Ultrahigh-field hole cyclotron resonance absorption in ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ films

We have carried out an ultrahigh-field cyclotron resonance (CR) study of $p$-type ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ films, with $\mathrm{Mn}$ composition $x$ ranging from 0 to 2.5%, grown on $\mathrm{GaAs}$ by low-temperature molecular-beam epitaxy. Pulsed magnetic fields up to $500\mathrm{T}$ were used to make cyclotron resonance observable in these low-mobility samples. Clear CR spectra have been observed for all the samples at high fields in the megagauss range and even at room temperature. It was found that the observed cyclotron masses are not significantly dependent on the $\mathrm{Mn}$ concentration, indicating a large number of itinerant, effective-mass-$p$-type holes rather than $d$-like holes exist. It further suggests that the $p\text{−}d$ exchange mechanism is more favorable than the double exchange mechanism in this narrow gap $\mathrm{InAs}$-based dilute magnetic semiconductor. In addition to the fundamental heavy-hole and light-hole cyclotron resonance absorption appearing near the high-magnetic-field quantum limit, we observed many inter-Landau-level absorption bands whose transition probabilities are strongly dependent on the sense of circular polarization of the incident light. It has been found that the detailed theoretical calculation in terms of the effective mass theory explains the most of the CR spectra quantitatively, including the polarization dependence.

Figure 1

Room-temperature cyclotron resonance spectra for ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ with various $x$ taken with hole-active circularly-polarized $5.53$ and $10.6\mu \mathrm{m}$ radiation.

Figure 2

Deduced cyclotron masses (a) and cyclotron mobilities (b) at $291\mathrm{K}$ as functions of $\mathrm{Mn}$ content, $x$. Open circles and open triangles show cyclotron masses at $5.53$ and $10.6\mu \mathrm{m}$, respectively. Closed circles and closed triangles denote the cyclotron mobilities at $5.53$ and $10.6\mu \mathrm{m}$, respectively.

Figure 3

Temperature-dependent cyclotron resonance traces for ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ with (a) $x=0.006$ and (b) $x=0.025$. A new absorption band, labeled $\alpha$, appears at low temperatures.

Figure 4

Temperature dependence of cyclotron mobilities of heavy hole CR at $10.6\mu \mathrm{m}$ for ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ ($x=0,0.006$,0.025). The dashed curve is a guide for the eyes for the $\mathrm{InAs}$ data.

Figure 5

Cyclotron resonance in ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ $\left(x=0.006\right)$ at multi-megagauss fields. Only the HH CR is observed at $3.39\mu \mathrm{m}$ and $14\mathrm{K}$. The absorption band observed at low fields and low temperatures for the wavelength of $5.53\mu \mathrm{m}$ (the band labeled $\alpha$) is not observed. The absorption band observed at high field over $300\mathrm{T}$ for $10.6\mu \mathrm{m}$ ends at around $450\mathrm{T}$ due to the destruction of the flux compression method. However, we obtained nearly the same CR spectrum in $\mathrm{InAs}$ (not shown) by another experiment. Hence, it is suggested that the absorption around the $450\mathrm{T}$ shown in the figure is not an artifact but the CR absorption.

Figure 6

Summary of the observed hole-active cyclotron resonance peak positions for four samples with different $\mathrm{Mn}$ contents. The solid curves are calculations based on an 8-band effective mass model for bulk $\mathrm{InAs}$.

Figure 7

Calculated Landau levels of the valence band at the $\Gamma$ point and CR absorption as functions of the magnetic field for $x=0$ at $20\mathrm{K}$. The Fermi energy corresponding to the hole concentration $1\times {10}^{19}{\mathrm{cm}}^{-3}$ is also shown as the dashed line. The lower panel shows the CR spectrum which corresponds to the inter-Landau-level transitions shown in the upper panel.

Figure 8

Calculated energy $E$ versus wavevector $k$ (in the magnetic field direction) for $B=350\mathrm{T}$.

Figure 9

Cyclotron resonance in ${\mathrm{In}}_{1-x}{\mathrm{Mn}}_x\mathrm{As}$ ( $x=0$, 0.006) at $10.6\mu \mathrm{m}$ (the upper part of the figure) and at $5.53\mu \mathrm{m}$ (the lower part of the figure). The right hand side of the figure corresponds to the results using the hole active circularly polarization of the radiation and the left hand side of the figure shows the results using the electron active circularly polarization.

Figure 10

Calculated CR spectra which can be directly compared to the experimental results shown in Fig. 9.