Monochromatic submillimeter radiation — a fundamental tool in magneto spectroscopy of solids

~ ) Pergamon

In#ared Phys. Technol. Vol.36, No. I, pp. 321 331, 1995

1350-4495(94)00076-X

Copyright~, 1995ElsevierScienceLtd Printed in Great Britain. All rightsreserved 1350-4495/95$9.50+ 0.00

MONOCHROMATIC SUBMILLIMETER R A D I A T I O N - A F U N D A M E N T A L TOOL IN MAGNETO SPECTROSCOPY OF SOLIDS MICHAEL VON ORTENBERG Chair of Magnetotransport, Institute of Physics, Humboldt-Universitfit zu Berlin, lnvalidenstral3e 110. D-10115 Berlin, Germany (Received 30 May 1994)

A~traet--Submillimeter radiation offers one of the most effectiveenergy probes for the investigation of energy levels in solids. In combination with high magnetic fields magneto spectroscopy using monochromatic submillimeter radiation has the additional advantage of a process filter selecting essentially electronic properties from other interactions. In a review of various examples using lasers as well as back-wave oscillators as radiation source the efficiencyof the method is demonstrated.

I. I N T R O D U C T I O N Electronic properties of solids, especially of semiconducting materials, have been at the center of solid state activities in the last decades. Both scientific and technological aspects have met in a large stimulation of the corresponding research programs. Especially quantization effects with characteristic energies of some meV require a suitable energy measure to probe the corresponding system. Electromagnetic radiation of the submillimeter range represents an ideal realization of this measure with the additional advantage of a polarization dependent interaction matrix element sensitive to the spatial distribution of the energy states involved. For a long time submillimeter radiation was neglected in experimental physics due to the lack of a powerful source. With the invention of the molecular-gas laser by Gebbie in 1964, however, a revival of this spectral range was started, m Up to now some hundred laser lines have been tested and successfully applied to spectroscopy using discrete frequencies of the stimulated quantum transitions. ~2~However, the limitation to selected, discrete radiation sources on the frequency axis induces also the longing for a continuously tunable source with comparable power output. A continuous tunability is ensured by wave optical resonance generators. The most effective realization of this kind for the submillimeter radiation is the back wave oscillator (bwo), where the resonance condition of the geometrically fixed system is obtained by externally tunable parameters as magnetic and electric fields acting on the electrons. ~31 In this way submillimeter radiation exhibits a pronounced double character: despite the fact of a very well defined quantum energy, E = hog, the radiation can be generated by wave-typical resonance methods. This complementary double aspect is an essential feature for submillimeter radiation characterizing the transition range between short wave radiation with dominant quantum effects and low frequency radio waves, as shown in Fig. 1.

1I. S U B M I L L I M E T E R S P E C T R O S C O P Y IN S O L I D S T A T E P H Y S I C S Solid state devices are the challenging request of modern high-tech industries, which have created the new branch of energy-band engineering in materials science. To characterize these new materials with respects to the electronic properties is one of the objectives of modern experimental solid state physics. One of the most efficient tools in the investigation of electronic energy levels in solids is m y ~6,~ v

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submillimeter magnetospectroscopy,t4) The external magnetic field tunes the electronic energy levels involved in a controlled way, so that monochromatic submillimeter radiation can probe the energy separation of the different levels by resonance interaction. The fundamental development of high magnetic field equipment has progressed so much, that nowadays magnetic field intensities of some MegaGauss can be handled in laboratory environment,tS) This progress has in turn highly stimulated the source technology for submillimeter radiation. Whereas the initial experiments in magnetoscoscopy where performed by use of microwaves,(6~ later the application of molecular-gas lasers started a new area of solid state investigations centered on cyclotron and spin resonance in this frequency range. The request of a quasi-continuous spectrum of laser energies had a tremendous feedback on FIR-laser development. Very often, however, the quasicontinuity of the spectrum was accompanied with a lack in intensity. This is the reason why for more sophisticated experiments carcintrons or back-wave oscillators have attracted increasing attention. As a result of the worldwide political changes back-wave oscillators have lost their military potential and have become freely accessible for research application. The continuous tunability of these sources, however, has to be considered in comparison with relatively high financial investment.

Basic evaluation concepts of magneto spectroscopy The principal objective in materials characterization is the understanding and modelling of microscopic electronic interactions from macroscopic experimental data. The actual connection between both is a complicated evaluation process based in the first step on a macroscopic analysis of the arbitrary experimental situation as described by the dielectric boundary conditions following from Maxwell's equations. In this abstraction process from the actual experiment all material relevant information is concentrated into the wavenumber and frequency dependent dielectric tensor function ~(k, to), as indicated schematically in Fig. 2. The second step manifests in the microscopic modelling of this central quantity and thus extraction of the relevant classical parameters as are the sign of the charge 4-e of the carriers, their total concentration n, their effective mass m* (related directly to the energy band structure), their lifetime • (related to the energy broadening of the levels involved), and their effective g-factor g* of the spin. It should be noted that the effective mass m*, the lifetime ~, and their effective g-factor g* have tensor properties. ~a~ Often, however, experimentalists are tempted to shortcut the evaluation process by direct assignment of data structures to values of microscopic parameters and this actually results in a misinterpretation of their experiment. °~ Transmission experiments are especially sensitive to this fact due to interference effects of the coherent radiation.

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Experimental setups for submillimeter magneto spectroscopy Submillimeter magnetospectroscopy is submillimeter spectroscopy in the presence of an external magnetic field B modifying the sample's properties. To take advantage of a process filter to select only electronic interactions the external magnetic field is varied for fixed radiation frequency co to obtain a B-cut of the dielectric tensor function ~(k, 09, B). At the Humboldt High Magnetic Field Center in Berlin a setup is being installed including both types of radiation sources, optically pumped molecular gas-lasers and a spectrometer containing ten different interchangeable bwos in connection with magnetic field generators up to MegaGauss fields: 8) We demonstrate the efficiency of both molecular-gas lasers and back wave oscillators in the application of magnetospectroscopy on both semiconducting and magnetic materials. The submillimeter molecular-gas lasers are of the waveguide type pumped by COz-radiation. The back wave oscillator-system MASS 4 was constructed by the Russian Academy of Science, Moscow. The design of this spectrometer in the submillimeter and millimeter range corresponds to a frequency range between 36 and 1200 GHz. The efficiency allows the complex transmission or reflection coefficients to be measured without any mechanical adjustments during the electronic frequency scan. The measuring quality peaks up in a phase sensitivity ~0.005 rad, an amplitude reproducibility ~ 1%, a dynamic range -~ 10 7, and a phase shift range of 105 angle rad. TM This spectrometer can be operated in magnetospectroscopy for both B- and co-cuts. A demonstration for the continuous og-operation for one of the high frequency bwos is demonstrated in Fig. 3 for a plane parallel quartz plate. The detection of a resonance interaction of both radiation and carriers in the sample can be realized in different ways. We distinguish between the measurement of a radiation or a sample

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parameter. Whereas the incident radiation can be changed by the resonance interaction with respect to the following parameters, intensity, polarization, energy and propagation direction, the change of the sample parameters are mostly detected in a cross-modulation experiment concentrating on the d.c. electronic properties hence a photo response detection. Depending on the carrier concentration the dielectric properties of the sample may vary over a wide range so that transmission, reflection, or even multi-reflection set-ups in the strip line realization may be favorite. (4~The carrier concentration may be actually so high that the attenuation of the radiation is so large that the radiation field cannot anymore be considered as constant over the characteristic dimension of the electronic state function and the usual local approximation of the dielectric function ~(k = 0, co, B) has to be replaced by the inclusion of non-local effects in the form of an explicitely k-dependent ~(k, co, B). (9) Different types of experiments using d.c. magnetic fields up to 18 T and pulsed fields up to the MegaGauss regime are presented and discussed within the corresponding theoretical framework in the following. III. S E L E C T E D E X A M P L E S OF S U B M I L L I M E T E R M A G N E T O S P E C T R O S C O P Y ON M A G N E T I C A N D S E M I C O N D U C T I N G SYSTEMS Due to the increased manifestation of many-body correlation effects in lower dimensions, D < 3, an increasing interest for such systems has been observed in the past for both magnetic and semiconducting materials. For magnetic materials the Haldane conjecture for a one-dimensional, antiferromagnetically coupled spin chain of S = I "°) and for semiconductors the Quantum Hall Effect are the well known exponents. "~

Spin resonances in the Haldane-gap materials NENP and NINO Haldane has conjectured that a one-dimensional linear spin chain with antiferromagnetic coupling and S = 1 differs from a corresponding spin chain with S = 1/2 by the existence of an energy gap between the ground and the first excited state. This theoretical postulation has stimulated materials science to define and grow appropriate materials with the most realistic representation of this concept. Of course, not a single linear spin chain could be realized, but materials with a regular pattern of chains along the c-axis of the crystallographic structure

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embedded in an almost inert environment: N E N P , N I N O and N I N A Z are some of the materials investigated now as shown schematically for N E N P in Fig. 4. tt°~ The linear spin chains manifest by S = I components formed by a valence bond solid like combination of two S = !/2 spins of the Ni-ions. In contrast to semiconductors for magnetic materials the electrons are localized and the actual spatial distribution of the electrons is irrelevant but manifests in an orientation dependent exchange interaction. The dominant exchange interaction is only along the chain direction, whereas the inter chain interaction is weak, however not negligible, and differs from material to material. The contribution of these anisotropy terms to the total Hamiltonian requires that the Haldane gap cannot be measured directly, but has to be evaluated from a detailed analysis of the magnetic field dependent transitions within the system of one singlet ground state and a triplet excited state, as shown in Fig. 5. "°~ To corroborate the Haldane conjecture has been a demanding challenge for submillimeter magnetospectroscopy. In Fig. 6 we represent some typical transmission curves, demonstrating by both intensity and line width the different quality of the transitions for the two magnetic field ranges separated by B c. The data are obtained by an optically pumped submiilimeter wave-guide laser and a superconducting solenoid. They show clearly resonant transmission minima without any distortion by interference effects as are familiar for strong resonances in the interaction process. Please note that at Bc the quantum numbers of the ground state [S = 0, S_. = 0~ change due to level crossing to [S = 1, S: = - 1~>, so that the interaction matrix element changes from forbidden to allowed in magnetic dipole approximation. This change of the ground state from non-magnetic S = 0 to magnetic S = 1 properties has also been observed in the corresponding

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measurement of the magnetization. (13) A summary of the different resonance positions is given in Fig. 7 together with theoretical transitions energies within the model of an effective single spin hamiltonian. Please note that the magnetic field dependence of the transitions cannot be explained by the anisotropy term, but require definitely the energy Eg of the Haldane gap. Special attention should be given to the range of the level crossing. An experimental study with subsequent analysis shows that the direct crossing is lifted by an additional interaction between the IS = 0, S_. = 0) and S = 1, IS: = - 1 ) states, so that the actual states are a mixture of the two pure states and repel each other. This interaction is probably also responsible for the breaking of the selection rule for the observed transitions for magnetic fields below B,. The temperature dependence of these transitions can only be explained by a temperature dependent matrix element in addition to thermodynamic population effects.(14)To map the transition energies near Be requires a continuous variation of the radiation energy for long wavelength, which can be obtained by application of bwos. To extract the typical elements of the Haldane concept out of experimental data, materials with different intra and inter exchange coupling of the chains have to be investigated. A slight modification of the embedding matrix is encountered for NINO and NINAZ. In Fig. 8 a preliminary result for NINO is shown. 05) The nearly continuous variation of the radiation energy indicates the application of bwos. The plotted branch of the transition energies corresponds to the forbidden [S = 0, S = 0 ) to IS = 1, S: = + 1 ) and IS = 0, So) to IS = 1, S_.= 0) transitions. So far the transitions to the other excited states have not been detected for unknown reason. The above results for magnetic resonances in Haldane gap materials demonstrate the efficiency of monochromatic submillimeter radiation in magneto spectroscopy, but also indicate the vast area of research still open in the investigation of spin resonances.

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Landau level resonances in semiconducting HgSe The essential feature of semiconductors is the presence of mobile charge carriers in delocalized states. These states and corresponding energy levels are easily controlled and tuned via an external magnetic field and condense into a system of spin split Landau levels. The state function represents the total intrinsic interactions with the lattice via Coulomb and spin energies. From the corresponding energy/wavenumber relation E(k) the most important parameters of the effective mass m* can be obtained. Since the Landau quantization is essentially a spatial quantization as characterized by the parameter of the magnetic length Rc = (h/eB) ~/2 any additional potential fluctuation over a distance of R¢ will also change the resulting energy levels. For a field of B = I 0 T, Rc = 8 nm. In this way magnetospectroscopy is the most suitable experimental method for the investigation of nanostructured systems, which have raised more and more interest due to the application potential, c~6~ Among semiconducting materials there is an increasing tendency to engineer materials according to technological requests. Whereas in the early stages of semiconductor application the elementary materials Ge and Si were dominant, now for advanced applications compound materials of the III-V-class are used. In expectation of more complex applications in the form of integrated lasers, detectors and other sensors recently special attention is paid to epitaxial layers of the semiconducting II-VI-group as, i.e., HgSe and related semimagnetic compounds, where the cyclotron resonance manifests in a multi-line spectrum. {2~)In HgSe:Fe the Fe-ion manifests as a donor about 210 meV above the conduction band edge and thus degenerate with the quasi-free conduction band states. At the limit of an Fe-concentration of riFe = 5 x 10 ~scm -3 the Fermi energy enters the donor level and henceforth a Fermi-level pinned system in the mixed valence regime of Fe 2+- and Fe 3~ -ions is created. The special feature of this system is a pronounced mobility increase of the declocalized carriers and hence a considerable narrowing of the line width of any corresponding resonance.

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These effects have been studied in samples of bulk material. Due to the high carrier concentration of n = 5 x 10 ~8cm -3 of the Fermi-level pinned system no transmission of submillimeter radiation could be detected even for the thinnest samples of HgSe:Fe with a thickness of 2/~m. To escape this unfavorable experimental situation reflection experiments were considered. To increase the weak magnetic field dependent structure in the reflection of the cyclotron resonance of a nearly totally reflecting sample a multireflection experiment was performed in a strip line arrangement, a microscopic, single moded wave-guide whose one confining wall is made of the material under investigation3 4) The attenuation of the strip line reflects directly the magnetic field dependent structure of the dielectric tensor function as shown for the orientation of the strip line propagation parallel to the external magnetic field in Fig. 9 for various radiation frequencies, tg) The strip line transmission curves show a multi line spectrum with different resonance intensity. In Fig. 10 we have summarized the resonance positions in a scaling plot and verify by extrapolation to the origin for zero magnetic field the quality of free-carrier resonances. The slopes of the extrapolation lines are in harmonic ratio. The striking fact is that a carrier system with isotropic Fermi surface, as in HgSe:Fe, should not exhibit any resonances in the dielectric tensor component cz:(k = 0, co) which becomes effective in the parallel configuration, since no tilted orbit resonances are present, t4~ This result holds, however, only for the local approximation of the dielectric tensor. In HgSe:Fe, however, the attenuation of the radiation field is so strong that the skin depth becomes comparable to Rc and non-local effects have to be included and require the detailed calculation of the k-depence of c=(k, From the view of classical physics this means that retardation effects of the radiation have to be included with respect to the reference system of the moving electron. For the quantum mechanical treatment we have to replace the vacuum radiation field by the effective wave in the medium with its actual non-negligible (O).

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space dependence resulting in non-zero transition matrix elements for the polarization parallel to the magnetic field for the fundamental and harmonic cyclotron resonances, In Fig. 11 we have plotted both experimental data and simulation based on the classical concept for the parallel and perpendicular strip line configuration. Please note that even the relative intensities of the resonances are reproduced correctly for the different configurations. °~ This experiment allowed for the first time to measure the cyclotron mass of HgSe:Fe at the Fermi energy. The obtained high accuracy value is me = (0.064 ___0.002) • m0, which is the mass of the undoped material HgSe, thus indicating that there is no measureable hybridization of the Fe 2÷-donor states and the quasi-free band states. After an effort over many years, also for the first time, HgSe and the semimagnetic modification HgSe:Fe were successfully grown as epitaxial layers and elucidated now for the latter in high quality samples the characteristics of a Fermi-level pinned system with extremely high carrier mobility. ~s) These materials offer a special advantage for device technology of the next generation making use of the special features of low-dimensional structures. The connection of these frontiers in materials engineering and magnetospectroscopy results in a feed-back also in the extension of the limits of the experimental method: to apply a direct magnetotransmission experiment the range of the submillimeter radiation has to be overrun into the infrared with higher frequencies. Higher frequencies, however, involve also higher magnetic fields in the MegaGauss range. These fields cannot be generated continuously and are excited only by short pulses in the order of some /~s.C5) Whereas the usual experimental setup for quasi continuous and slow pulse fields allows the application of phase sensitive modulation to increase the signal to noise ratio of the data, 1'9~ this technique cannot be used for MegaGauss fields. The magnetic field and hence time dependent signal has to be recorded directly. Nevertheless the progress in high-tech equipment allows to record also these data in superior quality as shown in Fig. 12. ~2°~ Here the magneto transmission spectra for CO2-1aser radiation through an epitaxial layer of HgSe on GaAs are plotted as a function of the magnetic field for different temperatures. Again we observe a pronounced multi-line resonance spectrum. The splitting of the two dominant double peak structures is due to the spin splitting in agreement with theoretical models. The origin and strong temperature dependence of the high field peaks, however, cannot be explained so far.

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SUMMARY

The discussed data demonstrate the strong mutual stimulation of both new material research and experimental analysis using magneto spectroscopy. New materials require novel experimental techniques for the characterization and extended possibilities in advanced analytic methods, which in turn allow the testing of more sophisticated materials. The extrapolation of this concept into the future promises an exciting development for the application of monochromatic submillimeter radiation and the neighbouring frequency ranges. REFERENCES 1. H. A. Gebie, F. D. Finlay, N. W. B. Stone and J. A. Ross, Nature, Lond. 202, 169 (1964). 2. N. G. Douglas, Millimetre and Submillimetre Wavelength Lasers. Springer Series in Optical Science. Springer, Berlin (1989). 3. E. A. Vinogradow, 2nd Int. Conf. on Millimeter and Far-Infrared Technology, Beijing, China (Edited by Gail M. Tucker), p. 261. Publishing House of Electronics Industry (1992). 4. M. von Ortenberg, Infrared and Millimeter Waves (Edited by K. J. Button), Vol. 3, p. 275. Academic Press, New York (1989). 5. N. Miura and F. Herlach, in Strong and Ultrastrong Magnetic Fields (Edited by F. Herlach), p. 23. Springer, Berlin (1985). 6. G. Dresselhaus, A. F. Kip and C. Kittel, Phys. Rev. 92, 827 (1953). 7. T. L. Cronburg and B. Lax, Phys. Lett. 37A, 135 (1971). 8. M. von Ortenberg, O. Portugall, H.-U. Miiller, N. Puhlmann, G. Machel, M. Barczewski and J. Breitlow-Hertzfeld, Proc. Int. Symp. Frontiers in High Magnetic Fields (Edited by N. Miura), Physica, in press.

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9. K. Buchholz-Stepputtis, O. Portugall, M. von Ortenberg and W. Dobrowolski, Proc. 21st Int. Conf. on the Physics of Semiconductors, Beijing, p. 1844 (1992). 10. F. D. H. Haldane, Phys. Rev. Lett. 50, 1153 (1983). 11. K. yon Klitzing, G, Dorda and M. Pepper, Phys. Rev. Lett. 67, 494 (1980). 12. W. Lu, J. Tuchendler, M. yon Ortenberg and J. P. Renard, Phys. Rev. Lett. 67, 3716 (1991). 13. K. Katsumata, H. Hori, T. Takeuchi, M. Date, A. Yamaguchi and J. P. Renard, Phys. Rev. Lett. 63, 86 (1989). 14. W. Lu, J. Tuchendler, M. yon Ortenberg and J. P. Renard, Physica B177, 393 (1992). 15. S. Luther, M. von Ortenberg, J. Tuchendler and J. P. Renard, Physica, in press. 16. M. von Ortenberg, Proc. Int. Syrup. Frontiers in High Magnetic Fields (Edited by N. Miura), Physica, in press. 17. M. yon Ortenberg, Physica B184, 432 (1993). 18. D. Schikora, T, Widmer, R. Schoenfeld, C. Giftge, M. von Ortenberg, H. Hausleitner, M. Lang, K. H. Grel~lehner, K. Lischka, K. Lfibke, C. R. Becker and S. Einfeldt, Proc. 6th Int. Conf. on I1- VI-Compounds and Related Optoelectronic Material, Newport, R.I. (1993). 19. M. von Ortenberg, W. Staguhn, F. BSbel, S. Takeyama, T. Sakakibara and N. Miura, J. Phys. E22, 359 (1989). 20. O. Portugall, N. Miura, G. Bauer, R. Schoenfeld and M. yon Ortenberg, Proc. Int. S.vmp. Frontiers in High Magnetic Fields (Edited by N. Miura), Physica, in press.