Crystal-Field and Strain Effects on Minimum-Spin-Splitting Surfaces in Bulk Wurtzite Materials

• Published in: Journal of the Physical Society of Japan 2010-09, Vol.79 (9), p.093705-093705-4
• Main Authors: Wu, Chieh-Lung, Tsay, Shiow-Fon, Wang, Wan-Tsang, Gau, Ming-Hong, Chiang, Jih-Chen, Lo, Ikai, Kao, Hsiu-Fen, Hsu, Yu-Chi, Jang, Der-Jun, Lee, Meng-En, Chen, Chun-Nan
• Format: Article
• Language: English
• Subjects: Condensed matter: electronic structure, electrical, magnetic, and optical properties; Crystal and ligand fields; Electron states; Exact sciences and technology; Level splitting and interactions; Physics
• ISSN: 0031-9015; 1347-4073
• DOI: 10.1143/JPSJ.79.093705

The spin-splitting energies in strained bulk wurtzite aluminum nitride (AlN) are studied using the linear combination of atomic orbital method. It is found that strain and crystal field induce not only a linear-$k$ ($\alpha_{\text{wz}}$) but also two cubic-$k$ terms ($\gamma'$ and $\lambda'$) in the two-band $\mathbf{k}\cdot \mathbf{p}$ Hamiltonian $H_{\text{SO}}(\mathbf{k}) = (\alpha_{\text{wz}}-\gamma'k_{\|}^{2} + \lambda'k_{z}^{2})(\sigma_{x}k_{y}-\sigma_{y}k_{x}) + H_{\text{SO}}^{0}$, where $H_{\text{SO}}^{0} = (-\gamma_{0}k_{\|}^{2} + \lambda_{0}k_{z}^{2})$ $(\sigma_{x}k_{y}-\sigma_{y}k_{x})$ is for ideal wurtzite and generates a cone-shaped minimum-spin-splitting (MSS) surface. As biaxial strain increases, the shape of the MSS surface changes from a hexagonal hyperboloid of two sheets in unstrained AlN to a hexagonal cone, and eventually becomes a hyperboloid of one sheet.