Current Induced g-Factor Shift in Modulation Doped Si Quantum Wells
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0984-MM11-02
Current Induced g-Factor Shift in Modulation Doped Si Quantum Wells Hans Malissa1, Wolfgang Jantsch1, Friedrich Schäffler1, and Zbyslaw Wilamowski2 1 Institute of Semiconductor and Solid State Physics, Johannes Kepler University Linz, Altenbergerstr. 69, Linz, 4040, Austria 2 Institute of Physics, Polish Academy of Sciences, Warsaw, Poland
ABSTRACT We report the observation of a particularly simple effect of spin-orbit coupling which allows for efficient manipulation of spins by an electric current in semiconductor nanostructures. Passing an electric current density of j = 2.5 mA cm through a modulation doped Si quantum well (density of 5 ×1011 cm-2 ) perpendicular to an in-plane magnetic field, we observe a shift of the of the conduction electron spin resonance (CESR) by about 0.1 mT . This shift reverses sign when we invert (i) the current direction, (ii) the magnetic field direction and it vanishes for perpendicular magnetic field. We show that this current-induced shift in g-factor, i.e., its dependence on current and carrier density, its temperature dependence and its anisotropy can be consistently and quantitatively explained in terms of the Bychkov-Rashba coefficient determined earlier from the CESR broadening and the g-factor anisotropy [1]. Other sources of magnetic field (e.g. the Oersted effect) are negligible. This effect can be utilized for g-factor tuning, and thus for local spin manipulation: passing a current through some part of a sample may be utilized to bring those electrons into resonance with a microwave field. These spins are thus excited to Rabi oscillations and, using current pulses of suitable duration, π rotations (or by any other angle) can be achieved. INTRODUCTION
The lowest order term in spin-orbit interaction which is linear in the electron momentum hk and its spin σ is allowed only for systems without mirror symmetry [2]. This term leads to spin splitting even at zero magnetic field and can be described in terms of an effective magnetic r r ‘Bychkov-Rashba’ (BR) field BBR = α BR k × zˆ gµB (where zˆ is the direction of the broken r
( )
symmetry, g the Landé g-factor, µB the Bohr magneton and α BR the Bychkov-Rashba parameter which depends on the structure and material) [1]. In solids, the broken mirror symmetry may be imposed by the bulk crystal itself (bulk inversion asymmetry, BIA), by the structure (structure r inversion asymmetry, SIA) or by an electrical field E 0 parallel to zˆ [2]. In a 2D electron gas (2DEG) structure, the electrical field originates from one sided modulation doping, where the donors are located at a distance of about 10 nm from the quantum r well. E 0 zˆ is therefore perpendicular to the 2DEG layer, and in thermal equilibrium, without r
additional fields, the electron momentum vectors hk are distributed randomly within the 2DEG r layer. BBR is thus in-plane but without any preferential direction. In electron spin resonance (ESR) experiments, the
resonance condition hω = gµB B is fulfilled at a value of the magnetic field that r r corresp
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