Many striking non-equilibrium phenomena have been discovered or predicted in opticallydriven quantum solids 1 , ranging from light-induced superconductivity 2,3 to Floquetengineered topological phases 4-8 . These effects are expected to lead to dramatic changes in electrical transport, but can only be comprehensively characterized or functionalized with a direct interface to electrical devices that operate at ultrafast speeds 1-8 . Here, we make use of laser-triggered photoconductive switches 9 to measure the ultrafast transport properties of monolayer graphene, driven by a mid-infrared femtosecond pulse of circularly polarized light. The goal of this experiment is to probe the transport signatures of a predicted light-induced topological band structure in graphene 4,5 , similar to the one originally proposed by Haldane 10 . We report the observation of an anomalous Hall effect in the absence of an applied magnetic field. We also extract quantitative properties of the non-equilibrium state. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect the effective band structure expected from Floquet theory. This includes a ∼60 meV wide conductance plateau centered at the Dirac point, where a gap of approximately equal magnitude is expected to open. We also find that when the Fermi level lies within this plateau, the estimated anomalous Hall conductance saturates around ∼1.8±0.4 e 2 /h.Optical driving has been proposed as a means to engineer topological properties in topologically trivial systems 4-8 . One proposal for such a 'Floquet topological insulator' is based on breaking time-reversal symmetry in graphene through a coherent interaction with circularly polarized light 4 . In this theory, the light field drives electrons in circular trajectories through the band structure (Fig. 1a). Close to the Dirac point, these states are predicted to acquire a non-adiabatic Berry phase every optical cycle, which is equal and opposite for the upper and lower band. This time-averaged extra phase accumulation amounts to an energy * These authors contributed equally to this work

In ferromagnetic nanostructures domain walls as emergent entities separate uniformly magnetized regions. They are describable as quasi particles and can be controlled by magnetic fields or spin-polarized currents. Below critical driving forces domain walls are rigid conserving their spin structure. Like other quasi particles internal excitations influence the domain wall dynamics above a critical velocity known as the Walker breakdown. This complex nonlinear motion has not been observed directly. Here we present direct time-resolved x-ray microscopy of structural transformations of domain walls during motion. Although governed by nonlinear dynamics the displacement of the wall on the observed time scale can still be described by an analytical model. Using a reduced dynamical domain-wall width the model enables us to determine the mass of a vortex wall experimentally. Further we observe the creation and the mutual annihilation of domain walls. The intrinsic nanometer length and nanosecond time-scales are determined directly.

The dynamics of emergent magnetic quasiparticles, such as vortices, domain walls and bubbles are studied by scanning transmission X-ray microscopy (STXM), combining magnetic (XMCD) contrast with about 25 nm lateral resolution as well as 70 ps time resolution. Essential progress in the understanding of magnetic vortex dynamics is achieved by vortex core reversal observed by sub-GHz excitation of the vortex gyromode, either by ac magnetic fields or spin transfer torque. The basic switching scheme for this vortex core reversal is the generation of a vortex-antivortex pair. Much faster vortex core reversal is obtained by exciting azimuthal spin wave modes with (multi-GHz) rotating magnetic fields or orthogonal monopolar field pulses in the x and y direction, down to 45 ps in duration. In that way unidirectional vortex core reversal to the vortex core "down" or "up" state only can be achieved with switching times well below 100 ps. Coupled modes of interacting vortices mimic crystal properties. The individual vortex oscillators determine the properties of the ensemble, where the gyrotropic mode represents the fundamental excitation. By self-organized state formation we investigate distinct vortex core polarization configurations and understand these eigenmodes in an extended Thiele model. Analogies with photonic crystals are drawn. Oersted fields and spin-polarized currents are used to excite the dynamics of domain walls and magnetic bubble skyrmions. From the measured phase and amplitude of the displacement of domain walls we deduce the size of the non-adiabatic spin-transfer torque. For sensing applications, the displacement of domain walls is studied and a direct correlation between domain wall velocity and spin structure is found. Finally the synchronous displacement of multiple domain walls using perpendicular field pulses is demonstrated as a possible paradigm shift for magnetic memory and logic applications.

We have investigated the generation of magnetic domain walls by nanosecond magnetic field pulses of a strip line. Domain wall creation is sensitive to an externally applied field concerning wall type and threshold amplitudes. The domain wall creation is stochastic similar to domain wall depinning. In the experiment reliable domain wall generation require up to 8 ns long pulses at the threshold field amplitude. The required pulse length can be reduced by higher field amplitudes. Time-resolved measurements and micromagnetic simulations show that the domain wall is generated within three nanoseconds. The creation proceeds via vortex core formation under the strip line. V

We study the creation and annihilation of domain walls in a permalloy nanowire by local Oersted fields of current pulses passing through a perpendicularly aligned stripline. The occurrence of both processes is investigated for current pulses of different polarities and for various external magnetic fields. Reliable creation and annihilation are achieved for small and zero external fields, while higher externally applied fields lead to the suppression of both processes as well as to the creation of multiple domain walls in the wire.