Anisotropic magneto-optical effects in one-dimensional diluted magnetic semiconductors

Yukihiro Harada, Takashi Kita, Osamu Wada, and Hiroaki Ando

Phys. Rev. B 74, 245323 – Published 19 December 2006

Abstract

Anisotropic magnetic-field evolution of the valence-band states in ideal ${Cd}_{1 - x} {Mn}_{x} Te$ quantum wire structures have been studied theoretically by using multiband effective-mass method. The heavy- and light-hole bands show significant mixing owing to both the one-dimensional quantum confinement and the p-d exchange interaction. Because of the anisotropy of the initial quantization condition determined by the one-dimensional confinement, the Zeeman diagram of the valence bands exhibits anisotropic characteristics depending on the direction of the external magnetic field. According to the magnetic-field evolution of the valence-band states, the optical transition probability shows a dramatic change in the polarization.

Received 6 October 2006

DOI:https://doi.org/10.1103/PhysRevB.74.245323

Authors & Affiliations

Yukihiro Harada, Takashi Kita^*, and Osamu Wada

Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai 1-1, Nada, 657-8501 Kobe, Japan

Hiroaki Ando

Department of Physics, Faculty of Science and Engineering, Konan University, Okamoto 8-9-1, Higashi-Nada, 658-8501, Kobe, Japan

^*Electronic address: kita@eedept.kobe-u.ac.jp

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Vol. 74, Iss. 24 — 15 December 2006

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Images

Figure 1
Configuration of the ${Cd}_{1 - x} {Mn}_{x} Te$ QWR structure with a rectangular cross section. The potential height of the barrier layer is assumed to be infinite. In this calculation, the incident azimuth of the linearly polarized light is along the $z$ direction, and the external magnetic field is applied along the $x$ $(B_{⊥})$ or $y$ $(B_{‖})$ direction. $x$ , $y$ , and $z$ directions are parallel to the [100], [010], and [001] directions, respectively.Reuse & Permissions
Figure 2
(a) AR dependence of the heavy- and light-hole components of the highest valence subband at $Γ_{8}$ . Here, the AR of the QWR cross section is denoted by $L_{z} ∕ L_{x}$ . (b) AR dependence of the linear polarization of the optical transition probability between the lowest conduction and the highest valence subbands at $Γ_{8}$ . The polarization is defined as $P = (I_{‖} - I_{⊥}) ∕ (I_{‖} + I_{⊥})$ , where $I_{‖}$ and $I_{⊥}$ are the optical transition components of the parallel and perpendicular to the QWR, respectively.Reuse & Permissions
Figure 3
Magnetic field dependence of the Zeeman diagram of the valence subbands at $Γ_{8}$ for ${Cd}_{0.90} {Mn}_{0.10} Te$ QWR’s with cross-sectional areas of (a) $13 \times 10 {nm}^{2}$ , (b) $10 \times 10 {nm}^{2}$ , and (c) $7 \times 10 {nm}^{2}$ . The top and bottom display the results in the magnetic field applied perpendicular and parallel to the QWR direction, respectively.Reuse & Permissions
Figure 4
(Color online) Cross-sectional images of the highest valence subband wave function of the envelope components in the QWR with cross-sectional area of $10 \times 10 {nm}^{2}$ . (a), (b), and (c) are results in the zero-magnetic field, the perpendicular magnetic field, and the parallel magnetic field, respectively. Here, the magnitude of the applied magnetic field is $5 T$ . On the other hand, the top, middle, and bottom figures display the total wave function, the heavy-hole component $(j = - 3 ∕ 2)$ , and the light-hole component $(j = 1 ∕ 2)$ , respectively.Reuse & Permissions
Figure 5
Magnetic field dependence of the Zeeman shift of the highest valence subband in the ${Cd}_{0.90} {Mn}_{0.10} Te$ QWR’s with cross-sectional areas of (a) $13 \times 10 {nm}^{2}$ , (b) $10 \times 10 {nm}^{2}$ , and (c) $7 \times 10 {nm}^{2}$ . The solid and dashed lines represent results in the magnetic field applied perpendicular and parallel to the QWR, respectively.Reuse & Permissions
Figure 6
Magnetic field dependence of the linear polarization transition probability at $Γ_{8}$ of the ${Cd}_{0.90} {Mn}_{0.10} Te$ QWR’s with the cross-sectional areas of (a) $13 \times 10 {nm}^{2}$ , (b) $10 \times 10 {nm}^{2}$ , and (c) $7 \times 10 {nm}^{2}$ . As depicted in the inset of (a), closed circles represent the transition from the highest valence subband in the magnetic field perpendicular to the QWR, and open squares and triangles indicate results of the transition from the highest and the second-highest valence subbands in the parallel magnetic field, respectively.Reuse & Permissions

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