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A system that possesses translational symmetry but breaks orientational symmetry is known as a nematic phase. While there are many examples of nematic phases in a wide range of contexts, such as in liquid crystals, complex oxides, and superconductors, of particular interest is the magnetic analogue, where the spin, charge, and orbital degrees of freedom of the electron are intertwined. The difficulty of spin nematics is the unambiguous realization and characterization of the phase. Here we present an entirely new type of magnetic nematic phase, which replaces the basis of individual spins with magnetic helices. The helical basis allows for the direct measurement of the order parameters with soft X-ray scattering and a thorough characterization of the nematic phase and its thermodynamic transitions. We discover two distinct nematic phases with unique spatio-temporal correlation signatures. Using coherent X-ray methods, we find that near the phase boundary between the two nematic phases, fluctuations coexist on the timescale of both seconds and sub-nanoseconds. Additionally, we have determined that the fluctuations occur simultaneously with a reorientation of the magnetic helices, indicating that there is spontaneous symmetry breaking and new degrees of freedom become available. Our results provide a novel framework for characterizing exotic phases and the phenomena presented can be mapped onto a broad class of physical systems.

A central paradigm of non-equilibrium physics concerns the dynamics of heterogeneity and disorder, impacting processes ranging from the behavior of glasses to the emergent functionality of active matter. Understanding these complex mesoscopic systems requires probing the microscopic trajectories associated with irreversible processes, the role of fluctuations and entropy growth, and the timescales on which non-equilibrium responses are ultimately maintained. Approaches that illuminate these processes in model systems may enable a more general understanding of other heterogeneous non-equilibrium phenomena, and potentially define ultimate speed and energy cost limits for information processing technologies. Here, we apply ultrafast single shot x-ray photon correlation spectroscopy to resolve the non-equilibrium, heterogeneous, and irreversible mesoscale dynamics during a light-induced phase transition. This approach defines a new way of capturing the nucleation of the induced phase, the formation of transient mesoscale defects at the boundaries of the nuclei, and the eventual annihilation of these defects, even in systems with complex polarization topologies. A non-equilibrium response spanning >10 orders of magnitude in timescales is observed, with multistep behavior similar to the plateaus observed in supercooled liquids and glasses. We show how the observed time-dependent long-time correlations can be understood in terms of the stochastic dynamics of domain walls, encoded in effective waiting-time distributions with power-law tails. This work defines new possibilities for probing the non-equilibrium and correlated dynamics of disordered and heterogeneous media.

In the cuprate superconductors, the spatial coherence of the charge density wave (CDW) state grows rapidly below a characteristic temperature $T_\mathrm{CDW}$, the nature of which is debated. We have combined a set of x-ray scattering techniques to study La$_{1.88}$Sr$_{0.12}$CuO$_{4}$ ($T_\mathrm{CDW}$~$\approx$~80\,K) to shed light on this discussion. We observe the emergence of a crystal structure, which is consistent with the CDW modulation in symmetry, well above $T_\mathrm{CDW}$. This global structural change also induces strong fluctuations of local atomic disorder in the intermediate temperature region. At $T_\mathrm{CDW}$, the temperature dependence of this structure develops a kink, while the atomic disorder is minimized. We find that the atomic relaxation dynamics cross over from a cooperative to an incoherent response at $T_\mathrm{CDW}$. These results reveal a rich interplay between the CDWs and atomic fluctuations of distinct spatio-temporal scales. For example, the CDW coherence is enhanced on quasi-elastic timescales by incoherent atomic relaxation.

By measuring a linear response function directly, such as the dynamic susceptibility, one can understand fundamental material properties. However, a fresh perspective can be offered by studying fluctuations. This can be related back to the dynamic susceptibility through the fluctuation-dissipation theorem, which relates the fluctuations in a system to its response, an alternate route to access the physics of a material. Here, we describe a new x-ray tool for material characterization that will offer an opportunity to uncover new physics in quantum materials using this theorem. We provide details of the method and discuss the requisite analysis techniques in order to capitalize on the potential to explore an uncharted region of phase space. This is followed by recent results on a topological chiral magnet, together with a discussion of current work in progress. We provide a perspective on future measurements planned for work in unconventional superconductivity.

Superconductivity and charge density waves (CDW) are competitive, yet coexisting orders in cuprate superconductors. To understand their microscopic interdependence, a probe capable of discerning their interaction on its natural length and time scales is necessary. We use ultrafast resonant soft x-ray scattering to track the transient evolution of CDW correlations in YBa$_{2}$Cu$_{3}$O$_{6+x}$ following the quench of superconductivity by an infrared laser pulse. We observe a non-thermal response of the CDW order characterized by a near doubling of the correlation length within $\approx$ 1 picosecond of the superconducting quench. Our results are consistent with a model in which the interaction between superconductivity and CDW manifests inhomogeneously through disruption of spatial coherence, with superconductivity playing the dominant role in stabilizing CDW topological defects, such as discommensurations., Comment: Accepted version. 34 pages, 11 figures, Main text and Supplementary Materials

In the mixed-valence manganites, a near-infrared laser typically melts the orbital and spin order simultaneously, corresponding to the photoinduced $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ excitations in the Mott-Hubbard bands of manganese. Here, we use ultrafast methods -- both femtosecond resonant x-ray diffraction and optical reflectivity -- to demonstrate that the orbital response in the layered manganite Nd$_{1-x}$Sr$_{1+x}$MnO$_{4}$ ($\it{x}$ = 2/3) does not follow this scheme. At the photoexcitation saturation fluence, the orbital order is only diminished by a few percent in the transient state. Instead of the typical $d^{1}d^{0}$ $\xrightarrow{}$ $d^{0}d^{1}$ transition, a near-infrared pump in this compound promotes a fundamentally distinct mechanism of charge transfer, the $d^{0}$ $ \xrightarrow{}$ $d^{1}L$, where $\it{L}$ denotes a hole in the oxygen band. This novel finding may pave a new avenue for selectively manipulating specific types of order in complex materials of this class.

We performed ultrafast time-resolved near-infrared pump, resonant soft X-ray diffraction probe measurements to investigate the coupling between the photoexcited electronic system and the spin cycloid magnetic order in multiferroic TbMnO3 at low temperatures. We observe melting of the long range antiferromagnetic order at low excitation fluences with a decay time constant of 22.3 +- 1.1 ps, which is much slower than the ~1 ps melting times previously observed in other systems. To explain the data we propose a simple model of the melting process where the pump laser pulse directly excites the electronic system, which then leads to an increase in the effective temperature of the spin system via a slower relaxation mechanism. Despite this apparent increase in the effective spin temperature, we do not observe changes in the wavevector q of the antiferromagnetic spin order that would typically correlate with an increase in temperature under equilibrium conditions. We suggest that this behavior results from the extremely low magnon group velocity that hinders a change in the spin-spiral wavevector on these time scales., Comment: 9 pages, 4 figures

Static strain in complex oxide heterostructures has been extensively used to engineer electronic and magnetic properties at equilibrium. In the same spirit, deformations of the crystal lattice with light may be used to achieve functional control across hetero-interfaces dynamically. Here, by exciting large amplitude infrared-active vibrations in a LaAlO3 substrate we induce magnetic order melting in a NdNiO3 film across a hetero-interface. Femtosecond Resonant Soft X-ray Diffraction is used to determine the spatial and temporal evolution of the magnetic disordering. We observe a magnetic melt front that grows from the substrate interface into the film, at a speed that suggests electronically driven propagation. Light control and ultrafast phase front propagation at hetero-interfaces may lead to new opportunities in optomagnetism, for example by driving domain wall motion to transport information across suitably designed devices., Comment: 35 pages, 8 Figures (both incl. Supplement)

We use femtosecond resonant soft x-ray diffraction to measure the optically stimulated ultrafast changes of charge density wave correlations in underdoped YBa2Cu3O6.6. We find that when coherent interlayer transport is enhanced by optical excitation of the apical oxygen distortions, at least 50% of the in-plane charge density wave order is melted. These results indicate that charge ordering and superconductivity may be competing up to the charge ordering transition temperature, with the latter becoming a hidden phase that is accessible only by nonlinear phonon excitation., Comment: 22 pages (including Supplement), 3 figures

We report femtosecond resonant soft X-ray diffraction measurements of the dynamics of the charge order and of the crystal lattice in non-superconducting, stripe-ordered La1.875Ba0.125CuO4. Excitation of the in-plane Cu-O stretching phonon with a mid-infrared pulse has been previously shown to induce a transient superconducting state in the closely related compound La1.675Eu0.2Sr0.125CuO4. In La1.875Ba0.125CuO4, we find that the charge stripe order melts promptly on a sub-picosecond time scale. Surprisingly, the low temperature tetragonal distortion is only weakly reduced, reacting on significantly longer time scales that do not correlate with light-induced superconductivity. This experiment suggests that charge modulations alone, and not the LTT distortion, prevent superconductivity in equilibrium., Comment: 16 pages, 3 figures

We investigate the order parameter dynamics of the stripe-ordered nickelate, La$_{1.75}$Sr$_{0.25}$NiO$_4$, using time-resolved resonant X-ray diffraction. In spite of distinct spin and charge energy scales, the two order parameters' amplitude dynamics are found to be linked together due to strong coupling. Additionally, the vector nature of the spin sector introduces a longer re-orientation time scale which is absent in the charge sector. These findings demonstrate that the correlation linking the symmetry-broken states does not unbind during the non-equilibrium process, and the time scales are not necessarily associated with the characteristic energy scales of individual degrees of freedom., Comment: 4 figures. Accepted by Physical Review Letter

Using a combination of resonant soft x-ray scattering, magnetometry, x-ray reflectivity and microscopy techniques we have investigated the magnetic properties and microstructure of a series of perpendicular anisotropy Co/Pt multilayer films with respect to structural disorder tuned by varying the sputtering deposition pressure. The observed magnetic changes in domain size, shape and correlation length originate from structural and chemical variations in the samples, such as chemical segregation and grain formation as well as roughness at the surface and interfaces, which are all impacted by the deposition pressure. For low pressure samples we find evidence of a random "gas-like" distribution of magnetic domains, while in the higher pressure samples the domain structure exhibits only short range "liquid-like" positional ordering. The structural and chemical disorder induced by the higher deposition pressure first leads to an increase in the number of magnetic point defects that limit free domain wall propagation. Then, as the sputtering pressure is further increased, the domain wall energy density is lowered due to the formation of local regions with reduced magnetic moment, and finally magnetically void regions appear that confine the magnetic domains and clusters, similar to segregated granular magnetic recording media., Comment: 17 pages, 18 figures, submitted to Phys. Rev. B

The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerged in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of its ability to measure material properties at atomic and electronic time scales and create excited states not accessible by the conventional means can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here, combining time-resolved femotosecond optical and resonant x-ray diffraction measurements on striped La1.75Sr0.25NiO4, we reveal unforeseen photo-induced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, unlike thermal phase fluctuations near the critical temperature in equilibrium10. Importantly, relaxation of the phase fluctuations are found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limit charge order recovery. This discovery of new aspect to phase fluctuation provides more holistic view for the importance of phase in ordering phenomena of quantum matter., Comment: 23 pages, 6 figures. Published version can be found at Nature Communications 3, 838 (2012)

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 re-orientation transition in CuO is limited by the long-wavelength magnetic excitation connecting the two phases., Comment: Accepted by Physical Review Letters (Dec. 2, 2011)

Measurements of the spatial and temporal coherence of single, femtosecond x-ray pulses generated by the first hard x-ray free-electron laser (FEL), the Linac Coherent Light Source (LCLS), are presented. Single shot measurements were performed at 780 eV x-ray photon energy using apertures containing double pinholes in "diffract and destroy" mode. We determined a coherence length of 17 micrometers in the vertical direction, which is approximately the size of the focused LCLS beam in the same direction. The analysis of the diffraction patterns produced by the pinholes with the largest separation yields an estimate of the temporal coherence time of 0.6 fs. We find that the total degree of transverse coherence is 56% and that the x-ray pulses are adequately described by two transverse coherent modes in each direction. This leads us to the conclusion that 78% of the total power is contained in the dominant mode., Comment: 6 pages, 4 figures

Optical control of magnetism, of interest for high-speed data processing and storage, has only been demonstrated with near-infrared excitation to date. However, in absorbing materials, such high photon energies can lead to significant dissipation, making switch back times long and miniaturization challenging. In manganites, magnetism is directly coupled to the lattice, as evidenced by the response to external and chemical pressure, or to ferroelectric polarization. Here, femtosecond mid-infrared pulses are used to excite the lattice in La0.5Sr1.5MnO4 and the dynamics of electronic order are measured by femtosecond resonant soft x-ray scattering with an x-ray free electron laser. We observe that magnetic and orbital orders are reduced by excitation of the lattice. This process, which occurs within few picoseconds, is interpreted as relaxation of the complex charge-orbital-spin structure following a displacive exchange quench - a prompt shift in the equilibrium value of the magnetic and orbital order parameters after the lattice has been distorted. A microscopic picture of the underlying unidirectional lattice displacement is proposed, based on nonlinear rectification of the directly-excited vibrational field, as analyzed in the specific lattice symmetry of La0.5Sr1.5MnO4. Control of magnetism through ultrafast lattice excitation has important analogies to the multiferroic effect and may serve as a new paradigm for high-speed optomagnetism., Comment: 10 pages manuscript, 4 figures

The coupling of multiple degrees of freedom - charge, spin, and lattice - in manganites has mostly been considered at the microscopic level. However, on larger length scales, these correlations may be affected by strain and disorder, which can lead to short range order in these phases and affect the coupling between them. To better understand these effects, we explore the dynamics of orbitally ordered domains in a half-doped manganite near the orbital ordering phase transition. Our results suggest that the domains are largely static, and exhibit only slow fluctuations near domain boundaries., Comment: 10 pages, 4 figures

Using coherent x-ray speckle metrology, we have measured the influence of disorder on major loop return point memory (RPM) and complementary point memory (CPM) for a series of perpendicular anisotropy Co/Pt multilayer films. In the low disorder limit, the domain structures show no memory with field cycling--no RPM and no CPM. With increasing disorder, we observe the onset and the saturation of both the RPM and the CPM. These results provide the first direct ensemble-sensitive experimental study of the effects of varying disorder on microscopic magnetic memory and are compared against the predictions of existing theories., Comment: 4 pages, 4 figures. Accepted for publication in Physical Review Letters in Nov. 2004