Ultrafast evolution and transient phases of the prototype out-of-equilibrium Mott-Hubbard material V2O3
G. Lantz, B Mansart, D. Grieger, D. Boschetto, N. Nilforoushan, E. Papalazarou, N. Moisan, L. Perfetti, V.L.R. Jacques, D. Le Bolloc'h, C. Laulhé, S. Ravy, J.-P. Rueff, T.E. Glover, M.P. Hertlein, Z. Hussain, S. Song, M. Chollet, M. Fabrizio, M. Marsi
UUltrafast evolution and transient phases of a prototype out-of-equilibriumMott-Hubbard material
G. Lantz,
1, 2
B. Mansart, D. Grieger, D. Boschetto, N. Nilforoushan, E. Papalazarou, N. Moisan, L. Perfetti, V. L. R. Jacques, D. Le Bolloch, C. Laulh´e,
6, 7
S. Ravy,
6, 1
J.-P. Rueff, T.E. Glover, M.P. Hertlein, Z. Hussain, S. Song, M. Chollet, M. Fabrizio, and M. Marsi Laboratoire de Physique des Solides, CNRS, Univ. Paris-Sud, Universit´e Paris-Saclay, 91405 Orsay, France Institute for Quantum Electronics, Physics Department, ETH Zurich, CH-8093 Zurich, Switzerland International School for Advanced Studies SISSA, Via Bonomea 265, 34136 Trieste, Italy Laboratoire d’Optique Appliqu´ee, ENSTA, CNRS, Ecole Polytechnique, F-91761 Palaiseau, France Laboratoire des Solides Irradi´es, Ecole Polytechnique-CEA/SSM-CNRS UMR 7642, 91128 Palaiseau, France Synchrotron SOLEIL, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette Cedex, France Univ. Paris-Sud, Universit´e Paris-Saclay, 91405 Orsay, France Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA SLAC National Accelerator Lab, Stanford PULSE Inst, Menlo Pk, CA 94025, USA (Dated: October 4, 2016)
PACS numbers:
The study of photoexcited strongly correlatedmaterials is attracting growing interest sincetheir rich phase diagram often translates into anequally rich out-of-equilibrium behavior, includ-ing non-thermal phases and photoinduced phasetransitions. With femtosecond optical pulses,electronic and lattice degrees of freedom can betransiently decoupled, giving the opportunity ofstabilizing new states of matter inaccessible byquasi-adiabatic pathways. Here we present astudy of the ultrafast non-equilibrium evolutionof the prototype Mott-Hubbard material V O ,which presents a transient non-thermal phase de-veloping immediately after photoexcitation andlasting few picoseconds. For both the insulat-ing and the metallic phase, the formation of thetransient configuration is triggered by the excita-tion of electrons into the bonding a g orbital, andis then stabilized by a lattice distortion charac-terized by a marked hardening of the A g coher-ent phonon. This configuration is in stark con-trast with the thermally accessible ones - the A g phonon frequency actually softens when heatingthe material. Our results show the importanceof selective electron-lattice interplay for the ul-trafast control of material parameters, and are ofparticular relevance for the optical manipulationof strongly correlated systems, whose electronicand structural properties are often strongly inter-twinned. The Mott metal-to-insulator transition (MIT)[1] is theperfect example of how thermodynamic parameters canaffect the electronic structure of a material and its con-ducting properties. At equilibrium, temperature, doping,and pressure act as driving forces for such transitions [2],that invariably involve also a lattice modification - eitherwith a change of symmetry, like for instance in VO [3] or with a lattice parameter jump like in V O [4]. It is ac-tually often unclear whether the lattice or the electronicstructure is the trigger for the MIT since at equilibriumboth change together. This ”chicken and egg” questioncan be answered by driving one far from equilibrium andobserving the reaction of the other. Thus, time-resolvedpump-probe techniques [5–9] can provide this answer, aslong as the response of the electrons and of the latticecan be separately analyzed.In this letter we use a combined experimental andtheoretical approach to study the ultrafast evolution ofthe Mott-Hubbard prototype (V − x Cr x ) O [10]. Thephase diagram of V O contains three phases, a param-agnetic metallic (PM) phase, a paramagnetic insulating(PI) phase, and antiferromagnetic insulator phase (AFI),see Fig. 1. The isostructural Mott transition is betweenthe PI and the PM phases [11]. In all our experiments,the energy of the pump pulses (1.5 eV) corresponds to thetransition from e πg to a g orbitals. Thus optical pump-ing directly increases the a g population while decreas-ing the e πg one. Using time-resolved PhotoElectron Spec-troscopy (trPES) we directly probe the electronic struc-ture, while time-resolved X-Ray Diffraction (trXRD) andCoherent Phonon Spectroscopy (CPS) give access to thelattice evolution [12–15]. Thanks to this multitechniqueapproach, we can unambiguously disentangle the contri-bution of electrons and lattice to the non-equilibrium dy-namics of the system. Furthermore, this archetypal ma-terial gives the opportunity of comparatively observingthe ultrafast evolution of a Mott system starting bothfrom the insulating and the metallic phase, whereas pre-vious studies have generally focused only on the insulatoras ground state [5–9]. We find that in the PI phase thegap is instantaneously filled and a non-thermal transientstate that lasts 2 ps is created. In the PM phase, thequasiparticle (QP) signal shows an immediate apprecia-ble spectral redistribution across E F which also lasts 2 a r X i v : . [ c ond - m a t . s t r- e l ] A ug a bc I ∝ |F hkl (t)| trXrd Pump 1.5 eV X-ray 6 keV e - E-E f trPES CPS Reflectivity(CPS) Probe1.5 eV crossover regionPI PMAFI + Ti + Cr T ( K ) (V M x ) O I n t e n s i t y ( a r b . u . ) -0.4 -0.2 0.0 0.2E-E F (eV)X2X4 V O pure (PM) 290 K 205 K ∆ T=20 K V O ∆ T=20 K t a σ a σ∗ e g π PM PI FFT sc a tt e r ed i n t en s i t y -3x10 -3 -2-10 Δ R / R a b c d V V a e g π c FIG. 1: a) : (V − x Cr x ) O phase diagram; the crossesindicate the experimental data points. b) : Temperaturedependence of the equilibrium photoemission spectra for(V − x Cr x ) O (x=0.028 PI phase, x=0 PM phase). Temper-ature differences are shown for each doping, which are usedas a thermal equilibrium reference in the comparison withthe photoexcited spectra. Upon increasing the temperature,the spectral weight is transferred into the Mott gap in the PIphase, whereas the QP peak weakens in the PM phase. c) :representation of the orbital splitting and their geometry. d) :Schematic of the experiments using an optical pump and dif-ferent probes: X-ray diffraction, photoemission, and coherentphonon spectroscopy. ps, once again not compatible with thermal heating. Inboth phases we find that the lattice conspires to stabi-lize the non-thermal transient electronic state. Ab-initioDFT-GGA results supplemented by simple Hartree-Fockcalculations suggest that the gap filling is driven by thenon-equilibrium population imbalance between the e πg and a g orbitals, which effectively weakens the correla-tion strength.In vanadium sesquioxide the octahedral crystal fieldleads to the d -orbital splitting into a lower t g and anupper e σg . Since the octahedron has a trigonal distor-tion, the t g are split into a lower twofold degenerate e πg orbital and an upper non-degenerate a g (Fig. 1).The hybridization between the two nearest vanadiumatoms, which are lined up along the c -axis, causes alarge splitting between bonding a g ( σ ) and antibonding a g ( σ ∗ ) states. In spite of that, the a g orbital remainsmostly unoccupied in the PI phase, whereas the e πg or-bitals are occupied by almost one electron each[16, 17]. V O PI can thus be viewed as a half-filled 2-band Mottinsulator stabilized by the correlation-enhanced trigonalfield that pushes above the Fermi energy (E F ) the a g orbitals[16, 18], whose occupancy indeed jumps acrossthe doping- or temperature-driven Mott transition[19],whilst is smoother across the pressure driven one[11, 20].This inequivalent behavior in temperature versus pres-sure of the MIT and the related deep intertwining be-tween strong correlations and lattice structure suggestthat a major issue in time-resolved experiments is to dis-tinguish a temperature increase from a transient non-thermal phase, such as hidden phases [21, 22].Before exploring the behavior of the system after pho-toexcitation, we present in Fig. 1 the photoemission re-sponses of the PI and PM phases at different tempera-tures, which give us reference energy distribution curves(EDC’s) for the system at equilibrium. In the PM phasethe weight near E F increases with decreasing tempera-tures, which is consistent with the expected behavior ofthe QP [23]. In the PI phase, the temperature increasefills the gap, which is consistent with the results fromMo et al. [24]. The temperature difference starting from200 K, ∆T = 20K, is the estimated temperature risebrought by the pump laser pulse for the fluence used inour pump-probe photoemission experiments (see supple-mentary materials). Therefore the difference curves be-tween high and low temperature spectra at fixed dopingmay serve to compare the non-equilibrium spectra withreference thermal ones.The non-equilibrium electron dynamics has been stud-ied with pump-probe photoemission. The differences be-tween positive and negative time delays are shown in Fig.2( a-c ) for the PI phase. As representative of the timeevolution, we consider the time-scan at -0.1 eV below E F (Fig. 2( a )), whose decay can be fitted with two expo-nentials. The first one of 76 fs corresponds to the hotelectron relaxation after photoexcitation and clearly in-dicates a strong electron-phonon coupling. We associatethe second longer timescale of 1.7 ps with the lifetime ofa transient state, as suggested by comparing the EDC’sat 50 fs, 400 fs, and 2 ps with the thermal differences atequilibrium (black). At 50 fs delay (red curve) an increasein spectral weight is clearly visible both below and aboveE F , an evidence of creation of in-gap states. The EDCcannot be fitted with a Fermi-Dirac distribution, sincethe system is still strongly out of equilibrium. The 400 fsdelay spectrum has instead no weight above E F : the ex-cess electrons have cooled down. Nevertheless, the spec-trum still deviates from the equilibrium one, in particularat -0.1 eV binding energy, indicating that, even thoughthe electrons have relaxed, the state is different from thethermal configuration. A spectral difference equivalentto the thermal state at equilibrium can instead be foundafter 2 ps, when the transient state has fully relaxed.Fig. 2( d-f ) reports the photoexcited behavior of pureV O (PM) at the same fluence of 1.8 mJ.cm − . The -10 ∆ I ( a r b . u . ) -0.4 -0.2 0.0 0.2E-E F (eV) 50 fs 400 fs ∆ T =20 K eq0.90.60.30 ∆ I ( a r b . u . ) F = -0.1 eV τ =76 fs, τ =1.7 ps10 ∆ I ( a r b . u . ) -0.4 -0.2 0.0 0.2E-E F (eV)X4X4X4 50 fs 400 fs 2 ps ∆ T=20 K eq 0.30.20.10.0 ∆ I ( a r b . u . ) E-E F =0.1 eV τ =70 fs τ =1.8 psbac efd0.50.0 D O S ( a r b . u . ) -0.4 -0.2 0.0 0.2E-E F (eV) e g π a D O S ( a r b . u . ) -0.4 -0.2 0.0 0.2E-E F (eV) e g π a Paramagnetic insulating phase Paramagnetic metallic phase
FIG. 2: trPES for (V − x Cr x ) O (x=0.028 PI phase and x=0 PM phase) at a fluence of 1.8 mJ.cm − . a) : Time evolution ofthe intensity difference at -0.1 eV, the curve is fitted with a double exponential. b) : PES intensity difference for ∆t=50 fs,400 fs , and 2 ps are shown for the PI phase as well as the equilibrium temperature difference from Fig. 1. The 50 fs and 400fs differences show that the spectral weight is transferred inside the Mott gap, differently from a purely thermal effect. Thisnon-thermal distribution relaxes within 2 ps. c) : Orbital character of the density-of-states near E F extracted from [16]. d-f ) :Same as ( a-c ) but for the PM phase. The time evolution is fitted with a double exponential for the energy above E F . time scan at 0.1 eV above E F (Fig. 2( d )) shows a fastdecay with a characteristic time of 70 fs and a slower oneof 1.8 ps, similar to the time constants found in the PIphase. Indeed the EDC differences at 50 fs and 400 fsdelays are compatible with the hot electrons not beingthermalized at 50 fs and almost thermalized at 400 fs.The observed spectral changes obtained around E F bykeeping the sample at T and photoexciting with a pumppulse cannot be ascribed to heating, but rather to a gen-uine non-thermal transient state[25, 26]. In particular,both spectra at 50 fs and 400 fs (Fig. 2( e )) suggest thatthere is more weight both below and above E F in thephotoexcited state at temperature T than in the equilib-rium state at T+∆T. Therefore, the reduction of densityof states around E F is lnot compatible with a thermallyexcited configuration. This non-thermal state relaxes in2 ps, similarly to the PI phase.Further evidence in support of a transient non-thermalphase comes from the lattice. In Fig. 3 we presentCPS measurements that provide information on the tran-sient response of the fully symmetric A g optical phonon,which corresponds to the breathing of one entity ofV O as shown in Fig. 1. Consistently with previousstudies[27, 28], we observe an electronic excitation peaklasting about 200 fs, similar to the trPES response ob-served in Fig. 2. The succeeding coherent oscillations canbe analyzed by Fourier transform, which is compared in Fig. 3( b-c ) with the A g mode measured with Ramanspectroscopy at equilibrium. Surprisingly, the mode dis-plays a blue-shift of up to 14% compared to the equilib-rium frequency for both PI and PM phases. Such a blue-shift, i.e. a phonon hardening, is certainly non-thermalin nature. Indeed a temperature increase causes insteadsoftening and consequently a red-shift [29]. Hardeningof the A g phonon actually corresponds to a decreaseof the average distance between the two closest vana-dium atoms, d(V -V ) [17], and as well to an overpop-ulation of the a g orbitals (see supplementary material).It should be underlined that this coherent phonon hard-ening is present for both the PM and PI phases, and thatits decoherence time is about 2 ps: these features are infull agreement with the behavior observed for the elec-tronic degrees of freedom with trPES (Fig. 2). There isconsequently a strong evidence of a transient phase thatdoes not correspond to any equilibrium phase of the sys-tem, involving both the electronic and lattice structureand present in both PM and PI phases.In order to verify our interpretation on the nature ofthis transient phonon blue-shift, we performed a trXRDstudy on the same crystals used for the trPES and CPSmeasurements. In Fig. 3( d-e ) we present the time depen-dent intensity of the Bragg reflections (116) and (204)for the PI phase. The peak positions do not changeuntil 4 ps, therefore the lattice parameters are constant N o r m a li z ed I n t en s i t y -V ) (Å)PICalculated F hkl (024) (116) min value-0.10-0.050.000.05 ( I - I O ff ) /I O ff d e -3 -2.5-2.0-1.5-1.0-0.50.0 Δ R / R -3 -4-20 PI PM 10864 Frequency (THz) PM FFT Raman FFT sc a tt e r ed i n t en s i t y b ca FIG. 3: a) : CPS traces for (V − x Cr x ) O (x=0.028 PI andx=0 PM) for a fluence of 8 mJ/cm : the A g coherent phononis clearly visible b-c) : Fast Fourier transform of CPS tracescompared to equilibrium Raman spectroscopy for the PMphase and PI phase respectively. The A g pump-probe fre-quencies (full) present a clear blue shift compared to the equi-librium frequency (dashed) in both phases. d) : trXRD mea-surements in the PI phase for a fluence of 8 mJ/cm , showingthe pump-probe diffraction peak intensities for the Bragg re-flections (116) and (024). The solid lines are the simulationas explained in text. e) shows the calculated structure fac-tor versus the shortest vanadium distance (V -V ). The blackdots represent the minimum distance observed extracted from d . during the first few picoseconds (see supplementary ma-terial). However the intensities of both Bragg reflec-tions vary before hand. The oxygen atoms do not af-fect much the diffraction intensity compared to the vana-dium atoms. Supposing that the symmetry of the crystalstays the same, the diffracted intensity can be simulatedby a change of the vanadium Wyckoff position, Z V , anda Debye-Waller factor [14]. The distance of the nearestvanadium atoms is given by the relation d(V -V )=(2Z V -0.5) c , where c is the lattice constant. The (116) and(024) structure factors vary in opposite directions withZ V . We find that, d(V -V ) goes from 2.744 ˚ A to a min-imum value of 2.71˚ A before 1 ps ( d(V -V ) P M =2.69 ˚ A ).The Debye-Waller is responsible for only 0.1% of the in-tensity change before 4 ps. The trXRD response was notable to resolve the coherent lattice oscillations, due tolimits in the signal-to-noise levels attainable during themeasurements, but it does confirm that the blue-shift inthe coherent phonon frequency is related to a transientreduction of the average distance d(V -V ). By compar-ing the temporal evolution of the different experimental results, the TR-PES measurements show that the elec-tronic structure is modified faster, and that the latticedeformation follows - which is expected for a prototypeMott system. The resulting non-thermal state is visiblymore metallic in the PI phase, and seems most likely moredelocalized in the PM one as well. In both cases, thisstate is stabilized by a transient lattice deformation thatshortens the distance between the two nearest vanadiumatoms and consequently increases the covalent bondingbetween the a g orbitals. The fact that trXRD gives aslightly longer relaxation time with respect to trPES canbe explained by the different probing depths of the twotechniques [6]. Theory : We considered a three-band Hubbard model atone-third filling for the t g orbitals with the tight-bindinghopping parameters of Ref. [17], and analyzed this modelby means of the Hartree-Fock (HF) approximation[18]using as control parameter, after a Legendre transform,the occupancy difference between e πg and a g orbitals. Inorder to describe an insulator within an independent par-ticle scheme as HF we had to allow for magnetism; ourinsulator is thus closer to the AFI low-temperature phaserather than to the high-temperature PI[18]. Within HF,the total energy, shown in Fig. 4( a ), has two minima, astable one at n a (cid:39) . n a (cid:39) .
625 that instead repre-sents a metal. In Fig. 4( b ) we plot the density of statesfor three different values of n , two in the insulating phaseand one in the metal. We modeled the experiment inthe PI phase starting from a Slater determinant thatdescribes the HF insulator with a number of electronstransferred from the valence band of mostly e πg characterto the conduction one, with a g character, and studiedits time evolution within time-dependent Hartree-Fock.We find it is enough to transfer ∼ .
13 electrons to theconduction band to drive the system into the metastablemetallic phase, as pictorially drawn in Fig. 4( a ), whichis consistent with the experimental excitation that are8% for a fluence of 8 mJ/cm in the trXrd and CPSexperiments and 3.1% for the trPES . In other words,the non-thermal phase appears in this theoretical sce-nario as a metastable state that preexists in equilibriumand can be nucleated within the stable insulator throughthe photoexcitation. Since time-dependent Hartree-Fockdoes not account for dissipation, we cannot describe thesubsequent break-up of the metastable metal nuclei backinto the stable insulator, which experimentally occurs af-ter few ps. Conclusion
With a combined experimental and the-oretical approach, we show that the ultrafast response ofthe prototype Mott-Hubbard compound (V − x Cr x ) O is characterized by a non-thermal transient phase inwhich the system remains trapped before relaxing to thefinal thermal state. The formation of this non-thermalphase is very fast for both PM and PI - faster than our ex-perimental time resolution - and it is eminently electronic ene r g y pe r a t o m ( e V ) ∆ n=n e g π - n a Metal Insulator 6050403020100 D O S ( a r b . u . ) F (eV) n a = 0.50 n a = 0.57 n a = 0.67 a b ∆ t = 400 fs ∆ t = 50 fs e π ga1g E - E F ( e V ) UHBLHB ∆ t = 0 fs c FIG. 4: a) : HF total energy as function of the occupancydifference between e πg and a g orbitals (the total occupancy is2); b) : Density of state (DOS) for different occupancies of thea g ; c) Schematic view of the proposed mechanism involved inthe photoexcitation of a Mott material, where the a g stateslower in energy both of the PM and PI phases. in nature, being driven by a transient overpopulation ofa bonding a g orbital. A selective lattice deformation,strikingly highlighted by the A g phonon hardening, fur-ther stabilizes this non-thermal transient phase, whoselifetime grows up to few ps: this direct comparative anal-ysis of the evolution of the metallic and insulating phasesis relevant for all the efforts aiming at photoinducingphase transitions in correlated materials, including possi-ble technological applications like ultrafast switches. Ourresults thus show that a selective electron-lattice cou-pling can play an important role in out-of-equilibriumMott systems, even though the main actor remains thestrong correlation; and appear to be of very general valid-ity, suggesting that similar non adiabatic pathways canbe found in other multi-band Mott compounds followingexcitation with ultrafast light pulses. Methods:
See Supplementary materials.
Acknowledgments.
GL, DG, EP, MF and MM ac-knowledge financial support by the EU/FP7 under thecontract Go Fast (Grant No. 280555). GL, NM,LP, EP, and MM acknowledge financial support b ”In-vestissement d’Avenir Labex PALM (ANR-10-LABX-0039-PALM), by the Equipex ATTOLAB (ANR11-EQPX0005-ATTOLAB) and by the R´egion Ile-de-Francethrough the program DIM OxyMORE. DB acknowledgesthe financial support of the French Procurement Agency(DGA) of the French Ministry of Defense. The Ad-vanced Light Source is supported by the Director, Officeof Science, Office of Basic Energy Sciences, of the U.S.Department of Energy under Contract No. DE-AC02-05CH11231. Use of the Linac Coherent Light Source (LCLS), SLAC National Accelerator Laboratory is sup-ported by the U.S. Department of Energy, Office of Sci-ence, Office of Basic Energy Sciences under Contract No.DE-AC02-76SF00515. [1] N. Mott and R. Peierls, in
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