The ultrafast Einstein-de Haas effect.

The Einstein-de Haas effect was originally observed in a landmark experiment1 demonstrating that the angular momentum associated with aligned electron spins in a ferromagnet can be converted to mechanical angular momentum by reversing the direction of magnetization using an external magnetic field. A related problem concerns the timescale of this angular momentum transfer. Experiments have established that intense photoexcitation in several metallic ferromagnets leads to a drop in magnetization on a timescale shorter than 100 femtoseconds-a phenomenon called ultrafast demagnetization2-4. Although the microscopic mechanism for this process has been hotly debated, the key question of where the angular momentum goes on these femtosecond timescales remains unanswered. Here we use femtosecond time-resolved X-ray diffraction to show that most of the angular momentum lost from the spin system upon laser-induced demagnetization of ferromagnetic iron is transferred to the lattice on sub-picosecond timescales, launching a transverse strain wave that propagates from the surface into the bulk. By fitting a simple model of the X-ray data to simulations and optical data, we estimate that the angular momentum transfer occurs on a timescale of 200 femtoseconds and corresponds to 80 per cent of the angular momentum that is lost from the spin system. Our results show that interaction with the lattice has an essential role in the process of ultrafast demagnetization in this system.

Exchange scaling of ultrafast angular momentum transfer in 4f antiferromagnets.

Ultrafast manipulation of magnetism bears great potential for future information technologies. While demagnetization in ferromagnets is governed by the dissipation of angular momentum1-3, materials with multiple spin sublattices, for example antiferromagnets, can allow direct angular momentum transfer between opposing spins, promising faster functionality. In lanthanides, 4f magnetic exchange is mediated indirectly through the conduction electrons4 (the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction), and the effect of such conditions on direct spin transfer processes is largely unexplored. Here, we investigate ultrafast magnetization dynamics in 4f antiferromagnets and systematically vary the 4f occupation, thereby altering the magnitude of the RKKY coupling energy. By combining time-resolved soft X-ray diffraction with ab initio calculations, we find that the rate of direct transfer between opposing moments is directly determined by this coupling. Given the high sensitivity of RKKY to the conduction electrons, our results offer a useful approach for fine tuning the speed of magnetic devices.

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.

Nonlinear Electron-Phonon Coupling in Doped Manganites.

We employ time-resolved resonant x-ray diffraction to study the melting of charge order and the associated insulator-to-metal transition in the doped manganite Pr_{0.5}Ca_{0.5}MnO_{3} after resonant excitation of a high-frequency infrared-active lattice mode. We find that the charge order reduces promptly and highly nonlinearly as function of excitation fluence. Density-functional theory calculations suggest that direct anharmonic coupling between the excited lattice mode and the electronic structure drives these dynamics, highlighting a new avenue of nonlinear phonon control.

Itinerant and Localized Magnetization Dynamics in Antiferromagnetic Ho.

Using femtosecond time-resolved resonant magnetic x-ray diffraction at the Ho L_{3} absorption edge, we investigate the demagnetization dynamics in antiferromagnetically ordered metallic Ho after femtosecond optical excitation. Tuning the x-ray energy to the electric dipole (E1, 2p→5d) or quadrupole (E2, 2p→4f) transition allows us to selectively and independently study the spin dynamics of the itinerant 5d and localized 4f electronic subsystems via the suppression of the magnetic (2 1 3-τ) satellite peak. We find demagnetization time scales very similar to ferromagnetic 4f systems, suggesting that the loss of magnetic order occurs via a similar spin-flip process in both cases. The simultaneous demagnetization of both subsystems demonstrates strong intra-atomic 4f-5d exchange coupling. In addition, an ultrafast lattice contraction due to the release of magneto-striction leads to a transient shift of the magnetic satellite peak.

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.

Fermi Surface of Three-Dimensional La(1-x)Sr(x)MnO3 Explored by Soft-X-Ray ARPES: Rhombohedral Lattice Distortion and its Effect on Magnetoresistance.

Electronic structure of the three-dimensional colossal magnetoresistive perovskite La(1-x)Sr(x)MnO3 has been established using soft-x-ray angle-resolved photoemission spectroscopy with its intrinsically sharp definition of three-dimensional electron momentum. The experimental results show much weaker polaronic coupling compared to the bilayer manganites and are consistent with the theoretical band structure including the empirical Hubbard parameter U. The experimental Fermi surface unveils the canonical topology of alternating three-dimensional electron spheres and hole cubes, with their shadow contours manifesting the rhombohedral lattice distortion. This picture has been confirmed by one-step photoemission calculations including displacement of the apical oxygen atoms. The rhombohedral distortion is neutral to the Jahn-Teller effect and thus polaronic coupling, but affects the double-exchange electron hopping and thus the colossal magnetoresistance effect.

Multiferroic properties of o-LuMnO3 controlled by b-axis strain.

Strain is a leading candidate for controlling magnetoelectric coupling in multiferroics. Here, we use x-ray diffraction to study the coupling between magnetic order and structural distortion in epitaxial films of the orthorhombic (o-) perovskite LuMnO(3). An antiferromagnetic spin canting in the E-type magnetic structure is shown to be related to the ferroelectrically induced structural distortion and to a change in the magnetic propagation vector. By comparing films of different orientations and thicknesses, these quantities are found to be controlled by b-axis strain. It is shown that compressive strain destabilizes the commensurate E-type structure and reduces its accompanying ferroelectric distortion.

Imprinting magnetic information in manganites with x rays.

The effect of x rays on an orbital and charge ordered epitaxial film of a Pr0.5Ca0.5MnO3 is presented. As the film is exposed to x rays, the antiferromagnetic response increases and concomitantly the conductivity of the film improve. These results are discussed in terms of a persistent x-ray induced doping, leading to a modification of the magnetic structure. This effect allows writing electronic and magnetic information in the film and represents a novel way of manipulating magnetism.

Origin of the large polarization in multiferroic YMnO3 thin films revealed by soft- and hard-X-ray diffraction.

We investigated the magnetic structure of an orthorhombic YMnO(3) thin film by resonant soft x-ray and hard x-ray diffraction. We observed a temperature-dependent incommensurate magnetic reflection below 45 K and a commensurate lattice-distortion reflection below 35 K. These results demonstrate that the ground state is composed of coexisting E-type and cycloidal states. Their different ordering temperatures clarify the origin of the large polarization to be caused by the E-type antiferromagnetic states in the orthorhombic YMnO(3) thin film.

Competing ferri- and antiferromagnetic phases in geometrically frustrated LuFe2O4.

We present a detailed study of magnetism in LuFe(2)O(4), combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of T(N) involves a metamagnetic transition separating an antiferro- and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above T(N) is explained in terms of near degeneracy of the magnetic phases.

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.

Magnetic and electronic properties of RNiO3 (R = Pr, Nd, Eu, Ho and Y) perovskites studied by resonant soft x-ray magnetic powder diffraction.

Soft x-ray resonant magnetic powder diffraction of the ([Formula: see text]) reflection at the Ni L(2, 3) edges is used to study the magnetic and electronic properties of a series of RNiO(3) materials (with R = Pr, Nd, Eu, Ho and Y) below the metal-insulator transition. The polarization and energy dependence of the reflection gives further support for a non-collinear magnetic structure and charge disproportionation in the whole RNiO(3) series. Only small changes in the spectra of the magnetic ([Formula: see text]) reflection and in the absorption spectra could be detected. The results are discussed with comparison to charge transfer multiplet calculations. Our results emphasize that the lighter and heavier RNiO(3) compounds are very similar from the point of view of their local electronic and magnetic state despite the strong change of the metal-to-insulator transition temperature.

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.

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.

Spatial displacement of forward-diffracted X-ray beams by perfect crystals.

Time-delayed, narrow-band echoes generated by forward Bragg diffraction of an X-ray pulse by a perfect thin crystal are exploited for self-seeding at hard X-ray free-electron lasers. Theoretical predictions indicate that the retardation is strictly correlated to a transverse displacement of the echo pulses. This article reports the first experimental observation of the displaced echoes. The displacements are in good agreement with simulations relying on the dynamical diffraction theory. The echo signals are characteristic for a given Bragg reflection, the structure factor and the probed interplane distance. The reported results pave the way to exploiting the signals as an online diagnostic tool for hard X-ray free-electron laser seeding and for dynamical diffraction investigations of strain at the femtosecond timescale.

Ultrafast X-ray diffraction probe of terahertz field-driven soft mode dynamics in SrTiO3.

We use ultrafast X-ray pulses to characterize the lattice response of SrTiO3 when driven by strong terahertz fields. We observe transient changes in the diffraction intensity with a delayed onset with respect to the driving field. Fourier analysis reveals two frequency components corresponding to the two lowest energy zone-center optical modes in SrTiO3. The lower frequency mode exhibits clear softening as the temperature is decreased while the higher frequency mode shows slight temperature dependence.

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.