Mathematical Modelling of Bloch NMR to Explain the Rashba Energy Features

Moses E. Emetere

Department of Physics, Federal University of Technology Minna, Minna, Nigeria.

DOI: 10.4236/wjcmp.2013.31015                

Abstract

The Bloch NMR as an analytical tool was able to address the fundamental features in the learning of spintronics. Beside confirming past assertions on the Rashba spin-orbit interaction, thermal motion of hole and electron spin and features of the quantum well, it was also able to explain the condition necessary for Rashba splitting within the quantum well. When the Rashba energy is 43 meV, it modified the Ehrenfest’s theorem to hold for an external magnetic field. The confinement potential which is the strength of the Rashba spin-orbit interaction was shown to be controlled magnetically.

Keywords

Bloch NMR; Rashba Energy; Rashba Parameter; Quantum Well; Spin-Plit; Hole Spin Velocity

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	O. B. Awojoyogbe, “A Mathematical Model of Bloch NMR Equations for Quantitative Analysis of Blood Flow in Blood Vessels with Changing Cross-section II,” Physica A: Statistical Mechanics and Its Applications, Vol. 323, 2003, pp. 534-550. doi:10.1016/S0378-4371(02)02025-3
[2]	O. B. Awojoyogbe, “Analytical Solution of the Time Dependent Bloch NMR Equations: A Translational Mechanical Approach,” Physica A: Statistical Mechanics and Its Applications, Vol. 339, No. 3-4, 2004, pp. 437-460. doi:10.1016/j.physa.2004.03.061
[3]	E. P. Wigner, “On the Quantum Correction for Thermodynamic Equilibrium,” Physical Review, Vol. 40, No. 5, 1932, pp. 749-759. doi:10.1103/PhysRev.40.749
[4]	U. E. Uno and M. E. Emetere, “Analysis of the High Temperature Superconducting Magnetic Penetration Depth Using the Bloch NMR Equations,” Global Engineers and Technologist Review, Vol. 2, No. 1, 2012, pp. 14-21.
[5]	C. Benett and D. Di Vincenzo, “Quantum Information and Computation,” Nature, Vol. 404, 2000, pp. 247253. doi:10.1038/35005001
[6]	S. Yuasa, T. Nagahama, A. Fukushima, Y. Suzuki and K. Ando, “Giant Room-Temperature Magnetoresistance in Single-Crystal Fe/MgO/Fe Magnetic Tunnel Junctions,” Nature Materials, Vol. 3, No. 12, 2004, pp. 868-871. doi:10.1038/nmat1257
[7]	S. Parkin, C. Kaiser, A. Panchula, P. Rice, B. H. M. Samant and S. H. Yang, “Giant Tunnelling Magnetoresistance at Room Temperature with MgO(100) Tunnel Barriers,” Nature Materials, Vol. 3, 2004, pp. 862-867. doi:10.1038/nmat1256
[8]	T. Dietl, “Magnetic Anisotropy and Domain Structure in Carrier-Controlled Ferromagnetic Semiconductors,” Journal of Physics: Condensed Matter, Vol. 16, No. 48, 2004, p. S5471. doi:10.1088/0953-8984/16/48/001
[9]	T. Dietl, “Magnetic Anisotropy and Domain Structure in Carrier-Controlled Ferromagnetic Semiconductors,” Proceedings 27th International Conference on Physics of Semiconductors, Flagstaff, 2004, pp. 56-60.
[10]	F. H. L. Koppens, et al., “Driven Coherent Oscillations of a Single Electron Spin in a Quantum Dot,” Nature, Vol. 442, 2006, pp. 766-771. doi:10.1038/nature05065
[11]	Z. Wilamowski, W. Jantsch, N. Sandersfeld, M. Muhlberger, F. Schaffler and S. Lyon, “Spin Relaxation and g-Factor of Two-Dimensional Electrons in Si/SiGe Quantum Wells,” Physica E: Low-Dimensional Systems and Nanostructures, Vol. 16, No. 2, 2003, pp. 111-115. doi:10.1016/S1386-9477(02)00582-9
[12]	Y. Bychkov and E. I. Rashba, “Oscillatory Effects and the Magnetic Susceptibility of Carriers in Inversion Layers,” Journal of Physics C: Solid State Physics, Vol. 17, No. 33, 1984, pp. 6039-6045.
[13]	E. I. Rashba, “Theory of Electrical Spin Injection: Tunnel Contacts as a Solution ofthe Conductivity Mismatch Problem,” Physical Review B, Vol. 62, No. 24, 2000, pp. R16267-R16270. doi:10.1103/PhysRevB.62.R16267
[14]	F. Meier, V. Petrov, S. Guerrero, C. Mudry, L. Patthey, J. Osterwalder and J. H. Dil, “Unconventional Fermi Surface Spin Textures in the BixPb1-x/Ag(111) Surface Alloy,” Physical Review B, Vol. 79, No. 24, 2009, pp. 241408-241412. doi:10.1103/PhysRevB.79.241408
[15]	J. Nitta, T. Akazaki and H. Takayanagi, “Gate Control of Spin-Orbit Interaction in an Inverted In0.53Ga0.47As/ In0.52Al0.48As Heterostructure,” Physical Review Letters, Vol. 78, No. 7, 1997, pp. 1335-1338. doi:10.1103/PhysRevLett.78.1335
[16]	S. V. Eremeev, I. A. Nechaev, Y. M. Koroteev, P. M. Echenique and E. V. Chulkov, “Ideal Two-Dimensional Electron Systems with a Giant Rashba-Type Spin Splitting in Real Materials: Surfaces of Bismuth Tellurohalides,” Physical Review Letters, Vol. 108, No. 24, 2012, pp. 246802-246807. doi:10.1103/PhysRevLett.108.246802
[17]	Y. A. Bychkov and E. I. Rashba, “Properties of a 2D Electron Gas with Lifted Spectral Degeneracy,” JETP Letters, Vol. 39, No. 2, 1984, pp. 78-83.
[18]	L. Petersen and P. Hedegard, “A Simple Tight-Binding Model Of Spin-Orbit Splitting Of Sp-Derived Surface States,” Surface Science, Vol. 459, No. 1-2, 2000, pp. 49-56. doi:10.1016/S0039-6028(00)00441-6
[19]	J. P. Stanley, N. Pattinson, C. J. Lambert and J. H. Jefferson, “Rashba Spin-Splitting in Narrow Gap III-V Semiconductor Quantum Wells,” Physica E: Low-Dimensional Systems and Nanostructures, Vol. 20, No. 3-4, 2004, pp. 433-435. doi:10.1016/j.physe.2003.08.052
[20]	M. I. Dyakonov and V. Y. Kachorovskii, “Spin Relaxation of Two Dimensional Electrons in Noncentrosymetric Semiconductors,” Soviet Physics: Semiconductors, Vol. 20, 1986, pp. 110-116.
[21]	D. Pacilé, C. R. Ast, M. Papagno, C. Da Silva, L. Moreschini, M. Falub, A. P. Seitsonen and M. Grioni, “Electronic Structure of an Ordered Pb∕Ag(111) Surface Alloy: Theory and Experiment,” Physical Review B, Vol. 73, No. 24, 2006, pp. 245429-245435. doi:10.1103/PhysRevB.73.245429
[22]	C. R. Ast, K. Kern and M. Grioni, “Giant Spin Splitting through Surface Alloying,” Physical Review Letters, Vol. 98, No. 18, 2007, pp. 186807-186811. doi:10.1103/PhysRevLett.98.186807
[23]	K. He, T. Hirahara, T. Okuda, S. Hasegawa, A. Kakizaki and I. Matsuda, “Spin Polarization of Quantum Well States in Ag Films Induced by the Rashba Effect at the Surface,” Physical Review Letters, Vol. 101, No. 10, 2008, pp. 107604-107608. doi:10.1103/PhysRevLett.101.107604
[24]	E. Frantzeskakis, S. Pons, H. Mirhosseini, J. Henk, C. R. Ast and M. Grioni, “Tuning of Spin-Gaps at Silicon Interfaces,” Physical Review Letters, Vol. 101, No. 19, 2008, pp. 196805-196809. doi:10.1103/PhysRevLett.101.196805
[25]	R. F. Pierret, “Semiconductor Device Fundamentals,” Prentice Hall, New York, 1995.
[26]	P. Harrison, “Quantum Wells, Wires and Dots,” Wiley, New York, 2005. doi:10.1002/0470010827
[27]	Y. A. Serebrennikov, “Single-Hole Spin Dephasing in Bulk Crystals,” Physical Review B, Vol. 71, No. 23, 2005, pp. 233202-233206. doi:10.1103/PhysRevB.71.233202
[28]	D. Culcer and R. Winkler, “Spin Polarization Decay in Spin-1/2 and Spin-3/2 Systems,” Physical Review B, Vol. 76, No. 19, 2007, pp. 195204-195210. doi:10.1103/PhysRevB.76.195204
[29]	R. Winkler, “Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems,” Springer-Verlag Berlin Heidelberg, New York, 2003. doi:10.1007/b13586
[30]	Eerdunchaolu, W. Xin and Y.-W. Zhao, “Influence of Rashba SOI and Polaronic Effects on the Ground-State Energy of Electrons in Semiconductor Quantum Rings,” Chinese Physics Letters, Vol. 27, No. 1, 2010, pp. 017201-017201. doi:10.1088/0256-307X/27/1/017201