letters to nature and the persistent spin current that appears with a bias (SC). Fitting accumulation pro®le. This is consistent with the observation of variables are the amplitudes A, B and C (C is taken as non-zero only electron spin precession at a single frequency corresponding to the for positive biases), and the risetimes tA and tB. The other values are g-factor of ZnSe rather than GaAs. ®xed and obtained from complementary measurements, such as In summary, we show that persistent spin currents appear in resonance spectra or time scans from degenerate pump-probe biased spin injection studies of GaAs/ZnSe heterostructures. We arrangements. We note that the persistent spin current contribution ®nd thatÐunder electrical biasÐthe GaAs layer behaves as a p is sensitive only to spin that has arrived within a time T2ZnSe. Hence, coherently rotating spin reservoir that continuously sources current p for t . T2ZnSe, the epilayer polarization re¯ects the precession and to the ZnSe layer. As a result, the spin transfer ef®ciency is increased the lifetime of the spin current itself, which follows the reservoir markedly. Furthermore, the magnetic and electric responses spin dynamics. This explains why the average spin polarization in become interdependent, thus providing a new paradigm for the p the epilayer is characterized by qGaAs and T2GaAs although spins future development of magneto-electronic semiconductor devices p reside in ZnSe (and each spin has qZnSe and T2ZnSe). with qualitatively new functionality. M The changes in net spin transfer with bias are more evident in the absence of spin precession (B 0). In Fig. 3, time scans show an Received 28 February; accepted 2 April 2001. increase in the amplitude of the spin signal in ZnSe as the applied 1. Kikkawa, J. M. & Awschalom, D. D. Lateral drag of spin coherence in gallium arsenide. Nature 397, 139±141 (1999). bias is increased, while a reverse bias reduces the number of spins 2. Kikkawa, J. M., Smorchkova, I. P., Samarth, N. & Awschalom, D. D. Room-temperature spin memory that cross the interface. The most striking in¯uence of the persistent in two-dimensional electron gases. Science 277, 1284±1287 (1997). spin ¯ow (C) on spin transfer is to introduce an apparent offset to 3. Kikkawa, J. M. & Awschalom, D. D. Resonant spin ampli®cation in n-type GaAs. Phys. Rev. Lett. 80, the spin polarization. This offset is due to the long spin lifetimes in 4313±4316 (1998). 4. Prinz, G. A. Spin polarized transport. Phys. Today 48, 58±63 (1995). GaAs: the reservoir spin population decays only slightly before 5. Monzon, F. G. & Roukes, M. L. Spin injection and the local hall effect in InAs quantum wells. J. Mag. receiving a boost from the next pump pulse, sourcing a spin current Magn. Mater. 198, 632±635 (1999). that never reaches zero for E . 0. The inset in Fig. 3 shows the 6. Filip, A. T., Hoving, B. H., Jedema, F. J. & van Wees, B. J. Experimental search for the electrical spin injection in a semiconductor. Phys. Rev. B 62, 9996±9999 (2000). change in the total spin polarization transferred from the reservoir 7. Fiederling, R. et al. Injection and detection of a spin-polarized current in a light-emitting diode. to the epilayer, where modest electric ®elds increase spin transfer Nature 402, 787±790 (1999). nearly 500%. About 3/4 of this increase is due to the persistent 8. Ohno, Y. et al. Electrical spin injection in a ferromagnetic semiconductor heterostructure. Nature 402, current; mechanisms A and B, also enhanced by the bias, account for 790±792 (1999). 9. Malajovich, I., Kikkawa, J. M., Awschalom, D. D., Berry, J. J. & Samarth, N. Coherent transfer of spin the rest. We also ®nd that the change in spin transfer mimics through a semiconductor heterointerface. Phys. Rev. Lett. 84, 1015±1018 (2000). changes in charge current across the structure (from I±V measure- 10. Yeganeh, M. S., Qi, J., Yodh, A. G. & Tamargo, M. C. Interface quantum well states observed by three- ments), showing that spin and charge motion are coupled in wave mixing in ZnSe/GaAs heterostructures. Phys. Rev. Lett. 68, 3761±3764 (1992). mechanism C. 11. Schull, K. et al. Non-metal in situ and ex situ ohmic contacts to a n-ZnSe. Semicond. Sci. Technol. 12, 485±489 (1997). To see whether similar physics arises from the built-in interfacial 12. Malajovich, I., Kikkawa, J. M., Awschalom, D. D., Berry, J. J. & Samarth, N. Resonant ampli®cation of electric ®elds in a p±n junction, we also study spin transfer across a spin transferred across a GaAs/ZnSe interface. J. Appl. Phys. 87, 5073±5075 (2000). p-GaAs/n-ZnSe heterojunction. As a control, an undoped GaAs substrate is placed together with the p-type substrate in the growth Acknowledgements chamber, and 300 nm of n-ZnSe (n 1:5 3 1018 cm23) is deposited We thank M. E. Flatte, E. L. Hu, J. M. Kikkawa and H. Kroemer for discussions and simultaneously on both. Figure 4a shows a roughly 4,000% increase suggestions. Work supported by DARPA, ARD, NSF and ONR. in spin transfer due to the heterojunction voltage, compared with Correspondence and requests for materials should be addressed to D.D.A. the control. Degenerate pump-probe measurements of the ZnSe (e-mail: [email protected]). epilayers are nearly identical, with a slight change in spin lifetime (Fig. 4b). Therefore, the difference in the transferred spin signal amplitudes between the two samples shown in Fig. 4a is not due to differences in the ZnSe epilayers themselves. Unlike the n-doped ................................................................. GaAs `spin reservoirs',the electron spin lifetimes in the p-doped and undoped GaAs substrates are extremely short2 (a few picoseconds) Jamming phase diagram for so that persistent spin currents do not explain the observed increase. Instead, the data suggest enhancement of spontaneous transfer attractive particles mechanisms similar to A and B, but with a non-exponential spin V. Trappe*², V. Prasad*, Luca Cipelletti*², P. N. Segre*² & D. A. Weitz* * Department of Physics and DEAS, Harvard University, Cambridge, abMassachusetts 02138, USA .............................................................................................................................................. p-GaAs p-GaAs A wide variety of systems, including granular media, colloidal suspensions and molecular systems, exhibit non-equilibrium transitions from a ¯uid-like to a solid-like state, characterized undoped-GaAs solely by the sudden arrest of their dynamics. Crowding or × 10 undoped-GaAs (arbitrary units) jamming of the constituent particles traps them kinetically, precluding further exploration of the phase space1. The disor- ZnSe S dered ¯uid-like structure remains essentially unchanged at the B = 75 mT, T = 5 K transition. The jammed solid can be re¯uidized by thermaliza- 0 12 06 tion, through temperature or vibration, or by an applied stress. ∆t (ns) ∆t (ns) The generality of the jamming transition led to the proposal2 of a Figure 4 Time evolution of the spin polarization transfer across a p-GaAs/n-ZnSe heterojunction. Zn p-type doping concentration, 1019 cm-3. Transfer across an undoped- GaAs/n-ZnSe is shown for comparison. Dotted lines show the zeros, and an offset was ² Present addresses: Department of Physics, University of Fribourg, Fribourg, Switzerland (V.T.); added for clarity. a, Spins transported across the interface (two-colour pump probe). Department of Physics, University of Montpellier, Montpellier, France (L.C.); and NASA, Marshall b, Spins excited and measured in the ZnSe epilayer (degenerate pump probe). Space Flight Center, Huntsville, Alabama 35812, USA (P.N.S.). 772 © 2001 Macmillan Magazines Ltd NATURE | VOL 411 | 14 JUNE 2001 | www.nature.com letters to nature unifying description, based on a jamming phase diagram. It was tion is nearly identical and the structures on the ¯uid and solid side further postulated that attractive interactions might have the have very similar appearances. We identify a jammed solid by the same effect in jamming the system as a con®ning pressure, and existence of a stress-bearing, interconnected network, which results thus could be incorporated into the generalized description. Here in a low-frequency plateau of the elastic modulus, G9p (ref. 10). we study experimentally the ¯uid-to-solid transition of weakly As shown in Fig. 2a and b for carbon black, a well-de®ned attractive colloidal particles, which undergo markedly similar transition from ¯uid-like to solid-like behaviour can be found as gelation behaviour with increasing concentration and decreasing either f is increased at constant U,orU is increased at constant f. thermalization or stress. Our results support the concept of a The viscosity, h, diverges as some critical value is approached, jamming phase diagram for attractive colloidal particles, provid- whereupon G9p increases sharply. The phase boundary at fc can be 3 4,5 ing a unifying link between the glass transition , gelation and identi®ed by the critical-like behaviour of both h and G9p for ®xed U aggregation6±8. (Fig. 2a): As an intrinsic parameter to unify the description of all routes to h h f 2 f 2 nf 1 jamming, Liu and Nagel2 use the density of the system, r.For s c repulsive systems, a non-uniform, applied stress can increase r and and jam athermal systems1,9, whereas an osmotic or hydrostatic pressure G9 G9 f 2 f uf 2 is required to increase r and jam thermal systems; for attractive p f c systems, the interaction itself increases r and jams the system. where nf < 0:13, and uf < 4:0 and hs is the solvent viscosity; both Jamming is overcome and the system is ¯uidized by an increase in G9f, and fc depend on U. Similarly, Uc can be identi®ed by the temperature or by a uni-directional stress or load that exceeds the critical-like behaviour of h and G9p at ®xed f, (Fig.