Quantum Phase Transition of a Magnet in a Spin Bath

R ESEARCHA RTICLES18. The International HapMap Consortium, Nature 426,789 (2003).19. A. R. Templeton, E. Boerwinkle, C. F. Sing, Genetics117, 343 (1987).20. D. W. Schultz et al., Hum. Mol. Genet. 12, 3315(2003).21. M. Hayashi et al., Ophthalmic Genet. 25, 111 (2004).22. G. J. McKay et al., Mol. Vis. 10, 682 (2004).23. S. Rodríguez de Cordoba, J. Esparza-Gordillo, E.Goicoechea de Jorge, M. Lopez-Trascasa, P. Sanchez-Corral,Mol. Immunol. 41, 355 (2004).24. L. V. Johnson, W. P. Leitner, M. K. Staples, D. H.Anderson, Exp. Eye Res. 73, 887 (2001).25. R. F. Mullins, S. R. Russell, D. H. Anderson, G. S.Hageman, FASEB J. 14, 835 (2000).26. J. Ambati et al., Nat. Med. 9, 1390 (2003).27. G. S. Hageman et al., Prog. Retinal Eye Res. 20, 705(2001).28. J. Esparza-Gordillo et al., Immunogenetics 56, 77 (2004).29. G. Wistow et al., Mol. Vis. 8, 205 (2002).30. R. F. Mullins, N. Aptsiauri, G. S. Hageman, Eye 15, 390(2001).31. A. M. Blom, L. Kask, B. Ramesh, A. Hillarp, Arch.Biochem. Biophys. 418, 108 (2003).32. J. M. Seddon, G. Gensler, R. C. Milton, M. L. Klein, N.Rifai, JAMA 291, 704 (2004).33. The Raymond and Beverly Sackler Fund for Arts andSciences’ generous support made this project possible.We thank Raymond Sackler, J. Sackler, and E. Vosburgfor their input and encouragement. We also thankAREDS participants and investigators; G. Gensler, T.Clemons, and A. Lindblad for work on the AREDSGenetic Repository; S. Westman and A. Evan for assistancewith the microarrays; R. Fariss for the humanretinal sections and advice on confocal microscopy; E.Johnson for assistance with immunostaining; and J.Majewski for constructive comments on the manuscript.Partially funded by NIH-K25HG000060 andQuantum Phase Transition of aMagnet in a Spin BathH. M. Rønnow, 1,2,3 * R. Parthasarathy, 2 J. Jensen, 4 G. Aeppli, 5T. F. Rosenbaum, 2 D. F. McMorrow 3,4,6The excitation spectrum of a model magnetic system, LiHoF 4, was studiedwith the use of neutron spectroscopy as the system was tuned to its quantumcritical point by an applied magnetic field. The electronic mode softeningexpected for a quantum phase transition was forestalled by hyperfinecoupling to the nuclear spins. We found that interactions with the nuclearspin bath controlled the length scale over which the excitations could beentangled. This generic result places a limit on our ability to observe intrinsicelectronic quantum criticality.The preparation and preservation of entangledquantum states is particularly relevant for thedevelopment of quantum computers, whereinteracting quantum bits (qubits) must producestates sufficiently long lived for meaningfulmanipulation. The state lifetime, typically referredto as decoherence time, is derived fromcoupling to the background environment. Forsolid-state quantum computing schemes, thequbits are typically electron spins, and theycouple to two generic background environments(1). The oscillator bath—that is, delocalizedenvironmental modes (2) suchasthermalvibrations coupled via magnetoelastic terms tothe spins—can be escaped by lowering the temperatureto a point where the lattice is essentially1 Laboratory for Neutron Scattering, ETH-Zürich andPaul Scherrer Institut, 5232 Villigen, Switzerland.2 James Franck Institute and Department of Physics,University of Chicago, Chicago, IL 60637, USA. 3 RisøNational Laboratory, DK-4000 Roskilde, Denmark.4 Ørsted Laboratory, Niels Bohr Institute fAPG, Universitetsparken5, 2100 Copenhagen, Denmark. 5 LondonCentre for Nanotechnology and Department ofPhysics and Astronomy, University College London,London WC1E 6BT, UK.6 ISIS, Rutherford AppletonLaboratory, Chilton, Didcot OX11 0QX, UK.*To whom correspondence should be addressed.E-mail: henrik.ronnow@psi.chfrozen. Coupling to local degrees of freedom,such as nuclear magnetic moments that form aspin bath, may prove more difficult to avoid,because all spin-based candidate materials forquantum computation have at least one naturallyoccurring isotope that carries nuclear spin.Experimental work in this area has beenlargely restricted to the relaxation of single,weakly interacting magnetic moments such asthose on large molecules (3); much less is knownabout spins as they might interact in a realquantum computer. In this regard, the insightthat quantum phase transitions (QPTs) (4) area good arena for looking at fundamental quantumproperties of strongly interacting spinsturns out to be valuable, as it has already beenfor explorations of entanglement. In particular,we show that coupling to a nuclear spin bathlimits the distance over which quantum mechanicalmixing affects the electron spin dynamics.QPTs are transitions between differentground states driven not by thermal fluctuationsbut by quantum fluctuations controlled by aparameter such as doping, pressure, or magneticfield (5, 6). Much of the interest in QPTs stemsfrom their importance for understandingmaterials with unconventional properties, suchas heavy fermion systems and high-temperatureNIH-R01EY015771 (J.H.), Macula Vision ResearchFoundation and the David Woods Kemper MemorialFoundation (C.B.), NIH-R01MH44292 (J.O.), and NIH-K01RR16090 and Yale Pepper Center for Study ofDiseases in Aging (C.Z.). This work also benefited fromthe International HapMap Consortium making theirdata available prior to publication.Supporting Online Materialwww.sciencemag.org/cgi/content/full/1109557/DC1Materials and MethodsFig. S1Tables S1 to S5References10 January 2005; accepted 22 February 2005Published online 10 March 2005;10.1126/science.1109557Include this information when citing this paper.REPORTSsuperconductors. However, these materials arerather complex and do not easily lend themselvesto a universal understanding of QPTs. Tothis end, it is desirable to identify quantumcritical systems with a well-defined and solvableHamiltonian and with a precisely controllabletuning parameter. One very simple modeldisplaying a QPT is the Ising ferromagnet in atransverse magnetic field (5, 7–9) with theHamiltonianH 0 j X J ij si z I sj z j G X six ð1Þijiwhere J ijis the coupling between the spins onsites i and j represented by the Pauli matricess z with eigenvalues T1. In the absence of amagnetic field, the system orders ferromagneticallybelow a critical temperature T c.Thetransverse-field G mixes the two states andleads to destruction of long-range order in aQPT at a critical field G c,evenatzerotemperature.In the ferromagnetic state at zerofield and temperature, the excitation spectrumis momentum independent and is centered atthe energy 4 P J j ijassociated with single-spinreversal. Upon application of a magnetic field,however, the excitations acquire a dispersion,softening to zero at the zone center q 0 0when the QPT is reached.We investigated the excitation spectrumaround the QPT in LiHoF 4, which is an excellentphysical realization of the transverse-fieldIsing model, with an added term accountingfor the hyperfine coupling between electronicand nuclear moments (10–12). The dilutionseries LiHo xY 1–xF 4is the host for a widevariety of collective quantum effects, rangingfrom tunneling of single moments and domainwalls to quantum annealing, entanglement,and Rabi oscillations (13–17). These intriguingproperties rely largely on the ability of atransverse field, whether applied externally orgenerated internally by the off-diagonal part ofthe magnetic dipolar interaction, to mix twodegenerate crystal field states of each Ho ion.www.sciencemag.org SCIENCE VOL 308 15 APRIL 2005 389

R EPORTSThe Ho ions in LiHoF 4are placed on atetragonal Scheelite lattice with parametersa 0 5.175 ) and c 0 10.75 ). The crystal-fieldground state is a G 3,4doublet with only a ccomponent to the angular momentum andhence can be represented by the s z 0T1Isingstates. A transverse field in the a-b planemixes the higher lying states with the groundstate; this produces a splitting of the doublet,equivalent to an effective Ising model field.The phase diagram of LiHoF 4(Fig. 1A) wasdetermined earlier by susceptibility measurements(10) and displays a zero-field T cof 1.53K and a critical field of H c0 49.5 kOe in thezero temperature limit. The same measurementsconfirmed the strong Ising anisotropy,with longitudinal and transverse g factors differingby a factor of 18 (10). The suddenincrease in H cbelow 400 mK was explained byalignment of the Ho nuclear moments throughthe hyperfine coupling. Corrections to phasediagrams as a result of hyperfine couplingshave a long history (18) and were noted for theLiREF 4(RE 0 rare earth) series, of whichLiHoF 4is a member, more than 20 years ago(19). What is new here is that the applicationof a transverse field and the use of highresolutionneutron scattering spectroscopy allowus to carefully study the dynamics as wetune through the quantum critical point (QCP).We measured the magnetic excitationspectrum of LiHoF 4with the use of theTAS7 neutron spectrometer at RisL NationalLaboratory, with an energy resolution (fullwidthathalfmaximum)of0.06to0.18meV(20). The transverse field was aligned to betterthan 0.35-, and the sample was cooled in adilution refrigerator. At the base temperature of0.31 K, giving a critical field of 42.4 kOe, theexcitation spectrum was mapped out below, at,and above the critical field (Fig. 2). For allfields, a single excitation branch dispersesupward from a minimum gap at (2,0,0) toward(1,0,0). From (1,0,0) to (1,0,1), the mode showslittle dispersion but appears to broaden. Thediscontinuity on approaching (1,0,1 – e) and(1 þ e,0,1) as e Y 0 reflects the anisotropyand long-range nature of the magnetic dipolecoupling. However, the most important observationis that the (2,0,0) energy, which isalways lower than the calculated single-ionenergy (È0.39 meV at 42.4 kOe), shrinksupon increasing the field from 36 to 42.4 kOeandthenhardensagainat60kOe.Atthisqualitative level, what we see agrees with themode softening predicted for the simple Isingmodel in a transverse field. However, it appearsthat the mode softening is incomplete. Atthe critical field of 42.4 kOe, the mode retains afinite energy of 0.24 T 0.01 meV. This result isapparent in Fig. 1B, which shows the gapenergy as a function of the external field.To obtain a quantitative understanding ofour experiments, we consider the full rare-earthHamiltonian, which closely resembles that ofFig. 1. (A) Phase diagram ofLiHoF 4as a function of transversemagnetic field and temperaturefrom susceptibility (10) (circles)and neutron scattering (squares)measurements. Lines are 1/z calculationswith (solid) and without(dashed) hyperfine interaction.Horizontal dashed guide marksthe temperature 0.31 K at whichinelastic neutron measurementswere performed. (B) Field dependenceof the lowest excitationenergy in LiHoF 4measured atQ 0 (1 þ e,0,1). Lines are calculatedenergies scaled by Z 0 1.15with (solid) and without (dashed)hyperfine coupling. The dashedvertical guides show how in eithercase the minimum energy occursat the field of the transition[compare with (A)]. (C) Schematicof electronic (blue) and nuclear(red) levels as the transverse fieldis lowered toward the QCP.Neglecting the nuclear spins, the electronic transition (light blue arrow) would soften all the way tozero energy. Hyperfine coupling creates a nondegenerate multiplet around each electronic state. TheQCP now occurs when the excited-state multiplet through level repulsion squeezes the collective modeof the ground-state multiplet to zero energy, hence forestalling complete softening of the electronicmode. Of course, the true ground and excited states are collective modes of many Ho ions and shouldbe classified in momentum space. (D) Calculated ratio of the minimum excitation energy E cto thesingle-ion splitting D at the critical field as a function of temperature. This measures how far theelectronic system is from the coherent limit, for which E c/D 0 0.HoF 3(21, 22). Each Ho ion is subject to thecrystal field, the Zeeman coupling, and thehyperfine coupling. The interaction betweenmoments is dominated by the long-rangedipole coupling, with a small nearest neighborexchange interaction J 12:H 0 X EH CFðJ i ÞþAJ i I I i j gm B J i I H^ij 1 X XJ2D D ab ðijÞJ ia J jbijj 1 2abX n:n:ijJ 12 J i I J jð2Þwhere J and I are the electronic and nuclearmoments, respectively, and for 165 Ho 3þ J 0 8and I 0 7/2. Hyperfine resonance (23)andheatcapacity measurements (24) show the hyperfinecoupling parameter A 0 3.36 meV as forthe isolated ion, with negligible nuclearquadrupolecoupling. The Zeeman term isreduced by the demagnetization field. Thenormalized dipole tensor D ab(ij) is directly calculable,and the dipole coupling strength J Dissimply fixed by lattice constants and the magneticmoments of the ions at J D0 (gm B) 2 N 01.1654 meV, where m Bis the Bohr magneton.This leaves as free parameters various numbersappearing in the crystal-field HamiltonianH CFand the exchange constant J 12. The formerare determined (25) largely from electron spinresonance for dilute Ho atoms substituted forYinLiYF 4, whereas the latter is constrainedby the phase diagram determined earlier (10)(Fig. 1A). We have used an effective mediumtheory (9) previously applied to HoF 3(26) tofit the phase diagram, and we conclude that agood overall description—except for a modest(14%) overestimate of the zero-field transitiontemperature—is obtained for J 120 –0.1 meV.On the basis of quantum Monte Carlo simulationdata, others (27) have also concluded thatJ 12is substantially smaller than J D.Having established a good parameterizationof the Hamiltonian, we model the dynamics,where expansion to order 1/z (where z is thenumber of nearest neighbors of an ion in thelattice) leads to an energy-dependent renormalizationE1 þ S(w)^–1 (on the order of10%) of the dynamic susceptibility calculatedin the random phase approximation, with theself energy S(w) evaluated as described in(26). For the three fields investigated in detail,the dispersion measured by neutron scatteringis closely reproduced throughout the Brillouinzone. As indicated by the solid lines in Fig. 2,the agreement becomes excellent if the calculatedexcitation energies are multiplied by a renormalizationfactor Z 0 1.15. The point is notthat the calculation is imperfect but rather thatit matches the data as closely as it does. Indeed,it also predicts a weak mode splitting of about0.08 meV at (1,0,1 – e), consistent with theincreased width in the measurements. Theagreement for the discontinuous jump between(1,0,1 – e) and(1þ e,0,1) as a result of thelong-range nature of the dipole coupling showsthat this is indeed the dominant coupling.39015 APRIL 2005 VOL 308 SCIENCE www.sciencemag.org

R EPORTSFig. 2. Pseudocolor representationof the inelastic neutron scatteringintensity for LiHoF 4at T 00.31 K observed along the reciprocalspace trace (2,0,0) Y (1,0,0)Y (1,0,1) Y (1.15,0,1). Whitelines show the 1/z calculation forthe excitation energies asdescribed in the text. White ellipsesaround the (2,0,0) Bragg peakindicate 5 times the resolution tail(full width at half maximum).Fig. 3. Measured intensities of the excitationsalong Q 0 (h,0,0) at the same values of thefield as in Fig. 2. Lines are calculated withgeometric and resolution corrections appliedto allow comparison to the neutron data.The simple origin of the incomplete softeningand enhanced critical field (Fig. 1, B andC) is easiest to understand if we start fromthe polarized paramagnetic state above H c,where the experiment, the purely electroniccalculation, and the theory including the hyperfinecoupling all coincide. At high fields,the only effect of the hyperfine term is tosplit both the ground state and the electronicexcitation modes into multiplets that aresimply the direct products of the electronicand nuclear levels, with a total span of2AbJÀI , 0.1meV(Fig.1C).Uponloweringthe field, the electronic mode softens andwould reach zero energy at H c00 36 kOe inthe absence of hyperfine coupling. The hyperfinecoupling, however, already mixesthe original ground and excited (soft mode)states above H c. As this happens, the formationof a composite spin from mixednuclear and electronic contributions immediatelystabilizes ordering along the c axisof the crystal. In other words, the hyperfinecoupling shunts the electronic mode, raisingthe critical field to the observed H c0 42.4kOe, where the mode reaches a nonzero minimum.This process is accompanied by transferof intensity from the magnetic excitation ofelectronic origin to soft modes of much lowerenergy (in the 10-meV range) that have anentangled nuclear/electronic character. Coolingto very low temperatures would revealthese modes as propagating and softeningto zero at the QCP, but at the temperaturesreachable in our measurements there is thermalization,dephasing the composite modes toyield the strong quasi-elastic scattering appearingaround Q 0 (2,0,0) and zero energyat the critical field, as in Fig. 2.The intensities of the excitations are simplyproportional to the matrix elements kbf k P jexp(iQ I R j)J jþk0Àk 2 , and therefore provide adirect measure of the wave functions via theinterference effects implicit in the spatialFourier transform of J j. Figure 3 showsintensities recorded along (h,0,0) for the threefields 36, 42.4, and 60 kOe. They follow amomentum dependence characterized by abroad peak near (2,0,0), which is welldescribed by our theory. In the absence ofhyperfine interactions, the intensity at H c0would diverge as q approaches (2,0,0),reflecting that the real-space dynamical coherencelength x cof the excited state grows toinfinity. The finite width of the peak observedat H ccorresponds in real space to a distanceon the order of the interholmium spacing;because the hyperfine interactions forestall thesoftening of the electronic mode, the implicationis that these interactions also limit thedistance over which the electronic wavefunctions can be entangled (4).Thus,Fig.3is a direct demonstration of the limitation ofquantum coherence in space via coupling to anuclear spin bath. x cis obtained from a sumover matrix elements connecting the groundstate to a particular set of excited states,whereas the thermodynamic correlation lengthx tis derived from the equal time correlationfunction S(r), which is the sum over all finalstates. x tdiverges at second-order transitionssuch as those in LiHoF 4, where the quasielasticcomponent seen in our data dominates thelong-distance behavior of S(r) atT c(H). It isthe electronic mode, and hence x c, that dictatesto what extent LiHoF 4can be characterizedand potentially exploited as a realization of theideal transverse-field Ising model.Beyond providing a quantitative understandingof the excitations near the QCP of a modelexperimental system, we obtain new insight bybringing together the older knowledge from rareearthmagnetism and the contemporary ideas ofentanglement, qubits, and decoherence. Althoughthe notion of the spin bath was developed toaddress decoherence in localized magneticclusters and molecules (1), our work disclosesits importance for QPTs. In particular, weestablish that the spin bath is a generic featurethat will limit our ability to observe intrinsicelectronic quantum criticality. This may notmatter much for transition metal oxides withvery large exchange constants, but it couldmatter for rare earth and actinide intermetalliccompounds, which show currently unexplainedcrossovers to novel behaviors at low (G1 K)temperatures Esee, e.g., (28)^.For magnetic clusters, decoherence can beminimized in a window between the oscillatorbath–dominated high-temperature regionsand the spin bath–dominated low-temperatureregions (29). Our calculations suggest thatthe dense quantum critical magnet shows analogousbehavior. Here the interacting electronspins themselves constitute the oscillator bath,and the extent to which the magnetic excitationsoftens at T c(H), as measured by the ratioof the zone center energy E cto the fieldinducedsingle-ion splitting D (Fig.1D),gaugesthe electronic decoherence. E c/D achieves itsminimum not at T 0 0 but rather at an intermediatetemperature T , 1 K, exactly wherethe phase boundary in Fig. 1A begins to beaffected by the nuclear hyperfine interactions.www.sciencemag.org SCIENCE VOL 308 15 APRIL 2005 391

R EPORTSReferences and Notes1. N. V. Prokof’ev, P. C. E. Stamp, Rep. Prog. Phys. 63,669 (2000).2. R. P. Feynman, F. L. Vernon, Ann. Phys. 24, 118 (1963).3. W. Wernsdorfer, S. Bhaduri, R. Tiron, D. N. Hendrickson,G. Christou, Phys. Rev. Lett. 89, 197201 (2002).4. A. Osterloh, L. Amico, G. Falci, R. Fazio, Nature 416,608 (2002).5. S. Sachdev, Phys. World 12, 33 (1999).6. S. Sachdev, Quantum Phase Transitions (CambridgeUniv. Press, Cambridge, 1999).7. P. G. de Gennes, Solid State Commun. 1, 132 (1963).8. R. J. Elliott, P. Pfeuty, C. Wood, Phys. Rev. Lett. 25,443 (1970).9. R. B. Stinchcombe, J. Phys. C 6, 2459 and 2484 (1973).10. D. Bitko, T. F. Rosenbaum, G. Aeppli, Phys. Rev. Lett.77, 940 (1997).11. T. F. Rosenbaum et al., J. Appl. Phys. 70, 5946 (1991).12. D. Bitko, thesis, University of Chicago (1997).13. R. Giraud et al., Phys. Rev. Lett. 87, 057203 (2001).14. J. Brooke, D. Bitko, T. F. Rosenbaum, G. Aeppli,Science 284, 779 (1999).15. J. Brooke, T. F. Rosenbaum, G. Aeppli, Nature 413,610 (2001).16. S. Ghosh, R. Parthasarathy, T. F. Rosenbaum, G.Aeppli, Science 296, 2195 (2002).17. S. Ghosh et al., Nature 425, 48 (2003).18. K. Andres, Phys. Rev. B 7, 4295 (1973).19. R. W. Youngblood, G. Aeppli, J. D. Axe, J. A. Griffin,Phys. Rev. Lett. 49, 1724 (1982).20. H. M. Rønnow, thesis, Risø National Laboratory,Denmark (2000).21. M. J. M. Leask et al., J. Phys. C 6, 505 (1994).22. A. P. Ramirez, J. Jensen, J. Phys. C 6, L215 (1994).23. J. Magariño, J. Tuchendler, P. Beauvillain, I. Laursen,Phys. Rev. B 21, 18 (1980).24. G. Mennenga, L. J. de Jongh, W. J. Huiskamp, J. Magn.Magn. Mater. 44, 59 (1984).25. H. M. Rønnow et al., in preparation.26. J. Jensen, Phys. Rev. B 49, 11833 (1994).27. P. B. Chakraborty, P. Henelius, H. Kjønsberg, A. W.Sandvik, S. M. Girvin, Phys. Rev. B 70, 144411 (2004).28. P. Gegenwart et al., Phys.Rev.Lett.89, 056402 (2002).29. P. C. E. Stamp, I. S. Tupitsyn, Phys. Rev. B 69, 014401(2004).30. We thank G. McIntyre for his expert assistanceduring complementary measurements on the D10diffractometer at the Institut Laue Langevin, Grenoble,France. Work at the University of Chicago wassupported by NSF Materials Research Science andEngineering Centers grant DMR-0213745. Work inLondon was supported by the Wolfson–Royal SocietyResearch Merit Award Program and the BasicTechnologies program of the UK Research Councils.6 December 2004; accepted 23 February 200510.1126/science.1108317Atomic-Scale Visualization ofInertial DynamicsA. M. Lindenberg, 1 J. Larsson, 2 K. Sokolowski-Tinten, 3K. J. Gaffney, 1 C. Blome, 4 O. Synnergren, 2 J. Sheppard, 5C. Caleman, 6 A. G. MacPhee, 7 D. Weinstein, 7 D. P. Lowney, 7T. K. Allison, 7 T. Matthews, 7 R. W. Falcone, 7 A. L. Cavalieri, 8D. M. Fritz, 8 S. H. Lee, 8 P. H. Bucksbaum, 8 D. A. Reis, 8 J. Rudati, 9P. H. Fuoss, 10 C. C. Kao, 11 D. P. Siddons, 11 R. Pahl, 12J. Als-Nielsen, 13 S. Duesterer, 4 R. Ischebeck, 4 H. Schlarb, 4H. Schulte-Schrepping, 4 Th. Tschentscher, 4 J. Schneider, 4D. von der Linde, 14 O. Hignette, 15 F. Sette, 15 H. N. Chapman, 16R. W. Lee, 16 T. N. Hansen, 2 S. Techert, 17 J. S. Wark, 5 M. Bergh, 6G. Huldt, 6 D. van der Spoel, 6 N. Timneanu, 6 J. Hajdu, 6R. A. Akre, 18 E. Bong, 18 P. Krejcik, 18 J. Arthur, 1 S. Brennan, 1K. Luening, 1 J. B. Hastings 1The motion of atoms on interatomic potential energy surfaces is fundamentalto the dynamics of liquids and solids. An accelerator-based source offemtosecond x-ray pulses allowed us to follow directly atomic displacementson an optically modified energy landscape, leading eventually to thetransition from crystalline solid to disordered liquid. We show that, to firstorder in time, the dynamics are inertial, and we place constraints on the shapeand curvature of the transition-state potential energy surface. Our measurementspoint toward analogies between this nonequilibrium phase transitionand the short-time dynamics intrinsic to equilibrium liquids.In a crystal at room temperature, vibrationalexcitations, or phonons, only slightly perturbthe crystalline order. In contrast, liquidsexplore a wide range of configurations setby the topology of a complex and timedependentpotential energy surface (1, 2). Byusing light to trigger changes in this energylandscape, well-defined initial and final statescan be generated to which a full range oftime-resolved techniques may be applied. Inparticular, light-induced structural transitionsbetween the crystalline and liquid states ofmatter may act as simple models for dynamicsintrinsic to the liquid state or to transitionstates in general (3).In this context, a new class of nonthermalprocesses governing the ultrafast solid-liquidmelting transition has recently emerged,supported by time-resolved optical (4–7) andx-ray (8–10) experiments and with technologicalapplications ranging from micromachiningto eye surgery (11). Intense femtosecondexcitation of semiconductor materials resultsin the excitation of a dense electron-holeplasma, with accompanying dramatic changesin the interatomic potential (12–14). At sufficientlyhigh levels of excitation, it is thoughtthat this process leads to disordering of thecrystalline lattice on time scales faster than thetime scale for thermal equilibration Eoftenknown as the electron-phonon coupling time,on the order of a few picoseconds (15)^. Inapioneering study, Rousse et al. (9) determinedthat the structure of indium antimonide (InSb)changes on sub-picosecond time scales, butthe mechanism by which this occurs and themicroscopic pathways the atoms follow haveremained elusive, in part because of uncertaintiesin the pulse duration of laser-plasmasources and signal-to-noise limitations.Research and development efforts leadingtoward the Linac Coherent Light Source(LCLS) free-electron laser have facilitated theconstruction of a new accelerator-based x-raysource, the Sub-Picosecond Pulse Source(SPPS), which uses the same linac-basedacceleration and electron bunch compressionschemes to be used at future free-electronlasers (16, 17). In order to produce femtosecondx-ray bursts, electron bunches at theStanford Linear Accelerator Center (SLAC)are chirped and then sent through a series ofenergy-dispersive magnetic chicanes to create80-fs electron pulses. These pulses are thentransported through an undulator to create sub-100-femtosecond x-ray pulses (18). In order toovercome the intrinsic jitter between x-raysand a Ti:sapphire-based femtosecond laser1 Stanford Synchrotron Radiation Laboratory/StanfordLinear Accelerator Center (SLAC), Menlo Park, CA 94025,USA. 2 Department of Physics, Lund Institute of Technology,Post Office Box 118, S-22100, Lund, Sweden.3 Institut für Optik und Quantenelektronik, Friedrich-Schiller Universität Jena, Max-Wien-Platz 1, 07743 Jena,Germany.4 Deutsches Elektronen-Synchrotron DESY,Notkestrasse 85, 22607 Hamburg, Germany. 5 Departmentof Physics, Clarendon Laboratory, Parks Road,University of Oxford, Oxford OX1 3PU, UK. 6 Departmentof Cell and Molecular Biology, BiomedicalCentre, Uppsala University, SE-75124 Uppsala, Sweden.7 Department of Physics, University of California,Berkeley, CA 94720, USA. 8 FOCUS (Frontiers in OpticalCoherent and Ultrafast Science) Center, Departmentof Physics and Applied Physics Program,University of Michigan, Ann Arbor, MI 48109, USA.9 Advanced Photon Source,10 Materials Science Division,Argonne National Laboratory, Argonne, IL 60439,USA.11 National Synchrotron Light Source, BrookhavenNational Laboratory, Upton, NY 11973, USA.12 Consortium for Advanced Radiation Sources, Universityof Chicago, Chicago, IL 60637, USA.13 NielsBohr Institute, Copenhagen University, 2100 CopenhagenØ, Denmark. 14 Institut für Experimentelle Physik,Universität Duisburg-Essen, D-45117 Essen, Germany.15 European Synchrotron Radiation Facility, 38043Grenoble Cedex 9, France.16 Physics Department,Lawrence Livermore National Laboratory, Livermore,CA 94550, USA. 17 Max Plank Institute for BiophysicalChemistry, Am Fabberg 11, 37077 Göttingen, Germany.18 SLAC, Menlo Park, CA 94025, USA.39215 APRIL 2005 VOL 308 SCIENCE www.sciencemag.org