Distinguishing the ultrafast dynamics of spin and orbital moments in solids

Time-Resolved Circular Dichroism in Molecules: Experimental and Theoretical Advances

Following changes in chirality can give access to relevant information on the function or reactivity of molecular systems. Time-resolved circular dichroism (TRCD) spectroscopy proves to be a valid tool to achieve this goal. Depending on the class of molecules, different temporal ranges, spanning from seconds to femtoseconds, need to be investigated to observe such chiroptical changes. Therefore, over the years, several approaches have been adopted to cover the timescale of interest, especially based on pump-probe schemes. Moreover, various theoretical approaches have been proposed to simulate and explain TRCD spectra, including linear and non-linear response methods as well as non-adiabatic molecular dynamics. In this review, an overview on both experimental and theoretical advances in the TRCD field is provided, together with selected applications. A discussion on future theoretical developments for TRCD is also given.

Direct Probe of Conical Intersection Photochemistry by Time-Resolved X-ray Magnetic Circular Dichroism

The direct probing of photochemical dynamics by detecting the electronic coherence generated during passage through conical intersections is an intriguing challenge. The weak coherence signal and the difficulty in preparing purely excited wave packets that exclude coherence from other sources make it experimentally challenging. We propose to use time-resolved X-ray magnetic circular dichroism to probe the wave packet dynamics around the conical intersection. The magnetic field amplifies the relative strength of the electronic coherence signal compared to populations through the magnetic field response anisotropy. More importantly, since the excited state relaxation through conical intersections involves a change of parity, the magnetic coupling matches the symmetry of the response function with the electronic coherence, making the coherence signal only sensitive to the conical intersection induced coherence and excludes the pump pulse induced coherence between the ground state and excited state. In this theoretical study, we apply this technique to the photodissociation dynamics of a pyrrole molecule and demonstrate its capability of probing electronic coherence at a conical intersection as well as population transfer. We demonstrate that a magnetic field can be effectively used to extract novel information about electron and nuclear molecular dynamics.

Microscopic evaluation of spin and orbital moment in ferromagnetic resonance

Time-resolved X-ray magnetic circular dichroism under the effects of ferromagnetic resonance (FMR), known as X-ray ferromagnetic resonance (XFMR) measurements, enables direct detection of precession dynamics of magnetic moment. Here we demonstrated XFMR measurements and Bayesian analyses as a quantitative probe for the precession of spin and orbital magnetic moments under the FMR effect. Magnetization precessions in two different Pt/Ni-Fe thin film samples were directly detected. Furthermore, the ratio of dynamical spin and orbital magnetic moments was evaluated quantitatively by Bayesian analyses for XFMR energy spectra around the Ni L 2 , 3 absorption edges. Our study paves the way for a microscopic investigation of the contribution of the orbital magnetic moment to magnetization dynamics.

Optical-Helicity-Dependent Orbital and Spin Dynamics in Two-Dimensional Ferromagnets

Disentangling orbital (OAM) and spin (SAM) angular momenta in the ultrafast spin dynamics of two-dimensional (2D) ferromagnets on subfemtoseconds is a challenge in the field of ultrafast magnetism. Herein, we employed a non-collinear spin version of real-time time-dependent density functional theory to investigate the orbital and spin dynamics of the 2D ferromagnets Fe3GeTe2 (FGT) induced by circularly polarized light. Our results show that the demagnetization of the Fe sublattice in FGT is accompanied by helicity-dependent precession of the OAM and SAM excited by circularly polarized lasers. We further identify that precession of the OAM and SAM in FGT is faster than demagnetization within a few femtoseconds. Remarkably, circularly polarized lasers can significantly induce a periodic transverse linear response of the OAM and SAM on very ultrafast time scales of ∼600 attoseconds. Our finding suggests a powerful new route for attosecond regimes of the angular momentum manipulation to coherently control helicity-dependent orbital and spin dynamics in 2D ferromagnets.

Unlocking Ultrafast Spin Transfer in Single-Magnetic-Center-Decorated Triangulene Systems

Triangulene, as a typical open-shell graphene fragment, has attracted widespread attention for nanospintronics, promising to serve as building blocks in spin-logic units. Here, using ab initio calculations, we systematically study the laser-induced ultrafast spin-dynamic processes on triangulene nanoflakes, decorated with a transition-metal atom. The results reveal a competition between the induced magnetic center and the carbon edge of the triangulene, resulting in the coexistence of dual spin-density-distribution patterns on such single-magnetic-center systems, thus opening up possibilities of complex spin-dynamic scenarios beyond the spin flip. Interestingly, no matter what direction the spin points to, it is possible to achieve reversible spin-transfer processes using the same laser pulse. Increasing the pool of elementary processes to contain not only spin-direction-dependent but also spin-direction-independent scenarios allows for more versatile spin-logic operations, including classical handling of information and quantum computing. In the present work, we suggest downscaling nanospintronic devices by integrating triangulene-based nanostructures.

Perspectives: Light Control of Magnetism and Device Development

Accurately controlling magnetic and spin states presents a significant challenge in spintronics, especially as demands for higher data storage density and increased processing speeds grow. Approaches such as light control are gradually supplanting traditional magnetic field methods. Traditionally, the modulation of magnetism was predominantly achieved through polarized light with the help of ultrafast light technologies. With the growing demand for energy efficiency and multifunctionality in spintronic devices, integrating photovoltaic materials into magnetoelectric systems has introduced more physical effects. This development suggests that sunlight will play an increasingly pivotal role in manipulating spin orientation in the future. This review introduces and concludes the influence of various light types on magnetism, exploring mechanisms such as magneto-optical (MO) effects, light-induced magnetic phase transitions, and spin photovoltaic effects. This review briefly summarizes recent advancements in the light control of magnetism, especially sunlight, and their potential applications, providing an optimistic perspective on future research directions in this area.

Ultrafast Chiral Precession of Spin and Orbital Angular Momentum Induced by Circularly Polarized Laser Pulse in Elementary Ferromagnets

Despite spin (SAM) and orbital (OAM) angular momentum dynamics being well-studied in demagnetization processes, their components receive less focus. Here, we utilize real-time time-dependent density functional theory (rt-TDDFT) to unveil significant x and y components of SAM and OAM induced by circularly left (σ+) and right (σ-) polarized laser pulses in ferromagnetic Fe, Co, and Ni. Our results show that the magnitude of the OAM is an order of magnitude larger than that of the SAM, highlighting a stronger optical response from the orbital degrees of freedom of electrons. Intriguingly, σ+ and σ- pulses induce chirality in the precession of SAM and OAM, respectively, with clear associations with laser frequency and duration. Finally, we demonstrate the time scale of the OAM and SAM precession occurs even earlier than that of the demagnetization process and the OISTR effect. Our results provide detailed insight into the dynamics of SAM and OAM during and shortly after a polarized laser pulse.

Light-induced ultrafast spin transport in multilayer metallic films originates from sp-d spin exchange coupling

Ultrafast interaction between the femtosecond laser pulse and the magnetic metal provides an efficient way to manipulate the magnetic states of matter. Numerous experimental advancements have been made on multilayer metallic films in the last two decades. However, the underlying physics remains unclear. Here, relying on an efficient ab initio spin dynamics simulation algorithm, we revealed the physics that can unify the progress in different experiments. We found that light-induced ultrafast spin transport in multilayer metallic films originates from the sp-d spin-exchange interaction, which can induce an ultrafast, large, and pure spin current from ferromagnetic metal to nonmagnetic metal without charge carrier transport. The resulting trends of spin demagnetization and spin flow are consistent with most experiments. It can explain a variety of ultrafast light-spin manipulation experiments with different systems and different pump-probe technologies, covering a wide range of work in this field.

Ultrafast THz probing of nonlocal orbital current in transverse multilayer metallic heterostructures

THz generation from femtosecond photoexcited spintronic heterostructures has become a versatile tool for investigating ultrafast spin-transport and transient charge-current in a non-contact and non-invasive manner. The equivalent effect from the orbital degree of freedom is still in the primitive stage. Here, we experimentally demonstrate orbital-to-charge current conversion in metallic heterostructures, consisting of a ferromagnetic layer adjacent to either a light or a heavy metal layer, through detection of the emitted THz pulses. Our temperature-dependent experiments help to disentangle the orbital and spin components that are manifested in the respective Hall-conductivities, contributing to THz emission. NiFe/Nb shows the strongest inverse orbital Hall effect with an experimentally extracted value of effective intrinsic Hall-conductivity, [Formula: see text], while CoFeB/Pt shows maximum contribution from the inverse spin Hall effect. In addition, we observe a nearly ten-fold enhancement in the THz emission due to pronounced orbital-transport in W-insertion heavy metal layer in CoFeB/W/Ta heterostructure as compared to CoFeB/Ta bilayer counterpart.

High-order harmonic generation by aligned homonuclear diatomic cations

We introduce the theory of high-order harmonic generation by aligned homonuclear diatomic cations using a strong-field approximation. The target cation is represented as a system which consists of two atomic (ionic) centres and one active electron, while the driving field is either a monochromatic or bichromatic field. For a linearly polarised driving field, we investigate the differences between the harmonic spectra obtained with a neutral molecule and the corresponding molecular cation. Due to the larger ionisation potential, the molecular cations can withstand much higher laser-field intensity than the corresponding neutral molecule before the saturation effects become significant. This allows one to produce high-order harmonics with energy in the water-window interval or beyond. Also, the harmonic spectrum provides information about the structure of the highest-occupied molecular orbital. In order to obtain elliptically polarised harmonics, we suggest that an orthogonally polarised two-colour field is employed as a driving field. In this case, we analyse the harmonic ellipticity as a function of the relative orientation of the cation in the laser field. We show that the regions with large harmonic ellipticity in the harmonic energy-orientation angle plane are the broadest for cations whose molecular orbital does not have a nodal plane. Finally, we show that the molecular cations exposed to an orthogonally polarised two-colour field represent an excellent setup for the production of elliptically polarised attosecond pulses with a duration shorter than 100 as.

Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten

The emerging field of orbitronics exploits the electron orbital momentum L. Compared to spin-polarized electrons, L may allow the transfer of magnetic information with considerably higher density over longer distances in more materials. However, direct experimental observation of L currents, their extended propagation lengths and their conversion into charge currents has remained challenging. Here, we optically trigger ultrafast angular-momentum transport in Ni|W|SiO2 thin-film stacks. The resulting terahertz charge-current bursts exhibit a marked delay and width that grow linearly with the W thickness. We consistently ascribe these observations to a ballistic L current from Ni through W with a giant decay length (~80 nm) and low velocity (~0.1 nm fs-1). At the W/SiO2 interface, the L flow is efficiently converted into a charge current by the inverse orbital Rashba-Edelstein effect, consistent with ab initio calculations. Our findings establish orbitronic materials with long-distance ballistic L transport as possible candidates for future ultrafast devices and an approach to discriminate Hall-like and Rashba-Edelstein-like conversion processes.

Optically Driven Both Classical and Quantum Unary, Binary, and Ternary Logic Gates on Co-Decorated Graphene Nanoflakes

Nanospintronics holds great potential for providing high-speed, low-power, and high-density logic and memory elements in future computational devices. Here, using ab initio many-body theory, we suggest a nanoscale framework for building quantum computation elements, based on individual magnetic atoms deposited on graphene nanoflakes. We show the great possibilities of this proposal by exemplarily presenting four quantum gates, namely, the unary Pauli-X, Pauli-Y, Pauli-Z, and Hadamard gates, as well as the universal classical ternary Toffoli gate, which preserves information entropy and is therefore fully reversible and minimally energy consuming. All our gates operate within the subpicosecond time scale and reach fidelities well above 90%. We demonstrate the ability to control the spin direction and localization, as well as to create superposition states and to control the quantum phase of states, which are indispensable ingredients of quantum computers. Additionally, being optically driven, their predicted operating speed by far beats that of modern quantum computers.

Spin current driven by ultrafast magnetization of FeRh

Laser-induced ultrafast demagnetization is an important phenomenon that probes arguably the ultimate limits of the angular momentum dynamics in solid. Unfortunately, many aspects of the dynamics remain unclear except that the demagnetization transfers the angular momentum eventually to the lattice. In particular, the role and origin of electron-carried spin currents in the demagnetization process are debated. Here we experimentally probe the spin current in the opposite phenomenon, i.e., laser-induced ultrafast magnetization of FeRh, where the laser pump pulse initiates the angular momentum build-up rather than its dissipation. Using the time-resolved magneto-optical Kerr effect, we directly measure the ultrafast-magnetization-driven spin current in a FeRh/Cu heterostructure. A strong correlation between the spin current and the magnetization dynamics of FeRh is found even though the spin filter effect is negligible in this opposite process. This result implies that the angular momentum build-up is achieved by an angular momentum transfer from the electron bath (supplier) to the magnon bath (receiver) and followed by the spatial transport of angular momentum (spin current) and dissipation of angular momentum to the phonon bath (spin relaxation).

Generation of the isolated highly elliptically polarized attosecond pulse using the polarization gating technique: TDDFT approach

This paper theoretically investigates the generation of isolated elliptically polarized attosecond pulses with a tunable ellipticity from the interaction of Cl₂ molecule and a polarization-gating laser pulse. A three-dimensional calculation based on the time-dependent density functional theory is done. Two different methods are proposed for generating elliptically polarized single attosecond pulses. The first method is based on applying a single-color polarization gating laser and controlling the orientation angle of the Cl₂ molecule with respect to the polarization direction of the laser at the gate window. An attosecond pulse with an ellipticity of 0.66 and a pulse duration of 275 as is achieved by tuning the molecule orientation angle to 40° in this method and superposing harmonics around the harmonic cutoff. The second method is based on irradiating an aligned Cl₂ molecule with a two-color polarization gating laser. The ellipticity of the attosecond pulses obtained by this method can be controlled by adjusting the intensity ratio of the two colors. Employing an optimized intensity ratio and superposing harmonics around the harmonic cutoff would lead to the generation of an isolated, highly elliptically polarized attosecond pulse with an ellipticity of 0.92 and a pulse duration of 648 as.

Photon-shot-noise-limited transient absorption soft X-ray spectroscopy at the European XFEL

Femtosecond transient soft X-ray absorption spectroscopy (XAS) is a very promising technique that can be employed at X-ray free-electron lasers (FELs) to investigate out-of-equilibrium dynamics for material and energy research. Here, a dedicated setup for soft X-rays available at the Spectroscopy and Coherent Scattering (SCS) instrument at the European X-ray Free-Electron Laser (European XFEL) is presented. It consists of a beam-splitting off-axis zone plate (BOZ) used in transmission to create three copies of the incoming beam, which are used to measure the transmitted intensity through the excited and unexcited sample, as well as to monitor the incoming intensity. Since these three intensity signals are detected shot by shot and simultaneously, this setup allows normalized shot-by-shot analysis of the transmission. For photon detection, an imaging detector capable of recording up to 800 images at 4.5 MHz frame rate during the FEL burst is employed, and allows a photon-shot-noise-limited sensitivity to be approached. The setup and its capabilities are reviewed as well as the online and offline analysis tools provided to users.

Spin and Orbital Symmetry Breakings Central to the Laser-Induced Ultrafast Demagnetization of Transition Metals

The role of spin and orbital rotational symmetry on the laser-induced magnetization dynamics of itinerant-electron ferromagnets was theoretically investigated. The ultrafast demagnetization of transition metals is shown to be the direct consequence of the fundamental breaking of these conservation laws in the electronic system, an effect that is inherent to the nature of spin-orbit and electron-lattice interactions. A comprehensive symmetry analysis is complemented by exact numerical calculations of the time evolution of optically excited ferromagnetic ground states in the framework of a many-body electronic Hamiltonian. Thus, quantitative relations are established between the strength of the interactions that break the rotational symmetries and the time scales that are relevant for the magnetization dynamics.

Inertial Spin Dynamics in Epitaxial Cobalt Films

We investigate the spin dynamics driven by terahertz magnetic fields in epitaxial thin films of cobalt in its three crystalline phases. The terahertz magnetic field generates a torque on the magnetization which causes it to precess for about 1 ps, with a subpicosecond temporal lag from the driving force. Then, the magnetization undergoes natural damped THz oscillations at a frequency characteristic of the crystalline phase. We describe the experimental observations solving the inertial Landau-Lifshitz-Gilbert equation. Using the results from the relativistic theory of magnetic inertia, we find that the angular momentum relaxation time η is the only material parameter needed to describe all the experimental evidence. Our experiments suggest a proportionality between η and the strength of the magnetocrystalline anisotropy.

Non-equilibrium heating path for the laser-induced nucleation of metastable skyrmion lattices

Understanding formation of metastable phases by rapid energy pumping and quenching has been intriguing scientists for a long time. This issue is crucial for technologically relevant systems such as magnetic skyrmions which are frequently metastable at zero field. Using Atomistic Spin Dynamics simulations, we show the possibility of creating metastable skyrmion lattices in cobalt-based trilayers by femtosecond laser heating. Similar to the formation of supercooled ice droplets in the gas phase, high temperature ultrafast excitation creates magnon drops and their fast relaxation leads to acquisition and quenching of the skyrmion topological protection. The interplay between different processes corresponds to a specific excitation window which can be additionally controlled by external fields. The results are contrasted with longer-scale heating leading to a phase transition to the stable states. Our results provide insight into the dynamics of the highly non-equilibrium pathway for spin excitations and pave additional routes for skyrmion-based information technologies.

Understanding magnetocrystalline anisotropy based on orbital and quadrupole moments

Understanding magnetocrystalline anisotropy (MCA) is fundamentally important for developing novel magnetic materials. Therefore, clarifying the relationship between MCA and local physical quantities observed by spectroscopic measurements, such as the orbital and quadrupole moments, is necessary. In this review, we discuss MCA and the distortion effects in magnetic materials with transition metals (TMs) based on the orbital and quadrupole moments, which are related to the spin-conserving and spin-flip terms in the second-order perturbation calculations, respectively. We revealed that orbital moment stabilized the spin moment in the direction of the larger orbital moment, while the quadrupole moment stabilized the spin moment along the longitudinal direction of the spin-density distribution. The MCA of the magnetic materials with TMs and their interfaces can be determined from the competition between these two contributions. We showed that the perpendicular MCA of the face-centered cubic Ni with tensile tetragonal distortion arose from the orbital moment anisotropy, whereas that of Mn-Ga alloys originated from the quadrupole moment of spin density. In contrast, in the Co/Pd(111) multilayer and Fe/MgO(001), both the orbital moment anisotropy and quadrupole moment of spin density at the interfaces contributed to the perpendicular MCA. Understanding the MCA of magnetic materials and interfaces based on orbital and quadrupole moments is essential to design MCA of novel magnetic applications.

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 momentum^1-3, 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.

Amplification of elliptically polarized sub-femtosecond pulses in neon-like X-ray laser modulated by an IR field

Amplification of attosecond pulses produced via high harmonic generation is a formidable problem since none of the amplifiers can support the corresponding PHz bandwidth. Producing the well defined polarization state common for a set of harmonics required for formation of the circularly/elliptically polarized attosecond pulses (which are on demand for dynamical imaging and coherent control of the spin flip processes) is another big challenge. In this work we show how both problems can be tackled simultaneously on the basis of the same platform, namely, the plasma-based X-ray amplifier whose resonant transition frequency is modulated by an infrared field.

Experimental and Theoretical Study of the Ultrafast Dynamics of a Ni2 Dy2 -Compound in DMF After UV/Vis Photoexcitation

We present a combined experimental and theoretical study of the ultrafast transient absorption spectroscopy results of a {Ni₂Dy₂}‐compound in DMF, which can be considered as a prototypic molecule for single molecule magnets. We apply state‐of‐the‐art ab initio quantum chemistry to quantitatively describe the optical properties of an inorganic complex system comprising ten atoms to form the chromophoric unit, which is further stabilized by surrounding ligands. Two different basis sets are used for the calculations to specifically identify two dominant peaks in the ground state. Furthermore, we theoretically propagate the compound's correlated many‐body wavefunction under the influence of a laser pulse as well as relaxation processes and compare against the time‐resolved absorption spectra. The experimental data can be described with a time constant of several hundreds of femtoseconds attributed to vibrational relaxation and trapping into states localized within the band gap. A second time constant is ascribed to the excited state while trap states show lifetimes on a longer timescale. The theoretical propagation is performed with the density‐matrix formalism and the Lindblad superoperator, which couples the system to a thermal bath, allowing us to extract relaxation times from first principles.

Bayesian optimal control of the ultrashort circularly polarized attosecond pulse generation by two-color polarization gating

We present ab initio simulations of optimal control of high-order-harmonic generation spectra that enable the synthesis of a circularly polarized 53-attosecond pulse in a single Helium atom response. The Bayesian optimization is used to achieve control of a two-color polarization gating laser waveform such that a series of harmonics in the plateau region are phase-matched, which can be used for attosecond pulse synthesis. To find the underlying mechanisms for generating these harmonics, we perform a wavelet analysis for the induced dipole moment in acceleration form, and compare the time-energy representation with the quantum paths extracted from the semiclassical calculation. We found that these coherent harmonics are excited along the short trajectories. The proposed method has the potential to migrate to laboratories for generation of isolated circularly polarized ultrashort attosecond pulses.

Ultrafast Optically Induced Ferromagnetic State in an Elemental Antiferromagnet

We present evidence for an ultrafast optically induced ferromagnetic alignment of antiferromagnetic Mn in Co/Mn multilayers. We observe the transient ferromagnetic signal at the arrival of the pump pulse at the Mn L_{3} resonance using x-ray magnetic circular dichroism in reflectivity. The timescale of the effect is comparable to the duration of the excitation and occurs before the magnetization in Co is quenched. Theoretical calculations point to the imbalanced population of Mn unoccupied states caused by the Co interface for the emergence of this transient ferromagnetic state.

Layer-selective magnetization switching in the chirped photonic crystal with GdFeCo

Here we propose a magnetophotonic structure for the layer-selective magnetization switching with femtosecond laser pulses of different wavelengths. It is based on a chirped magnetophotonic crystal (MPC) containing magnetic GdFeCo and nonmagnetic dielectric layers. At each operating wavelength the laser pulses heat up to necessary level only one GdFeCo layer that leads to its magnetization reversal without any impact on the magnetization of the other layers. Moreover, magneto-optical reading of the MPC magnetization state is discussed. Lateral dimensions of the considered MPC can be made small enough to operate as a unit cell for data storage.

Long-Distance Ultrafast Spin Transfer over a Zigzag Carbon Chain Structure

Using high-level ab initio quantum theory we suggest an optically induced subpicosecond spin-transfer scenario over 4.428 nm, a distance which is directly comparable to the actual CMOS scale. The spin-density transfer takes place between two Ni atoms and over a 40-atom-long zigzag carbon chain. The suitable combination of the local symmetries of the participating carbon atoms and the global symmetry of the whole molecule gives rise to what we term the dynamical Goodenough-Kanamori rules, allowing the long-range coupling of the two Ni atoms. We also present local spin-flip scenarios, and compare spin flip and spin transfer with respect to their sensitivity against an external static magnetic gradient. Finally, we use two identical laser pulses, rather than a single one, which allows us to accurately control local (intrasite) vs global (intersite) processes, and we thus solve the problem of embedding individually addressable molecular nanologic elements in an integrated nanospintronic circuit. Our results underline the great potential of carbon chain systems as building and supporting blocks for designing future all-optical magnetic processing units.

Relativistic slingshot: A source for single circularly polarized attosecond x-ray pulses

We propose a mechanism to generate a single intense circularly polarized attosecond x-ray pulse from the interaction of a circularly polarized relativistic few-cycle laser pulse with an ultrathin foil at normal incidence. Analytical modeling and particle-in-cell simulation demonstrate that a huge charge-separation field can be produced when all the electrons are displaced from the target by the incident laser, resulting in a high-quality relativistic electron mirror that propagates against the tail of the laser pulse. The latter is efficiently reflected as well as compressed into an attosecond pulse that is also circularly polarized.

Spin dynamics at interfaces on femtosecond timescales

The excitation of magnetically ordered materials with ultrashort laser pulses results in magnetization dynamics on femto- to picosecond timescales. These non-equilibrium spin dynamics have emerged as a rapidly developing research field in recent years. Unraveling the fundamental microscopic processes in the interaction of ultrashort optical pulses with the charge, spin, orbital, and lattice degrees of freedom in magnetic materials shows the potential for controlling spin dynamics on their intrinsic timescales and thereby bring spintronics applications into the femtosecond range. In particular, femtosecond spin currents offer fascinating new possibilities to manipulate magnetization in an ultrafast and non-local manner, via spin injection and spin transfer torque at the interfaces of ferromagnetic layered structures. This topical review covers recent progress on spin dynamics at interfaces on femtosecond time scales. The development of the field of ultrafast spin dynamics in ferromagnetic heterostructures will be reviewed, starting from spin currents propagating on nanometer length scales through layered structures before focusing on femtosecond spin transfer at interfaces. The properties of these ultrafast spin-dependent charge currents will be discussed, as well as the materials dependence of femtosecond spin injection, the role of the interface properties, and competing microscopic processes leading to a loss of spin polarization on sub-picosecond timescales.

Time-Resolved XUV Absorption Spectroscopy and Magnetic Circular Dichroism at the Ni M2,3-Edges

Ultrashort optical pulses can trigger a variety of non-equilibrium processes in magnetic thin films affecting electrons and spins on femtosecond timescales. In order to probe the charge and magnetic degrees of freedom simultaneously, we developed an X-ray streaking technique that has the advantage of providing a jitter-free picture of absorption cross-section changes. In this paper, we present an experiment based on this approach, which we performed using five photon probing energies at the Ni M2,3-edges. This allowed us to retrieve the absorption and magnetic circular dichroism time traces, yielding detailed information on transient modifications of electron and spin populations close to the Fermi level. Our findings suggest that the observed absorption and magnetic circular dichroism dynamics both depend on the extreme ultraviolet (XUV) probing wavelength, and can be described, at least qualitatively, by assuming ultrafast energy shifts of the electronic and magnetic elemental absorption resonances, as reported in recent work. However, our analysis also hints at more complex changes, highlighting the need for further experimental and theoretical studies in order to gain a thorough understanding of the interplay of electronic and spin degrees of freedom in optically excited magnetic thin films.

Ultrafast optical manipulation of magnetic order in ferromagnetic materials

The interaction between ultrafast lasers and magnetic materials is an appealing topic. It not only involves interesting fundamental questions that remain inconclusive and hence need further investigation, but also has the potential to revolutionize data storage technologies because such an opto-magnetic interaction provides an ultrafast and energy-efficient means to control magnetization. Fruitful progress has been made in this area over the past quarter century. In this paper, we review the state-of-the-art experimental and theoretical studies on magnetization dynamics and switching in ferromagnetic materials that are induced by ultrafast lasers. We start by describing the physical mechanisms of ultrafast demagnetization based on different experimental observations and theoretical methods. Both the spin-flip scattering theory and the superdiffusive spin transport model will be discussed in detail. Then, we will discuss laser-induced torques and resultant magnetization dynamics in ferromagnetic materials. Recent developments of all-optical switching (AOS) of ferromagnetic materials towards ultrafast magnetic storage and memory will also be reviewed, followed by the perspectives on the challenges and future directions in this emerging area.

Simultaneous two-color snapshot view on ultrafast charge and spin dynamics in a Fe-Cu-Ni tri-layer

Ultrafast phenomena on a femtosecond timescale are commonly examined by pump-probe experiments. This implies multiple measurements, where the sample under investigation is pumped with a short light pulse and then probed with a second pulse at various time delays to follow its dynamics. Recently, the principle of streaking extreme ultraviolet (XUV) pulses in the temporal domain has enabled recording the dynamics of a system within a single pulse. However, separate pump-probe experiments at different absorption edges still lack a unified timing, when comparing the dynamics in complex systems. Here, we report on an experiment using a dedicated optical element and the two-color emission of the FERMI XUV free-electron laser to follow the charge and spin dynamics in composite materials at two distinct absorption edges, simultaneously. The sample, consisting of ferromagnetic Fe and Ni layers, separated by a Cu layer, is pumped by an infrared laser and probed by a two-color XUV pulse with photon energies tuned to the M-shell resonances of these two transition metals. The experimental geometry intrinsically avoids any timing uncertainty between the two elements and unambiguously reveals an approximately 100 fs delay of the magnetic response with respect to the electronic excitation for both Fe and Ni. This delay shows that the electronic and spin degrees of freedom are decoupled during the demagnetization process. We furthermore observe that the electronic dynamics of Ni and Fe show pronounced differences when probed at their resonance, while the demagnetization dynamics are similar. These observations underline the importance of simultaneous investigation of the temporal response of both charge and spin in multi-component materials. In a more general scenario, the experimental approach can be extended to continuous energy ranges, promising the development of jitter-free transient absorption spectroscopy in the XUV and soft X-ray regimes.

A local view of the laser induced magnetic domain dynamics in CoPd stripe domains at the picosecond time scale

The dynamics of the magnetic structure in a well ordered ferromagnetic CoPd stripe domain pattern has been investigated upon excitation by femtosecond infrared laser pulses. Time-resolved x-ray magnetic circular dichroism in photoemission electron microscopy (TR-XMCD-PEEM) is used to perform real space magnetic imaging with 100 ps time resolution in order to show local transformations of the domains structures. Using the time resolution of the synchrotron radiation facility of the Helmholtz-Zentrum Berlin, we are able to image the transient magnetic domains in a repetitive pump and probe experiment. In this work, we study the reversible and irreversible transformations of the excited magnetic stripe domains as function of the laser fluence. Our results can be explained by thermal contributions, reducing the XMCD amplitude in each stripe domain below a threshold fluence of 12 mJ cm-2. Above this threshold fluence, irreversible transformations of the magnetic domains are observed. Static XMCD-PEEM images reveal the new partially ordered stripe domain structures characterized by a new local magnetic domain distribution showing an organized pattern at the micrometer scale. This new arrangement is attributed to the recovery of the magnetic anisotropy during heat dissipation under an Oersted field.

Ultrafast magnetic dynamics in insulating YBa2Cu3O6.1 revealed by time resolved two-magnon Raman scattering

Measurement and control of magnetic order and correlations in real time is a rapidly developing scientific area relevant for magnetic memory and spintronics. In these experiments an ultrashort laser pulse (pump) is first absorbed by excitations carrying electric dipole moment. These then give their energy to the magnetic subsystem monitored by a time-resolved probe. A lot of progress has been made in investigations of ferromagnets but antiferromagnets are more challenging. Here, we introduce time-resolved two-magnon Raman scattering as a real time probe of magnetic correlations especially well-suited for antiferromagnets. Its application to the antiferromagnetic charge transfer insulator YBa₂Cu₃O_6.1 revealed rapid demagnetization within 90 fs of photoexcitation. The relaxation back to thermal equilibrium is characterized by much slower timescales. We interpret these results in terms of slow relaxation of the charge sector and rapid equilibration of the magnetic sector to a prethermal state characterized by parameters that change slowly as the charge sector relaxes.

Topological Spin-Charge Gearbox on a Real Molecular Magnet

In this work, using ab initio many-body theory and inspired by an idea suggested by G. D. Mahan for an abstract N-dimensional chain composed of s-type atoms ( Phys. Rev. Lett. 2009, 102, 016801), we propose a functional topological spin-charge gearbox based on the real synthesized Co₃Ni(EtOH) cluster driven with laser pulses. We analyze the implications arising from the use of a real molecule with d-character functional orbitals rather than an extended system and discuss the role of the point group symmetry of the system and the transferability of the electronic and spin density between different many-body states using specially designed laser pulses. We thus find that first-row transition-metal elements can host unpaired yet correlated d electrons and thus act as sites for spin information carriers, while designated laser pulses induce symmetry operations leading to a realizable spin-charge gearbox.

Intense attosecond pulses carrying orbital angular momentum using laser plasma interactions

Light beams with helical phase-fronts are known to carry orbital angular momentum (OAM) and provide an additional degree of freedom to beams of coherent light. While OAM beams can be readily derived from Gaussian laser beams with phase plates or gratings, this is far more challenging in the extreme ultra-violet (XUV), especially for the case of high XUV intensity. Here, we theoretically and numerically demonstrate that intense surface harmonics carrying OAM are naturally produced by the intrinsic dynamics of a relativistically intense circularly-polarized Gaussian beam (i.e. non-vortex) interacting with a target at normal incidence. Relativistic surface oscillations convert the laser pulses to intense XUV harmonic radiation via the well-known relativistic oscillating mirror mechanism. We show that the azimuthal and radial dependence of the harmonic generation process converts the spin angular momentum of the laser beam to orbital angular momentum resulting in an intense attosecond pulse (or pulse train) with OAM.

Vortices in light fields are of growing importance in the XUV and X-ray ranges. Here the authors show by simulations that high harmonics and attosecond pulses, generated while irradiating a deformed thin foil with circularly-polarized Gaussian laser pulses, carry a well-defined orbital angular momentum.

Femtosecond X-ray induced changes of the electronic and magnetic response of solids from electron redistribution

Resonant X-ray absorption, where an X-ray photon excites a core electron into an unoccupied valence state, is an essential process in many standard X-ray spectroscopies. With increasing X-ray intensity, the X-ray absorption strength is expected to become nonlinear. Here, we report the onset of such a nonlinearity in the resonant X-ray absorption of magnetic Co/Pd multilayers near the Co L[Formula: see text] edge. The nonlinearity is directly observed through the change of the absorption spectrum, which is modified in less than 40 fs within 2 eV of its threshold. This is interpreted as a redistribution of valence electrons near the Fermi level. For our magnetic sample this also involves mixing of majority and minority spins, due to sample demagnetization. Our findings reveal that nonlinear X-ray responses of materials may already occur at relatively low intensities, where the macroscopic sample is not destroyed, providing insight into ultrafast charge and spin dynamics.

All-optical spin switching under different spin configurations

All-optical spin switching represents a new frontier in femtomagnetism. However, its underlying principles are quite different from traditional thermal activated spin switching. Here, we employ an atomic spin model and present a systematic investigation from a single spin to a large system of over a million spins. We find that for a single spin without an external perturbation, the conservation of total angular momentum requires that the spin change, if any, exactly matches the orbital momentum change, but a laser pulse significantly alters this relation, where the spin change does not necessarily follow the orbital change. This is reflected in the strong dependence of switching on laser polarization. To have an efficient spin switching, the electron initial momentum direction must closely follow the spin's orientation, so the orbital angular momentum is transverse to the spin and consequently the spin-orbit torque lies in the same direction as the spin. The module of the spin-orbit torque is [Formula: see text], where [Formula: see text] is the angle between spin [Formula: see text] and position [Formula: see text] (momentum [Formula: see text]) and [Formula: see text] is the angle between [Formula: see text] and [Formula: see text]. These findings are manifested in a much larger system. We find that the spin response depends on underlying spin structures. A linearly polarized laser pulse creates a dip in a uniform inplane-magnetized thin film, but has little effects on Néel and Bloch walls. Both right- and left- circularly polarized light ([Formula: see text] and [Formula: see text]) have stronger but different effects in both uniform spin domains and Néel walls. While [Formula: see text] light creates a basin of spins pointing down, [Formula: see text] light creates a mound of spins pointing up. In the vicinity of the structure spins are reversed, similar to the experimental observation. [Formula: see text] light has a dramatic effect, disrupting spins in Bloch walls. By contrast, [Formula: see text] light has a small effect on Bloch walls because [Formula: see text] only switches down spins up and once the spins already point up, there is no major effect. These findings are expected to have important implications in the future.

Role of initial magnetic disorder: A time-dependent ab initio study of ultrafast demagnetization mechanisms

Despite more than 20 years of development, the underlying physics of the laser-induced demagnetization process is still debated. We present a fast, real-time time-dependent density functional theory (rt-TDDFT) algorithm together with the phenomenological atomic Landau-Lifshitz-Gilbert model to investigate this problem. Our Hamiltonian considers noncollinear magnetic moment, spin-orbit coupling (SOC), electron-electron, electron-phonon, and electron-light interactions. The algorithm for time evolution achieves hundreds of times of speedup enabling calculation of large systems. Our simulations yield a demagnetization rate similar to experiments. We found that (i) the angular momentum flow from light to the system is not essential and the spin Zeeman effect is negligible. (ii) The phonon can play a role but is not essential. (iii) The initial spin disorder and the self-consistent update of the electron-electron interaction play dominant roles and enhance the demagnetization to the experimentally observed rate. The spin disorder connects the electronic structure theory with the phenomenological three-temperature model.

Angular Momentum Flow During Ultrafast Demagnetization of a Ferrimagnet

One of the key processes setting the speed of the ultrafast magnetization phenomena is the angular momentum transfer from and into the spin system. However, the way the angular momentum flows during ultrafast demagnetization and magnetization switching phenomena remains elusive so far. We report on time-resolved soft x-ray magnetic circular dichroism measurements of the ferrimagnetic GdFeCo alloy allowing us to record the dynamics of elemental spin and orbital moments at the Fe and Gd sites during femtosecond laser-induced demagnetization. We observe a complete transfer of spin and orbital angular momentum to the lattice during the first hundreds of femtoseconds of the demagnetization process.

Optical anisotropy of non-perturbative high-order harmonic generation in gapless graphene

High harmonic generation in atomic or molecular targets stands as a robust mechanism to produce coherent ultrashort pulses with controllable polarization in the extreme-ultraviolet. However, the production of elliptically or circularly-polarized harmonics is not straightforward, demanding complex combinations of elliptically or circularly-polarized drivers, or the use of molecular alignment techniques. Nevertheless, recent studies show the feasibility of high-harmonic generation in solids. In contrast with atoms and molecules, solids are high-density targets and therefore more efficient radiation sources. Among solid targets, 2D materials are of special interest due to their particular electronic structure, which conveys special optical properties. In this paper, we present theoretical calculations that demonstrate an extraordinary complex light-spin conversion in single-layer graphene irradiated at non perturbative intensities. Linearly-polarized drivings result in the emission of elliptically-polarized harmonics, and elliptically-polarized drivings may result in linearly-polarized or ellipticity-reversed harmonics. In addition, we demonstrate the ultrafast temporal modulation of the harmonic ellipticity.

Ultrafast Orbital-Oriented Control of Magnetization in Half-Metallic La0.7 Sr0.3 MnO3 Films

Manipulating spins by ultrafast pulse laser provides a new avenue to switch the magnetization for spintronic applications. While the spin-orbit coupling is known to play a pivotal role in the ultrafast laser-induced demagnetization, the effect of the anisotropic spin-orbit coupling on the transient magnetization remains an open issue. This study uncovers the role of anisotropic spin-orbit coupling in the spin dynamics in a half-metallic La_0.7 Sr_0.3 MnO₃ film by ultrafast pump-probe technique. The magnetic order is found to be transiently enhanced or attenuated within the initial sub-picosecond when the probe light is tuned to be s- or p-polarized, respectively. The subsequent slow demagnetization amplitude follows the fourfold symmetry of the d x 2 - y 2 orbitals as a function of the polarization angles of the probe light. A model based on the Elliott-Yafet spin-flip scatterings is proposed to reveal that the transient magnetization enhancement is related to the spin-mixed states arising from the anisotropic spin-orbit coupling. The findings provide new insights into the spin dynamics in magnetic systems with anisotropic spin-orbit coupling as well as perspectives for the ultrafast control of information process in spintronic devices.

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 demagnetization^2-4. 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.

M, G. V, M. V, J.-Y. B. Multiscale temporal probing of elemental ultrafast magnetization dynamics in permalloy using High order Harmonics

Chemically selective magnetization dynamics is probed in Ni8()Fe20 with High order Harmonics over a large temporal scale. It is shown that the ratio between effective exchange interaction constants of each element can be retrieved experimentally.

Evidence of depolarization and ellipticity of high harmonics driven by ultrashort bichromatic circularly polarized fields

High harmonics generated by counter-rotating laser fields at the fundamental and second harmonic frequencies have raised important interest as a table-top source of circularly polarized ultrashort extreme-ultraviolet light. However, this emission has not yet been fully characterized: in particular it was assumed to be fully polarized, leading to an uncertainty on the effective harmonic ellipticity. Here we show, through simulations, that ultrashort driving fields and ultrafast medium ionization lead to a breaking of the dynamical symmetry of the interaction, and consequently to deviations from perfectly circular and fully polarized harmonics, already at the single-atom level. We perform the complete experimental characterization of the polarization state of high harmonics generated along that scheme, giving direct access to the ellipticity absolute value and sign, as well as the degree of polarization of individual harmonic orders. This study allows defining optimal generation conditions of fully circularly polarized harmonics for advanced studies of ultrafast dichroisms.

Ultrafast Self-Induced X-Ray Transparency and Loss of Magnetic Diffraction

Using ultrafast ≃2.5  fs and ≃25  fs self-amplified spontaneous emission pulses of increasing intensity and a novel experimental scheme, we report the concurrent increase of stimulated emission in the forward direction and loss of out-of-beam diffraction contrast for a Co/Pd multilayer sample. The experimental results are quantitatively accounted for by a statistical description of the pulses in conjunction with the optical Bloch equations. The dependence of the stimulated sample response on the incident intensity, coherence time, and energy jitter of the employed pulses reveals the importance of increased control of x-ray free electron laser radiation.

Early Stages of Ultrafast Spin Dynamics in a 3d Ferromagnet

Prior to the development of pulsed lasers, one assigned a single local temperature to the lattice, the electron gas, and the spins. With the availability of ultrafast laser sources, one can now drive the temperature of these reservoirs out of equilibrium. Thus, the solid shows new internal degrees of freedom characterized by individual temperatures of the electron gas T_{e}, the lattice T_{l} and the spins T_{s}. We demonstrate an analogous behavior in the spin polarization of a ferromagnet in an ultrafast demagnetization experiment: At the Fermi energy, the polarization is reduced faster than at deeper in the valence band. Therefore, on the femtosecond time scale, the magnetization as a macroscopic quantity does not provide the full picture of the spin dynamics: The spin polarization separates into different parts similar to how the single temperature paradigm changed with the development of ultrafast lasers.

Revealing the Nature of the Ultrafast Magnetic Phase Transition in Ni by Correlating Extreme Ultraviolet Magneto-Optic and Photoemission Spectroscopies

By correlating time- and angle-resolved photoemission and time-resolved transverse magneto-optical Kerr effect measurements, both at extreme ultraviolet wavelengths, we uncover the universal nature of the ultrafast photoinduced magnetic phase transition in Ni. This allows us to explain the ultrafast magnetic response of Ni at all laser fluences-from a small reduction of the magnetization at low laser fluences, to complete quenching at high laser fluences. Both probe methods exhibit the same demagnetization and recovery timescales. The spin system absorbs the energy required to proceed through a magnetic phase transition within 20 fs after the peak of the pump pulse. However, the spectroscopic signatures of demagnetization of the material appear only after ≈200  fs and the subsequent recovery of magnetization on timescales ranging from 500 fs to >70  ps. We also provide evidence of two competing channels with two distinct timescales in the recovery process that suggest the presence of coexisting phases in the material.

Anatomy of interfacial spin-orbit coupling in Co/Pd multilayers using X-ray magnetic circular dichroism and first-principles calculations

Element-specific orbital magnetic moments and their anisotropies in perpendicularly magnetised Co/Pd multilayers are investigated using Co L-edge and Pd M-edge angle-dependent x-ray magnetic circular dichroism. We show that the orbital magnetic moments in Co are anisotropic, whereas those in Pd are isotropic. The first-principles density-functional-theory calculations also suggest that the Co/Pd interfacial orbital magnetic moments in Co are anisotropic and contribute to the perpendicular magnetic anisotropy (PMA), and that the isotropic ones in Pd manipulates the Co orbitals at the interface through proximity effects. Orbital-resolved anatomy of Co/Pd interfaces reveals that the orbital moment anisotropy in Co and spin-flipped transition related to the magnetic dipoles in Pd are essential for the appearance of PMA.

Ultrafast demagnetization at high temperatures

Time-resolved pump-probe measurements were made at variable heat accumulation in Co/Pd superlattices. Heat accumulation increases the baseline temperature and decreases the equilibrium magnetization. Transient ultrafast demagnetization first develops with higher fluence in parallel with strong equilibrium thermal spin fluctuations. The ultrafast demagnetization is then gradually removed as the equilibrium temperature approaches the Curie temperature. The transient magnetization time-dependence is well fit with the spin-flip scattering model.