Magnetophonon Resonance

Magnetophonon resonance was first predicted theoretically by Gurevich and Firsov in 1961 and was observed experimentally in 1964 using InSb by Puri and Geballe and Firsov et al. There have been several review articles [1-3] written on the subject. MPR has been seen in many semiconducting materials and alloys including: silicon; III-V e.g. InSb, GaAs and II-VI semiconductors e.g. CdTe, both for bulk and reduced dimensional materials.

Magnetophonon Resonance (MPR) is an additional scattering mechanism that occurs whenever the energy of an optic phonon is equal to an integer multiple N of the cyclotron energy. Under this condition electrons (or holes) may be resonantly scattered between Landau levels (LLs) by either emitting or absorbing an optic phonon.

The phonon involved is usually the bulk longitudinal optic (LO) phonon, as in this mode the motion of atoms within the crystal produces a bulk polarisation field with which the electron interacts.

The additional scattering at the MPR condition may be detected by measuring most transport coeffients as well as in optical absorption and cyclotron resonance. Very often it is detected via the electrical resistivity measured as a function of magnetic field. This shows a series of maxima, periodic in inverse magnetic field, as the resonance condition is satisfied for different numbers of LLs N being conincident with the phonon energy. By measuring the positions of these maxima values of the phonon energy and/or the electron effective mass in the material can be obtained.

MPR has a characteristic temperature dependence. At very low temperatures (where the thermal energy is much less than the LO phonon energy) the LO phonon population is small, thus electon-LO phonon scattering is negligable and MPR is not seen. At very high temperatures the LLs become very broad and, although electon-phonon scattering is strong the resonances disappear. Between these two limits the MPR amplitude will reach a maximum. The temperature at which the maximum occurs depends on the material as does the amplitude.

In all the early work, the resonances in the magnetoresistance could be described as a damped cosine series [4] .
In fact theory [5] predicted this expression as the first term in a series including higher harmonics. Experimentally the harmonics give rise to a peak sharpening, which was also observed for light mass materials like InSb.

In 2D systems the LLs are much sharper than for bulk materials so strong MPR is observed.

The figure shows a direct recording (blue curve) of the magnetoresistance of a GaAs-GaAlAs heterojunction in which N=1, 2 and 3 MPR features are clearly observed. The oscillations are enhanced in the red curve where the increasing background has been subtracted.

The cosine dependence arises when the Landau level width is fixed and the resonant electron-LO phonon interaction just varies the scattering rate. In all but the highest mobility heterostructures the LL width is determined by impurity scattering and so this is the case.

However, in extremely high mobility structures, with virtually no impurities, the Landau level width also depends strongly on the electron-LO phonon interaction, and more so the higher the magnetic field. At the MPR resonance condition the additional scattering broadens the LLs, which suppresses any increase in resistance. The result is that at the highest magnetic fields, where the strongest MPR might have been expected, it actually disappears in very high mobility samples!

This discovery can also be used to explain the MPR temperature dependence in all materials:

• At low temperature the LL width and the resistivity are both dominated by elastic impurity (or acoustic phonon) scattering, so MPR due to inelastic LO phonon scattering is not observed.
• At intermidiate temperatures the LL width depends on elastic scattering, but the resistivity is significantly influenced by LO phonon scattering, so MPR is strong.
• At the highest temperatures the LL width is also dominated by LO phonon scattering so there is no MPR.

Similarly the absence of observed magnetophonon resonsnce in the alkali halides can be explained. As these crystals are ionic the electron-phonon coupling is enormous, ~50 times larger than in the covalent semiconductor crystals, so MPR might be expected to be a very strong effect. While it is true that LO phonon scattering is the dominant scattering mechanism, it also determines the LL width so no resonances will appear.

For more details see my published MPR papers and the following reviews:

1. R.J. Nicholas, Prog. Quantum Electron. 10, 1 (1985)
2. R.J. Nicholas, in Landau Level Spectroscopy, Ed. G. Landwehr and E.I. Rashba (Elsevier, Amsterdam, 1991) p.777.
3. R.L. Pearson, in Semiconductors and Semimetals, Ed. R.K. Willardson and A.C. Beer (Academic Press, New York, 1975) Vol. 10, p.221.
4. R.A. Stradling and R.A. Wood, J. Phys. C, 1, 1711 (1968)
5. J.R. Barker, J. Phys. C, 5, 1657 (1970)

Last updated 06/02/97 by David Leadley

All rights reserved. Text and diagrams from this page may only be used for non-profit making academic excerises and then only when credited to D.R. Leadley, Warwick University 1997.