Magnetoacoustic resonance attenuation in Ga-doped Ge

The magnetoacoustic resonance attenuation (MARA), which is observed in Ga-doped Ge under strong magnetic field at low temperatures, is studied in detail by varying the acoustic frequency, the temperature, the magnetic field direction, the acceptor concentration, the acoustic power, the acoustic mode, the propagation direction, and the uniaxial stress. The experimental results are explained semiquantitatively in terms of the acceptor-hole-lattice interaction in the effective-mass approximation by taking account of the presence of the distributed local splittings and the quadratic Zeeman effect in addition to the linear Zeeman effect. Consequently, the Zeeman-splitting parameters of the ground state in Ga-doped Ge are obtained. The $g$ values are ${g_{\frac{1}{2}}}^{\prime }=-0.14\mathrm{}\pm 0.07$ and ${g_{\frac{3}{2}}}^{\prime }=0.02\mathrm{}\pm 0.03$ for $\overrightarrow{\mathrm{H}}\parallel \mathrm{}\left[001\right]\mathrm{}$. The discrepancy between the present results and the results derived from the magneto-optical absorption by Soepangkat and Fisher is resolved by proposing a new assignment of their magneto-optical spectra. The coefficients of the quadratic Zeeman effect are $q_2=(0.5\mathrm{}\pm 0.2)\times {10}^{-4\mathrm{}}$ K/k${\mathrm{G}}^2$ and $q_3=-(0.6\mathrm{}\pm 0.2)\times {10}^{-5\mathrm{}}$ K/k${\mathrm{G}}^2$. The present $g$ values, which are very small compared with the effective-mass calculations, seem to be consistent with the measured magnetothermal conductivity and the present status of the ESR study. From the line shape of the MARA, we evaluated the initial splittings of the acceptor ground-state. When we assume that their distribution is represented by the Gaussian form, the average splitting ${\Delta }_0$ and the variance $\sigma$ are obtained as -0.02 ± 0.006 K and 0.03-0.05 K, respectively.