In non-magnetic semiconductors the energy splitting between spin-up and spin-down electrons is due to the spin-orbit interactions and is typically limited to about 100 μeV per Tesla. This corresponds to spin precession frequencies of 10's of GHz per Tesla. In magnetic semiconductors, however, the electron spin splitting is enhanced by the exchange interaction, which occurs between electron spin and the spin of the magnetic-ion impurities. In II-VI semiconductors quantum wells, such as ZnCdSe-ZnSe, MnSe magnetic layers can be digitally doped directly within the quantum well, increasing the effective exchange overlap between the electron wave function and magnetic ions (Mn). This increases the effective g-factor up to two orders of magnitude larger than for non-magnetic structures and brings the spin splittings into the meV regime [see Paramagnetic Semiconductors (II-VI)]. Time-resolved optical spin spectroscopy (time-resolved Faraday rotation) allows for the observation of spin precession in these samples at terahertz (THz) frequencies and for the observation of coherent spin precession of magnetic ions.

Electronic control of electron spin dynamics has been accomplished in non-magnetic semiconductor quantum wells, such as parabolic quantum wells [see Electrical Control of Spin Coherence]. The band gap is parabolically graded to achieve a harmonic potential trap for electrons and holes. This grading is achieved by changing the chemical composition on the nanoscale using digital-alloying techniques by molecular beam epitaxy. Applying a vertical bias to such structures shifts the potential minimum along the growth axis. In other words, the bottom of the quantum well translates, and therefore the electron wave function within the well translates along with it. Thus the electron position can be controlled using a simple vertical gate. Since the effective g-factor changes with position, then the g-factor is electrically controlled. High-frequency modulation of such structures has been used to resonantly control electron and nuclear spin confined to these structures [see g-Tensor Modulation Resonance].

Here we describe the magnetic parabolic quantum well, in which vertical biasing is used to move the electron wave function with respect to magnetic ions deposited at the center of the well. This controllable exchange overlap effectively increases the range of g-factor tuning by at least an order of magnitude compared with non-magnetic structures. The samples are fabricated by molecular beam epitaxy in the lab of Professor Nitin Samarth, and consist of ZnCdSe-CdSe parabolic quantum wells. The Cd concentration is graded by digital shuttering to achieve a parabolic band gap profile. Submonolayers of MnSe are deposited at the center of the quantum wells. As shown in the figure below, biasing the structures shift the wave function position with respect to the magnetic layers.

The color intensity figure below shows the Kerr rotation measured as a function of delay time and vertical bias. The figure to the right shows a line cut of this data near 0 V, showing that two precession components are visible, the high frequency electron spin precession at short times, and the slower frequency Mn-ion spin precession persisting to long times. Decreasing the voltage shifts the electron wave function away from the Mn-ions, the effect of which is to reduce the electron spin precession frequency, as seen in the figure.

The effective electron g-factor is extracted from this data and plotted as a function of the vertical bias (open black circles) in the figure below. The total spin splitting in the conduction band is plotted as the right vertical axis in a 3 T magnetic field. Vertical bias is used to tune the spin splitting over 1 meV through controllable exchange overlap. Data shown in red are from a non-magnetic control sample; the inset shows this data on a finer vertical scale. The g-factor (spin splitting) tuning possible in this sample is characteristic of the spin-orbit interaction.

The exchange overlap is also varied by changing the excitation and probe energy of the laser used in this experiment (Ep). In the figure below the effective g-factor (left) and corresponding conduction band spin splitting at 3T (right) are plotted as a function of the Ep. The spin splitting is tunable with laser energy over 2 meV, corresponding to spin precession frequencies varying from 100's GHz to nearly THz.

The origin of this effect is from the difference in quantum well sub-level occupation with laser energy. At low laser energy, only the n=1 ground state of the quantum well is occupied. The electron wave function in this sublevel reaches a maximum over the center of the quantum well, thus the exchange overlap is large. At higher laser energies the n=2 sublevel becomes occupied. The electron wave function at this energy has a minimum (node) at the quantum well center leading to a decrease in the exchange overlap. The sublevel spacing for this parabolic well and the exchange splitting of these levels is calculable and matches well with the data in the figure above.

To learn more about our studies, please refer to "Optoelectronic control of spin dynamics at near-terahertz frequencies in magnetically doped quantum wells", R. C. Myers. K. C. Ku, X. Li, N. Samarth, and D. D. Awschalom, Phys. Rev. B 72, 041302(R) (2005).