● Problem addressed: Mn-doped GaAs is the leading material for spintronics applications. How does the ferromagnetism arise? ● Scanning Tunneling Microscopy allows visualization of electronic states in Ga 1- x Mn x As samples close to the metal-insulator transition. ● Doping-induced disorder produces strong spatial variations in the local tunneling conductance. ● Discovered sharp divergence of correlation length at the Fermi Energy near the metal- insulator transition. Visualizing Critical Correlations in Ga 1-x Mn x As Princeton Univ., Univ. Illinois and UC Santa Barbara A. Richardella et al., Science 327, 665 (2010) Princeton Center for Complex Materials

● Conductance maps af Fermi energy, become multifractal. ● At Fermi energy, where signatures of electron-electron interaction are the most prominent, a diverging spatial correlation length was observed. (right) ● Proximity to the metal-insulator transition plays a more important role in the underlying mechanism of magnetism of Ga 1-x Mn x As than previously anticipated. ● experimental approach provides a direct method to examine critical correlations for other material systems near a quantum phase transition. Above: dI/dV maps over areas of 700Å at Fermi energy for three different dopings. Princeton Center for Complex Materials

J. R. Petta, H. Lu, and A. C. Gossard, Science, 327, 669 (2010). The probability P s of observing final singlet state plotted as a function of the maximum well detuning  s and waiting time  s (scale bar for P s at right). Bright fringes indicate high probability that electron pair ends up in a triplet state. A direct analogy with optical beam splitter is shown in inset. Ultra-Fast Electrically Driven Single Spin Rotations (DMR ) Jason Petta 1, Hong Lu 2, Art Gossard 2 1 Department of Physics, Princeton University 2 Materials Department, University of California at Santa Barbara  S (ns)  S (mV) 0.6 PSPS B E = 100 mT  U1U1 U2U2 U3U3 Det. Mirror Ultrafast method (ns) to flip individual spins using gate voltage only without affecting neighboring spin. Separate electrons rapidly, allow states to evolve for  s (5-25 ns), then slowly recombine in right well. Quantum interference between triplet and singlet states visible as fringes in the probability P s of obtaining final singlet state (see figure). gQgQ 2 electrons trapped in quantum wells Princeton Center for Complex Materials