Towards X-ray transient grating spectroscopy.

The extension of transient grating spectroscopy to the x-ray regime will create numerous opportunities, ranging from the study of thermal transport in the ballistic regime to charge, spin, and energy transfer processes with atomic spatial and femtosecond temporal resolution. Studies involving complicated split-and-delay lines have not yet been successful in achieving this goal. Here we propose a novel, simple method based on the Talbot effect for converging beams, which can easily be implemented at current x-ray free electron lasers. We validate our proposal by analyzing printed interference patterns on polymethyl methacrylate and gold samples using ∼3 keV X-ray pulses.

Ultrafast Relaxation Dynamics of the Antiferrodistortive Phase in Ca Doped SrTiO_{3}.

The ultrafast dynamics of the octahedral rotation in Ca:SrTiO_{3} is studied by time-resolved x-ray diffraction after photoexcitation over the band gap. By monitoring the diffraction intensity of a superlattice reflection that is directly related to the structural order parameter of the soft-mode driven antiferrodistortive phase in Ca:SrTiO_{3}, we observe an ultrafast relaxation on a 0.2 ps timescale of the rotation of the oxygen octahedron, which is found to be independent of the initial temperature despite large changes in the corresponding soft-mode frequency. A further, much smaller reduction on a slower picosecond timescale is attributed to thermal effects. Time-dependent density-functional-theory calculations show that the fast response can be ascribed to an ultrafast displacive modification of the soft-mode potential towards the normal state induced by holes created in the oxygen 2p states.

Doping Evolution of Magnetic Order and Magnetic Excitations in (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7}.

We use resonant elastic and inelastic x-ray scattering at the Ir-L_{3} edge to study the doping-dependent magnetic order, magnetic excitations, and spin-orbit excitons in the electron-doped bilayer iridate (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} (0≤x≤0.065). With increasing doping x, the three-dimensional long range antiferromagnetic order is gradually suppressed and evolves into a three-dimensional short range order across the insulator-to-metal transition from x=0 to 0.05, followed by a transition to two-dimensional short range order between x=0.05 and 0.065. Because of the interactions between the J_{eff}=1/2 pseudospins and the emergent itinerant electrons, magnetic excitations undergo damping, anisotropic softening, and gap collapse, accompanied by weakly doping-dependent spin-orbit excitons. Therefore, we conclude that electron doping suppresses the magnetic anisotropy and interlayer couplings and drives (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} into a correlated metallic state with two-dimensional short range antiferromagnetic order. Strong antiferromagnetic fluctuations of the J_{eff}=1/2 moments persist deep in this correlated metallic state, with the magnon gap strongly suppressed.

Coupling between a Charge Density Wave and Magnetism in an Heusler Material.

The prototypical magnetic memory shape alloy Ni_{2}MnGa undergoes various phase transitions as a function of the temperature, pressure, and doping. In the low-temperature phases below 260 K, an incommensurate structural modulation occurs along the [110] direction which is thought to arise from the softening of a phonon mode. It is not at present clear how this phenomenon is related, if at all, to the magnetic memory effect. Here we report time-resolved measurements which track both the structural and magnetic components of the phase transition from the modulated cubic phase as it is brought into the high-symmetry phase. The results suggest that the photoinduced demagnetization modifies the Fermi surface in regions that couple strongly to the periodicity of the structural modulation through the nesting vector. The amplitude of the periodic lattice distortion, however, appears to be less affected by the demagnetization.

Ultrafast Formation of a Charge Density Wave State in 1T-TaS_{2}: Observation at Nanometer Scales Using Time-Resolved X-Ray Diffraction.

Femtosecond time-resolved x-ray diffraction is used to study a photoinduced phase transition between two charge density wave (CDW) states in 1T-TaS_{2}, namely the nearly commensurate (NC) and the incommensurate (I) CDW states. Structural modulations associated with the NC-CDW order are found to disappear within 400 fs. The photoinduced I-CDW phase then develops through a nucleation and growth process which ends 100 ps after laser excitation. We demonstrate that the newly formed I-CDW phase is fragmented into several nanometric domains that are growing through a coarsening process. The coarsening dynamics is found to follow the universal Lifshitz-Allen-Cahn growth law, which describes the ordering kinetics in systems exhibiting a nonconservative order parameter.

A time-dependent order parameter for ultrafast photoinduced phase transitions.

Strongly correlated electron systems often exhibit very strong interactions between structural and electronic degrees of freedom that lead to complex and interesting phase diagrams. For technological applications of these materials it is important to learn how to drive transitions from one phase to another. A key question here is the ultimate speed of such phase transitions, and to understand how a phase transition evolves in the time domain. Here we apply time-resolved X-ray diffraction to directly measure the changes in long-range order during ultrafast melting of the charge and orbitally ordered phase in a perovskite manganite. We find that although the actual change in crystal symmetry associated with this transition occurs over different timescales characteristic of the many electronic and vibrational coordinates of the system, the dynamics of the phase transformation can be well described using a single time-dependent 'order parameter' that depends exclusively on the electronic excitation.

Ultrafast structural dynamics of the Fe-pnictide parent compound BaFe(2)As(2).

Using femtosecond time-resolved x-ray diffraction we investigate the structural dynamics of the coherently excited A(1g) phonon mode in the Fe-pnictide parent compound BaFe(2)As(2). The fluence dependent intensity oscillations of two specific Bragg reflections with distinctly different sensitivity to the pnictogen height in the compound allow us to quantify the coherent modifications of the Fe-As tetrahedra, indicating a transient increase of the Fe magnetic moments. By a comparison with time-resolved photoemission data, we derive the electron-phonon deformation potential for this particular mode. The value of Δµ/Δz=-(1.0-1.5) eV/Å is comparable with theoretical predictions and demonstrates the importance of this degree of freedom for the electron-phonon coupling in the Fe pnictides.

Coherent structural dynamics of a prototypical charge-density-wave-to-metal transition.

Using femtosecond time-resolved x-ray diffraction, we directly monitor the coherent lattice dynamics through an ultrafast charge-density-wave-to-metal transition in the prototypical Peierls system K(0.3)MoO(3) over a wide range of relevant excitation fluences. While in the low fluence regime we directly follow the structural dynamics associated with the collective amplitude mode; for fluences above the melting threshold of the electronic density modulation we observe a transient recovery of the periodic lattice distortion. We can describe these structural dynamics as a motion along the coordinate of the Peierls distortion triggered by the prompt collapse of electronic order after photoexcitation. The results indicate that the dynamics of a structural symmetry-breaking transition are determined by a high-symmetry excited state potential energy surface distinct from that of the initial low-temperature state.

Structural and magnetic dynamics of a laser induced phase transition in FeRh.

We use time-resolved x-ray diffraction and magneto-optical Kerr effect to study the laser-induced antiferromagnetic to ferromagnetic phase transition in FeRh. The structural response is given by the nucleation of independent ferromagnetic domains (τ(1)~30 ps). This is significantly faster than the magnetic response (τ(2)~60 ps) given by the subsequent domain realignment. X-ray diffraction shows that the two phases coexist on short time scales and that the phase transition is limited by the speed of sound. A nucleation model describing both the structural and magnetic dynamics is presented.

Femtosecond dynamics of the collinear-to-spiral antiferromagnetic phase transition in CuO.

We report on the ultrafast dynamics of magnetic order in a single crystal of CuO at a temperature of 207 K in response to strong optical excitation using femtosecond resonant x-ray diffraction. In the experiment, a femtosecond laser pulse induces a sudden, nonequilibrium increase in magnetic disorder. After a short delay ranging from 400 fs to 2 ps, we observe changes in the relative intensity of the magnetic ordering diffraction peaks that indicate a shift from a collinear commensurate phase to a spiral incommensurate phase. These results indicate that the ultimate speed for this antiferromagnetic reorientation transition in CuO is limited by the long-wavelength magnetic excitation connecting the two phases.

Nonthermal melting of a charge density wave in TiSe2.

We use time-resolved optical reflectivity and x-ray diffraction with femtosecond resolution to study the dynamics of the structural order parameter of the charge density wave phase in TiSe2. We find that the energy density required to melt the charge density wave nonthermally is substantially lower than that required for thermal suppression and is comparable to the charge density wave condensation energy. This observation, together with the fact that the structural dynamics take place on an extremely fast time scale, supports the exciton condensation mechanism for the charge density wave in TiSe2.

Nonequilibrium charge-density-wave order beyond the thermal limit.

The interaction of many-body systems with intense light pulses may lead to novel emergent phenomena far from equilibrium. Recent discoveries, such as the optical enhancement of the critical temperature in certain superconductors and the photo-stabilization of hidden phases, have turned this field into an important research frontier. Here, we demonstrate nonthermal charge-density-wave (CDW) order at electronic temperatures far greater than the thermodynamic transition temperature. Using time- and angle-resolved photoemission spectroscopy and time-resolved X-ray diffraction, we investigate the electronic and structural order parameters of an ultrafast photoinduced CDW-to-metal transition. Tracking the dynamical CDW recovery as a function of electronic temperature reveals a behaviour markedly different from equilibrium, which we attribute to the suppression of lattice fluctuations in the transient nonthermal phonon distribution. A complete description of the system's coherent and incoherent order-parameter dynamics is given by a time-dependent Ginzburg-Landau framework, providing access to the transient potential energy surfaces.

Strain wave pathway to semiconductor-to-metal transition revealed by time-resolved X-ray powder diffraction.

One of the main challenges in ultrafast material science is to trigger phase transitions with short pulses of light. Here we show how strain waves, launched by electronic and structural precursor phenomena, determine a coherent macroscopic transformation pathway for the semiconducting-to-metal transition in bistable Ti3O5 nanocrystals. Employing femtosecond powder X-ray diffraction, we measure the lattice deformation in the phase transition as a function of time. We monitor the early intra-cell distortion around the light absorbing metal dimer and the long range deformations governed by acoustic waves propagating from the laser-exposed Ti3O5 surface. We developed a simplified elastic model demonstrating that picosecond switching in nanocrystals happens concomitantly with the propagating acoustic wavefront, several decades faster than thermal processes governed by heat diffusion.

Full reconstruction of a crystal unit cell structure during coherent femtosecond motion.

We present a complete characterization of the unit cell dynamics of a laser-excited tellurium crystal using femtosecond x-ray diffraction. The analysis offers a quantitative measure of the unit cell dynamics without making any assumptions on the symmetry of the excited-state motion. The results show a large-amplitude coherently excited A(1) mode quantitatively consistent with the predictions of a density functional theory model.

Ultrafast structural phase transition driven by photoinduced melting of charge and orbital order.

We use femtosecond x-ray diffraction to probe directly the structural dynamics of a charge ordered and orbitally ordered thin film of La0.42Ca0.58MnO3 initiated by an ultrafast optical pulse. At low excitation fluences we observe the displacive excitation of a coherent optical A(g) phonon. Under high excitation conditions we observe a complete phase transition within 1 ps via the disappearance of a superlattice reflection. The initial step of the phase transition occurs on a time scale significantly faster than the 200 fs time resolution of our experiment.

Watching ultrafast responses of structure and magnetism in condensed matter with momentum-resolved probes.

We present a non-comprehensive review of some representative experimental studies in crystalline condensed matter systems where the effects of intense ultrashort light pulses are probed using x-ray diffraction and photoelectron spectroscopy. On an ultrafast (sub-picosecond) time scale, conventional concepts derived from the assumption of thermodynamic equilibrium must often be modified in order to adequately describe the time-dependent changes in material properties. There are several commonly adopted approaches to this modification, appropriate in different experimental circumstances. One approach is to treat the material as a collection of quasi-thermal subsystems in thermal contact with each other in the so-called "N-temperature" models. On the other extreme, one can also treat the time-dependent changes as fully coherent dynamics of a sometimes complex network of excitations. Here, we present examples of experiments that fall into each of these categories, as well as experiments that partake of both models. We conclude with a discussion of the limitations and future potential of these concepts.

Ultrafast structural dynamics of the orthorhombic distortion in the Fe-pnictide parent compound BaFe2As2.

Using femtosecond time-resolved hard x-ray diffraction, we investigate the structural dynamics of the orthorhombic distortion in the Fe-pnictide parent compound BaFe2As2. The orthorhombic distortion analyzed by the transient splitting of the (1 0 3) Bragg reflection is suppressed on an initial timescale of 35 ps, which is much slower than the suppression of magnetic and nematic order. This observation demonstrates a transient state with persistent structural distortion and suppressed magnetic/nematic order which are strongly linked in thermal equilibrium. We suggest a way of quantifying the coupling between structural and nematic degrees of freedom based on the dynamics of the respective order parameters.

Femtosecond X-ray absorption study of electron localization in photoexcited anatase TiO2.

Transition metal oxides are among the most promising solar materials, whose properties rely on the generation, transport and trapping of charge carriers (electrons and holes). Identifying the latter's dynamics at room temperature requires tools that combine elemental and structural sensitivity, with the atomic scale resolution of time (femtoseconds, fs). Here, we use fs Ti K-edge X-ray absorption spectroscopy (XAS) upon 3.49 eV (355 nm) excitation of aqueous colloidal anatase titanium dioxide nanoparticles to probe the trapping dynamics of photogenerated electrons. We find that their localization at Titanium atoms occurs in <300 fs, forming Ti(3+) centres, in or near the unit cell where the electron is created. We conclude that electron localization is due to its trapping at pentacoordinated sites, mostly present in the surface shell region. The present demonstration of fs hard X-ray absorption capabilities opens the way to a detailed description of the charge carrier dynamics in transition metal oxides.

Large-amplitude spin dynamics driven by a THz pulse in resonance with an electromagnon.

Multiferroics have attracted strong interest for potential applications where electric fields control magnetic order. The ultimate speed of control via magnetoelectric coupling, however, remains largely unexplored. Here, we report an experiment in which we drove spin dynamics in multiferroic TbMnO3 with an intense few-cycle terahertz (THz) light pulse tuned to resonance with an electromagnon, an electric-dipole active spin excitation. We observed the resulting spin motion using time-resolved resonant soft x-ray diffraction. Our results show that it is possible to directly manipulate atomic-scale magnetic structures with the electric field of light on a sub-picosecond time scale.