Nuclear effects in Kerr rotation-detected magnetic resonance of electrons in GaAs
Introduction
Applications in spintronics and quantum information require electron spin states which can be manipulated and have good spin properties [1]. Long spin lifetimes are essential to prevent loss of information encoded in the electrons’ spin. Electron spins in GaAs are good candidates for spin qubits, as has been shown by the long spin lifetimes previously reported for electrons in bulk n-type GaAs [2], [3], [4], [5], [6], electrons in GaAs-related self-assembled quantum dots [7], and electrons in gated GaAs [8], [9], [10], [11], [12], [13] and GaAs-related [14] nanostructures.
Electron spin resonance techniques (ESR), including optically detected magnetic resonance (ODMR), provide a well-established tool for studying and manipulating spins [15], [16]. As opposed to the now-standard technique of time-resolved Faraday or Kerr rotation [17], which observes the precession of spins in the transverse plane of the Bloch sphere, ESR induces transitions between the spin-up and spin-down eigenstates and under the right conditions can make coherent rotations of the spin vector possible, for example, to observe Rabi oscillations and spin echoes.
Despite early success in p-type materials [18], ESR of electrons in n-type GaAs has proven more elusive. n-type material is desirable from a quantum information point of view, because only with added dopants can the spin lifetime extend beyond the optical lifetime. Aside from recent experiments in gated quantum dots [19], [20], the increased hyperfine interaction between electrons and nuclei that is present when electrons are localized has seriously impacted ESR experiments in GaAs. Thus, the only ESR experiments in bulk n-GaAs of which we are aware are high-field measurements by Seck et al. [21], and Kennedy et al. [22], where the electron–nuclei interaction substantially impacted the resonance lineshapes, and low-field measurements by Colton et al., where deliberate steps were taken to remove that interaction [23], [24]. The objectives of this work were to perform ODMR of electrons in n-type GaAs at moderate fields as a necessary prerequisite for coherent spin rotations, and to study and control the nuclear effects on the electron spins.
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Material and methods
The samples described in this paper are an GaAs layer, and a multi-quantum well (QW) sample modulation-doped at . The quantum well sample has wells of 2.8, 4.2, 6.2, 8.4, and 14 nm [25]; all of our results reported here are from the 14 nm well, which was selected by tuning our probe laser to the optical transition of that well. These two samples have been studied by several groups which have reported on the exciton and trion fine structure [25], as well as spin
Results and discussion
In spin resonance experiments, the peak position yields the -factor: ; and the peak width yields the spin lifetime: . Fig. 1 displays typical ODMR peaks of our two samples, with deduced QW -factors of −0.444 and −0.346 for the bulk and QW samples, respectively (negative signs taken from the literature). The bulk value is consistent with other measured values by our group and others [18], [22], [24]. The QW value matches the value given by Snelling et al.
Conclusions
In summary, we have used Kerr rotation to measure electron and nuclear spin properties in two n-type GaAs samples. We have measured and for electrons in a bulk sample and and for a 14 nm quantum well. Dynamic nuclear polarization caused by the electron–nuclear hyperfine interaction was significant–once polarized, the nuclear spins relaxed with a characteristic time of 2.7 min–but was controllable by resonating the three nuclear isotopes.
Acknowledgement
This work was supported by NSF grants 0419501, 0456074, and 0802831.
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Present address: School of Physics, Georgia Institute of Technology, Atlanta GA 30332, USA.
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Present address: 320 PAR Bldg, Cavalier Air Force Station, ND 58220, USA.