Self-assembled quantum dots (QDs) are unique structures in which to study spin coherence in zero-dimensions. They can be gated, doped, or put into more complicated heterostructures to tune their energy spectrum, control carrier occupancy, or modify coupling to the environment or neighboring dots. Such control may help to elucidate the underlying physics as well as enable new device paradigms. The InAs QDs studied here are grown with a partially-covered island technique which allows the ground-state energy of the QDs to be adjusted by changing the dot size and shape. Below (left) is a graph of photoluminescence (PL) intensity vs. detection energy for three samples with emission from the GaAs host at 1.52eV, the InAs wetting layer at 1.45eV, and several QD energy levels. At right is an AFM image showing the random distribution and excellent (<5%) size distribution.
The Hanle effect uses the degree of circular polarization r of photons from recombination to measure the component of carrier spin along the direction of observation. As illustrated in the inset below, a magnetic field along z causes the spins (initially along x) to precess in the x-y plane at the Larmor frequency W, which decreases the time-averaged spin along x. The time-averaged spin as a function of magnetic field gives the Lorentzian Hanle curve:
where Ω=2ΠgμBB/h , g is the Lande g-factor, and μB is the Bohr magneton. The curve width is inversely proportional to the effective transverse spin lifetime 1/T2*=1/ τr+1/τs. The experiment setup is shown below. A circularly polarized laser creates the spin polarized carriers. The resultant PL polarization is analyzed by a variable wave plate (VWP) which alternates between 1/4 and 3/4 – wave retardence and alinear polarizer (LP). Theintensities I+ and I- are detected with a photodiode (PD) and used to calculate the polarization as r = (I+-I-)/(I++I-). The monochromator enables the spin lifetimes in different QD energy states to be spectrally distinguished.
Below (top panel) are Hanle curves from one sample detecting at the ground state for five different temperatures. The curves are not single Lorentzians but can be fit well with bi-Lorentzians. This could result from a bi-exponential spin decay as has been seen in the chemically synthesized QDs (link). The lower panel shows scaled spin lifetimes extracted from the data for all three samples. While the short lifetime component does not change within experimental error, the longer component shows that the largest QDs are the most resilient to changes in temperature.
The spin lifetime also depends on which QD energy state is probed. Below (middle) is a density plot of PL polarization vs. magnetic field vs. detection energy. By normalizing the zero-field polarization to unity, the change in width of the Hanle curves is more apparent. The PL intensity (right) shows the ground and first excited states. Horizontal line-cuts (top) of the middle panel are Hanle curves at the peaks of the two states. The left panel is the zero-field polarization vs. detection energy.
Compared to exciting above the GaAs energy gap, intensity-induced spin relaxation is dramatically suppressed when exciting at the wetting layer. Below is a series of Hanle curves with increasing excitation intensity exciting above the GaAs band edge. The right inset shows how the middle lifetimes vary with excitation intensity for excitation at 1.58 eV (black; GaAs) and 1.45 eV (red; wetting layer). The lifetime is strongly intensity dependent for the former case but is roughly constant for the latter case.
Three concentric Lorentzian-like peaks appear at three field scales in these Hanle curves. There are peaks with widths of ~2 T, ~0.1T and ~0.001T. These may be due to different spin relaxation mechanisms each with their own characteristic relaxation time.
See Epstein et al, APL 78, 733 (2001) for further details.