be compressed. Accordingly, the megagauss fields can be produced even without the injected seed field. The high field in this case is, however, produced only in a very small volume. When we inject the seed field, on the other hand, the maximum field at the turnaround (see description below) becomes lower, but the rise time of the field becomes longer and we eventually obtain higher fields in a certain useful volume. The above mentioned process is described by a combination of equations of the classical electrodynamics and the classical law of motion. The process is rather complicated because of the non-uniform distribution of the magnetic field inside and outside the liner, the time dependence of the self-inductance of the liner, and the mutual inductance between the primary coil and the liner, the diffuse-in of the field into the liner, the temperature rise of the liner and the mechanical work done on the liner, etc. We have solved the equations with a computer program taking into account all the above mentioned effects [10]. An example of the calculated result is shown in fig. 1. All the parameters needed for the calculation were put equal to the values corresponding to the actual experiment. The secondary current i is first in the opposite direction to I, but it changes the sign at some time when the flux-compression starts, and it builds up rapidly as the radius r of the liner becomes smaller. At the same time the magnetic field H also builds up correspondingly. The radius of the liner starts to increase again after taking a minimum, and both i and H take maximum at the minimum point ofr. This phenomenon is called "turn-around". The turnaround takes place because the magnetic field inside the liner becomes so high that the outward Maxwell stress changes the direction of the liner motion. The results of observation for H and r are also plotted in fig. 1 for comparison. The agreement between the theory and experiment is considered to be excellent since we did not use any adjustable parameters in the computation. This computer simulation
N. Miura et al. / Megagauss fields for solid state physics
277
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mm. Two slots are cut in the plate as shown in fig, 3, and epoxy plates are thrust into the slots for insulation. These slots are important to keep the current path circular and to improve the uniformity of the field distribution avoiding the effect of the feed gap. This type of primary coil can be repeatedly used over 8 to 10 shots. The primary coil is clamped against the strong magnetic force by heat-treated thick steel plates with thick bolts as shown in fig. 3. The distribution of the magnetic field produced by such a massive coil is slightly different from that in a thin oneturn coil, because in the former coil a part of the current flows on both side surfaces. The effect of the side surface current has been taken into account in the computer simulation in fig. 1. The liner has normally a dimension 66 mm in outer diameter, 20 mm in length and 1.0 mm in thickness. It is machined from a copper pipe with a lathe. A phenolic tube with 2 mm thickness is inserted between the primary coil and the liner both for insulation and for vacuum seal as shown in fig. 2. The seed field is produced by a split-type coil in which copper wires are wound on stainless steel bobbins. The walls of the bobbin (6 mm thick) permit the slow injection field to pass through, but cut out the rapid rise of the field produced by the primary current to avoid induction of high voltage in the coil. By these solenoids, magnetic fields up to 3 T with a quarter
278
N. Miura et al. / Megagauss fields for solid state physics
Fig. 4. High speed photographrepresentingthe motion of the liner taken by an image converter camera. Interval between each frame is 2 tzs. Time sequence is from top-right to bottom left.
period of 1.8 ms were produced at.the center of the liner. The normal size of the sample is 2 mm in diameter. The sample is mounted in a thin black glass tube on which a pick-up coil is wound for measuring the field intensity. The temperature of the sample is decreased by flowing cold helium gas in the vicinity of the sample. The temperature is controlled in the range from 20 K to 300 K and measured with a thermocouple. The entire coil system including the collector plates is enclosed in a protecting shield box 1.4 X 1.5 X 1.6 m 3 made of 12 mm thick steel plates when the experiment is performed. The box is effective to conceal the burst and to shield the electromagnetic noise. The motion of the liner is monitored by an image converter camera. Fig. 4 shows an example of framing pictures of the motion of the liner. We see that the shape of the liner keeps the cylindrical symmetry during the squeezing. By the image converter camera, we can also obtain streak pictures from which the continuous decrease of the liner diameter is observed. The experimental curve for r in fig. 1 is obtained from the streak pictures. We have so far succeeded in generating magnetic fields up to 280 T by the above mentioned technique. 2.2. Measurement o f JTeld intensity The magnetic field intensity is measured by integrating the signal induced in a pick-up coil which is wound on the sample. As the pick-up coil is destroyed. together with the sample in every pulse to megagauss, we have to calibrate the field sensitivity of each pick-
up coil before the experiment for measuring the field accurately. We have made an apparatus for calibrating the field sensitivity accurately and easily [ 11 ]. The principle is that high frequency fields (about 60 kHz) with a constant amplitude are generated in a large coil, into which a pick-up coil with unknown field sensitivity is placed coaxially. The induced voltage in the pick-up coil is read with an ac digital voltmeter and is compared with that in a standard coil. The field sensitivity of the standard coil is calibrated by the Faraday rotation measurements in CdS. We measured the Faraday rotation for CdS at 632.8 nm wavelength by using a H e - N e laser, and found that the rotation is linear with respect to the field at least up to 100 T at this wavelength. Therefore, by knowing the exact value of the Verdet constant measured at lower field, the field intensity can be calculated accurately up to the megagauss range [11,12]. The integration of the induced voltage in the pickup coil is carried out by a 2-stage integrator to eliminate spurious voltage due to the stray inductance contained in the capacitor of the integrator [ 11 ]. The output signal from the integrator which is proportional to the field is recorded with a transient recorder (Biomation model 8100). The best time resolution is 10 ns and the maximum voltage resolution is 1 part in 28 or 0.4%. We are using three transient recorders of this model for recording the field intensity and other signals in the megagauss fields simultaneously. The output from the transient recorders can be conveniently fed into a computer to carry out various data processing [12]. 2.3. Measurement o f infrared cyclotron resonance The infrared cyclotron resonance measurements were performed by using pulsed molecular gas lasers operated at several different wavelengths as a radiation source. We used a 2 m long laser cavity operated with CO2 and H20. The pulsed output was obtained at 16.9/am and 28/am from the H20 laser [13]. For the CO~ laser the oscillation line was selected in the range from 9.4/am to 10.9/am by adjusting a grating in the cavity. The duration of the laser pulse was 100 ~ 200/as. The transmitted radiation through the sample was detected by Cu- or Ga-doped Ge cooled by liquid helium. The response time of the detector system including the amplifier was fast
N. Miura et al. / Megagaussfields for solid state physics enough for the present experiments [I 1]. By recording simultaneously the signals of the magnetic field and the transmission, we obtained the absorption coefficient vs. field curve after the data processing in the computer. 2.4. Magneto-optical spectroscopy in the visible region region Since the megagauss fields are transient and the sample is lost every time, it is important to obtain as much information as possible in each shot to the megagauss field. For the magneto-optical measurement in the megagauss fields, a time-resolving spectrometer can be conveniently utilized because it makes possible to obtain two-dimensional information i.e. the field dependence of the optical spectra in one shot. We have made a time-resolving spectrometer by using an image-converter camera (John Hadland Imacon 700 with a special large cathode). Fig. 5 schematically shows the block-diagram of our spectrometer. The image of the optical spectrum is focused on the photo-cathode, from which the photo-electrons are emitted, accelerated and focused on the phosphor screen, thus reproducing the optical image in the image-converter camera. During the flight of electrons, the electron beam is swept perpendicular to the spectrum line, by applying a voltage ramp to one of the pairs of electrodes. Consequently, the image on the phosphor screen is streaked by time, displaying a timeresolved spectrum. This image is then intensified by a
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279
3-stage intensifier and finally fLxed on a •m in the polaroid camera. In order to calibrate the time scale as a function of magnetic field, double short pulse voltage from the time marker generator is applied to the deflector plate to modulate the electron beam perpendicular to the sweep direction. The time marker signal is made visible more clearly by putting two tiny LED's (light emitting diode) at the both side ends on the spectrum line at the exit of the monochromator. Since there is a little time jitter in the rise of the magnetic field every time, the sweep of the image converter camera is started by a trigger pulse from the comparator which compares the field signal with a preset threshold voltage. The calibration of the wavelength scale is made by taking the line spectra of a Hg lamp. 2.5. Measurement o f magnetization In optically transparent magnetic substances we can obtain the information on the magnetization from the Faraday rotation measurements, because the Faraday rotation is related to the sublattice magnetizations. For various iron garnet crystals, we carded out the Faraday rotation measurements by using a YAG laser as a light source at 1.06/am wavelength [14]. It is very difficult to perform the direct magnetization measurements in the megagauss fields, because the magnetic flux of the magnetization is much smaller than that of the magnetic field. Slight failure of the compensation of the field signal will result in an enormours noise on the magnetization signals. Therefore we develop.ed a system for measuring reversible susceptibility by modulating the magnetization with high frequency magnetic field [7]. Using a high power oscillator, alternating field with a frequency 20 to 40 MHz is applied to the sample in a pulsed form with the width of 100/as through the small coil wound on the sample. In advance to every measurement the output from the detecting coil which is wound also on the sample is compensated with an oppositely wound compensating coil. On applying the high magnetic field, the reversible susceptibility is measured by detecting the high frequency component of the signal from the detecting coil. By the above mentioned technique the susceptibility measurement has so far become possible up to 70 T. Further improvement of the technique is being in progress.
280
At. Miura et al. / Megagauss fields for solid state physics
3. Experimental results on solid state physics
ling constants. The bare band edge masses were evaluated for these crystals [17].
3.1. Infrared cyclotron resonance 3.2. Interband Faraday rotation Infrared cyclotron resonance has been observed in a variety of semiconductors in the megagauss fields. Investigation has been made on the non-parabolicity of the conduction band deep away from the band minima, the energy band structure of substances with low mobility carriers, the field dependence of the line-width and the polaron pinning effect. Fig. 6 shows typical examples of the experimental traces of the cyclotron resonance for various crystals. In InSb, two absorption peaks were resolved corresponding to (0+ -* 1÷) and (0- -+ 13 transitions of electrons [15]. In Ge, the field dependence of the line width was investigated and we found that the relaxation time decreases in proportion to the inverse of the square root of the field at high fields, and that it is nearly independent of temperature in the range 130 ~ 300 K [ 16]. In CdS and CdSe, very large effect of the polaron pinning was observed near and above the reststrahlung frequency reflecting the large electron-phonon coupI
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The Zeeman splitting of the R lines in conc. ruby was observed by using the streak spectrometer. Fig. 8 shows an example of the streak spectra for H ± c. The two separate lines Ra and R2 were observed at H = O. They are split into several lines of which three strong ones are observed at high fields in case of H ± c. The absorption lines are plotted as a function of magnetic field in fig. 9. The theoretical lines expected from the low field data are also shown for comparison. For H I c, the lines are expected to show non-linearity due to the Paschen-Back effect [ 19]. The experimental points well agree with the theoretical lines except for a small discrepancy in the central line. As for H / / c , seven lines were resolved, some of which were not resolved in the lower field measurements [ 19]. At high
N. Miura et al. / MegagaussfieMs for solid state physics
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N. Miura et aL / Megagaussfields for solid state physics
282 145
energy region the experimental points deviated from the theoretical lines showing the non-linear dependence on field.
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3.4, Magneto-optical spectra o f excitons
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The magneto-optical spectra o f exciton absorption lines were observed in layer-type semiconductors GaSe and PbI2 [17]. Fig. 10 shows an example o f the streak photographs exhibiting the exciton-absorptions in the megagauss fields. The ground state line was found to shift to shorter wavelength considerably. This line also showed a splitting and broadening at high fields. The shift o f the N = 2 line was much larger than that o f the ground state. The shift in energy o f the ground state was in reasonably good agreement with existing theories of excitons in a magnetic field. In PbI2, the ground state line was found to shift only slightly (5 meV at 100 T) to higher energy even with the megagauss fields. F r o m the amount of the shift, the reduced effective mass o f exciton was evaluated [ 17].
Fig. 10. Streak photograph showing the magneto-optical spectrum of the exciton absorption lines in GaSe. T = 43 K; H//c.
N. Miura et al. / Megagauss fields for solid state physics
phenomena which may occur in the megagauss fields. We are planning to extend the present field intensity o f a few MG to 10 MG (1000 T) in future. F o r this purpose, we are hoping to install a condenser bank with the total energy o f 5 MJ. The fields up to 1000 T would enable us to perform various exciting experiments, which are challenging to theoretically unsolved problems.
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References
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Fig. 11. Faraday rotation in Y3Gao.sFe4.sOI 2 as a function of magnetic field. In the inset is shown the dbect Faraday rotation signal V before the arc-cosine transformation for Y3 GalFe4012- In the both curves, the critical fields for spinflip transition axe indicated by arrows.
3.5. Spin-flip transition in ferrimagnets Faraday rotation was observed for various iron garnets such as YIG, YaGaxFes_xO12, G d l G and ErIG at 1.06/~m wavelength in megagauss fields [20]. It was found that the Faraday rotation in YIG was linear as a function of field up to 140 T. In Y3GaxFes_x O12 with x = 0.5 and x = 1.0 and in G d l G , the s p i n flip transition was observed as a break in the graphs o f rotation vs. field [14]. Examples o f such graphs are displayed in fig. 11. By plotting the critical field for the s p i n - f l i p transition as a function o f temperature, the magnetic phase diagram was constructed and the exchange coefficients o f YIG were evaluated from the diagram. The s p i n - f l i p transition was also observed in GdIG, b y means ot the reversible susceptibility described in section 2.5.
4.Futureprospect The megagauss fields have an extremely large influence on the electronic system. Therefore, they would open up various new possibilities in solid state physics. The most striking thing is to observe drastic non-linear
[1] C.M. Fowler, W.B. Garn and R.S. Caird, J. Appl. Phys. 31 (1960) 588. [2] E.C. Chafe, J. Appl. Phys. 37 (1966) 3812. [3] S.G. Alikhanov, V.G. Belan, A.L Ivachenko, V.N. Kasjuk and G.N. Kichigin, J. Phys. E1 (1968) 543. [4] H.P. Furth, M.A. Levin and R.W. Waniek, Rev. Sci. Inst. 28 (1957) 949. [5] F. Herlach and R. McBroom, J. Phys. E6 (1973) 652. [6] N. Miura, G. Kido, I. Oguro and S. Chikazumi, Prec. Int. Colloq. on Physique sous Magn~tiques Intenses (Greno (Grenoble, CNRS, 1974) p. 345. [7] S. Chikazumi, N. Miura, G. Kido and M. Akihiro, IEEE Trans. Magnetics 14 (1978) 577. [8] C.M. Fowler, Science 180 (1973) 261. Further refs. axe cited in this paper. [9] F. Herlach, J. Davis, R. Schmidt and H. Specter, Phys. Rev. B10 (1974) 682. [10] N. Miura and S. Chikazumi, to be submitted to Jap. J. Appl. Phys. (1978). [11] G. Kido, N. Miura, K. Kawauchi, I. Oguro and S. Chikazumi, J. Phys. E (Sci. Inst.) 9 (1976) 587. [12] N. Miura, G. Kido, K. Suzuki and S. Chikazumi, Prec. Int. Conf. Application of High Magnetic Fields in Semiconductor Physics 0giirzburg, 1976) p. 441. [13] G. Kido and N. Miura, Appl. Phys. Lett. 33 (1978) 321. [14] N. Miura, G. Kido, I. Oguro, K. Kawauchi, S. Chikazumi, LF. Dillon, Jr and L.G. Van Uitert, Physica 86-88B (1977) 1219. [15] N. Miura, G. Kido and S. Chikazumi, Solid State Commun. 18 (1976) 885. [16] N. Miura and G. Kido, Prec. XIII Int. Conf. Phys. Semiconductors (Rome, 1976), ed. F.G. Fumi, p. 1149. [17] N. Miura, G. Kido and S. Chikazumi, to be published in Prec. XIV Int. Conf. Phys. Semiconductors (Edinburgh, 1978). [18] N. Miura, G. Kid0 and S. Chikazumi, Prec. Int. Conf. Application of High Magnetic Fields in Semiconductor Physics (Oxford, 1978) p. 233. [19] K. Aoyagi, A. Misu and S. Sugano, J. Phys. Soc. Japan 18 (1963) 1448. [20] This work was done in collaboration with Dr. J.F. Dillon, Jr. of Bell Laboratories.