The 2021 ultrafast spectroscopic probes of condensed matter roadmap

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light-matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

The role of ultrafast magnon generation in the magnetization dynamics of rare-earth metals

Ultrafast demagnetization of rare-earth metals is distinct from that of 3d ferromagnets, as rare-earth magnetism is dominated by localized 4f electrons that cannot be directly excited by an optical laser pulse. Their demagnetization must involve excitation of magnons, driven either through exchange coupling between the 5d6s-itinerant and 4f-localized electrons or by coupling of 4f spins to lattice excitations. Here, we disentangle the ultrafast dynamics of 5d6s and 4f magnetic moments in terbium metal by time-resolved photoemission spectroscopy. We show that the demagnetization time of the Tb 4f magnetic moments of 400 fs is set by 4f spin-lattice coupling. This is experimentally evidenced by a comparison to ferromagnetic gadolinium and supported by orbital-resolved spin dynamics simulations. Our findings establish coupling of the 4f spins to the lattice via the orbital momentum as an essential mechanism driving magnetization dynamics via ultrafast magnon generation in technically relevant materials with strong magnetic anisotropy.

Hidden order and beyond: an experimental-theoretical overview of the multifaceted behavior of URu2Si2

This topical review describes the multitude of unconventional behaviors in the hidden order, heavy fermion, antiferromagnetic and superconducting phases of the intermetallic compound URu₂Si₂ when tuned with pressure, magnetic field, and substitutions for all three elements. Such 'perturbations' result in a variety of new phases beyond the mysterious hidden order that are only now being slowly understood through a series of state-of-the-science experimentation, along with an array of novel theoretical approaches. Despite all these efforts spanning more than 30 years, hidden order (HO) remains puzzling and non-clarified, and the search continues in 2019 into a fourth decade for its final resolution. Here we attempt to update the present situation of URu₂Si₂ importing the latest experimental results and theoretical proposals. First, let us consider the pristine compound as a function of temperature and report the recent measurements and models relating to its heavy Fermi liquid crossover, its HO and superconductivity (SC). Recent experiments and theories are surmized that address four-fold symmetry breaking (or nematicity), Isingness and unconventional excitation modes. Second, we review the pressure dependence of URu₂Si₂ and its transformation to antiferromagnetic long-range order. Next we confront the dramatic high magnetic-field phases requiring fields above 40 T. And finally, we attempt to answer how does random substitutions of other 5f elements for U, and 3d, 4d, and 5d elements for Ru, and even P for Si affect and transform the HO. Commensurately, recent theoretical models are summarized and then related to the intriguing experimental behavior.

Hydrogen-Induced High-Temperature Superconductivity in Two-Dimensional Materials: The Example of Hydrogenated Monolayer MgB_{2}

Hydrogen-based compounds under ultrahigh pressure, such as the polyhydrides H_{3}S and LaH_{10}, superconduct through the conventional electron-phonon coupling mechanism to attain the record critical temperatures known to date. Here we exploit the intrinsic advantages of hydrogen to strongly enhance phonon-mediated superconductivity in a completely different system, namely, a two-dimensional material with hydrogen adatoms. We find that van Hove singularities in the electronic structure, originating from atomiclike hydrogen states, lead to a strong increase of the electronic density of states at the Fermi level, and thus of the electron-phonon coupling. Additionally, the emergence of high-frequency hydrogen-related phonon modes in this system boosts the electron-phonon coupling further. As a concrete example, we demonstrate the effect of hydrogen adatoms on the superconducting properties of monolayer MgB_{2}, by solving the fully anisotropic Eliashberg equations, in conjunction with a first-principles description of the electronic and vibrational states, and their coupling. We show that hydrogenation leads to a high critical temperature of 67 K, which can be boosted to over 100 K by biaxial tensile strain.

Magneto-optical properties of Au upon the injection of hot spin-polarized electrons across Fe/Au(0 0 1) interfaces

We demonstrate a novel method for the excitation of sizable magneto-optical effects in Au by means of the laser-induced injection of hot spin-polarized electrons in Au/Fe/MgO(0 0 1) heterostructures. It is based on the energy- and spin-dependent electron transmittance of Fe/Au interface which acts as a spin filter for non-thermalized electrons optically excited in Fe. We show that after crossing the interface, majority electrons propagate through the Au layer with the velocity on the order of 1 nm fs^-1 (close to the Fermi velocity) and the decay length on the order of 100 nm. Featuring ultrafast functionality and requiring no strong external magnetic fields, spin injection results in a distinct magneto-optical response of Au. We develop a formalism based on the phase of the transient complex MOKE response and demonstrate its robustness in a plethora of experimental and theoretical MOKE studies on Au, including our ab initio calculations. Our work introduces a flexible tool to manipulate magneto-optical properties of metals on the femtosecond timescale that holds high potential for active magneto-photonics, plasmonics, and spintronics.

Beyond a phenomenological description of magnetostriction

Magnetostriction, the strain induced by a change in magnetization, is a universal effect in magnetic materials. Owing to the difficulty in unraveling its microscopic origin, it has been largely treated phenomenologically. Here, we show how the source of magnetostriction-the underlying magnetoelastic stress-can be separated in the time domain, opening the door for an atomistic understanding. X-ray and electron diffraction are used to separate the sub-picosecond spin and lattice responses of FePt nanoparticles. Following excitation with a 50-fs laser pulse, time-resolved X-ray diffraction demonstrates that magnetic order is lost within the nanoparticles with a time constant of 146 fs. Ultrafast electron diffraction reveals that this demagnetization is followed by an anisotropic, three-dimensional lattice motion. Analysis of the size, speed, and symmetry of the lattice motion, together with ab initio calculations accounting for the stresses due to electrons and phonons, allow us to reveal the magnetoelastic stress generated by demagnetization.

Free surfaces recast superconductivity in few-monolayer MgB2: Combined first-principles and ARPES demonstration

Two-dimensional materials are known to harbour properties very different from those of their bulk counterparts. Recent years have seen the rise of atomically thin superconductors, with a caveat that superconductivity is strongly depleted unless enhanced by specific substrates, intercalants or adatoms. Surprisingly, the role in superconductivity of electronic states originating from simple free surfaces of two-dimensional materials has remained elusive to date. Here, based on first-principles calculations, anisotropic Eliashberg theory, and angle-resolved photoemission spectroscopy (ARPES), we show that surface states in few-monolayer MgB2 make a major contribution to the superconducting gap spectrum and density of states, clearly distinct from the widely known, bulk-like σ- and π-gaps. As a proof of principle, we predict and measure the gap opening on the magnesium-based surface band up to a critical temperature as high as ~30 K for merely six monolayers thick MgB2. These findings establish free surfaces as an unavoidable ingredient in understanding and further tailoring of superconductivity in atomically thin materials.

Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films

The conversion of charge currents into spin currents in nonmagnetic conductors is a hallmark manifestation of spin-orbit coupling that has important implications for spintronic devices. Here we report the measurement of the interfacial spin accumulation induced by the spin Hall effect in Pt and W thin films using magneto-optical Kerr microscopy. We show that the Kerr rotation has opposite sign in Pt and W and scales linearly with current density. By comparing the experimental results with ab initio calculations of the spin Hall and magneto-optical Kerr effects, we quantitatively determine the current-induced spin accumulation at the Pt interface as 5×10^{-12}  μ_{B} A^{-1} cm^{2} per atom. From thickness-dependent measurements, we determine the spin diffusion length in a single Pt film to be 11±3  nm, which is significantly larger compared to that of Pt adjacent to a magnetic layer.

Disparate ultrafast dynamics of itinerant and localized magnetic moments in gadolinium metal

The Heisenberg–Dirac intra-atomic exchange coupling is responsible for the formation of the atomic spin moment and thus the strongest interaction in magnetism. Therefore, it is generally assumed that intra-atomic exchange leads to a quasi-instantaneous aligning process in the magnetic moment dynamics of spins in separate, on-site atomic orbitals. Following ultrashort optical excitation of gadolinium metal, we concurrently record in photoemission the 4f magnetic linear dichroism and 5d exchange splitting. Their dynamics differ by one order of magnitude, with decay constants of 14 versus 0.8 ps, respectively. Spin dynamics simulations based on an orbital-resolved Heisenberg Hamiltonian combined with first-principles calculations explain the particular dynamics of 5d and 4f spin moments well, and corroborate that the 5d exchange splitting traces closely the 5d spin-moment dynamics. Thus gadolinium shows disparate dynamics of the localized 4f and the itinerant 5d spin moments, demonstrating a breakdown of their intra-atomic exchange alignment on a picosecond timescale.

Due the strength of the intra-atomic exchange interaction, it is generally assumed that alignment of spin moments in intra-atomic orbitals is quasi-instantaneous. Here, the authors demonstrate the breakdown of this relation between the 4f and 5d electrons in gadolinium following ultrashort optical excitation.

Magnetic polarization of the americium J=0 ground state in AmFe(2)

Trivalent americium has a nonmagnetic (J=0) ground state arising from the cancellation of the orbital and spin moments. However, magnetism can be induced by a large molecular field if Am^{3+} is embedded in a ferromagnetic matrix. Using the technique of x-ray magnetic circular dichroism, we show that this is the case in AmFe_{2}. Since ⟨J_{z}⟩=0, the spin component is exactly twice as large as the orbital one, the total Am moment is opposite to that of Fe, and the magnetic dipole operator ⟨T_{z}⟩ can be determined directly; we discuss the progression of the latter across the actinide series.

Ultrafast spin transport as key to femtosecond demagnetization

Irradiating a ferromagnet with a femtosecond laser pulse is known to induce an ultrafast demagnetization within a few hundred femtoseconds. Here we demonstrate that direct laser irradiation is in fact not essential for ultrafast demagnetization, and that electron cascades caused by hot electron currents accomplish it very efficiently. We optically excite a Au/Ni layered structure in which the 30 nm Au capping layer absorbs the incident laser pump pulse and subsequently use the X-ray magnetic circular dichroism technique to probe the femtosecond demagnetization of the adjacent 15 nm Ni layer. A demagnetization effect corresponding to the scenario in which the laser directly excites the Ni film is observed, but with a slight temporal delay. We explain this unexpected observation by means of the demagnetizing effect of a superdiffusive current of non-equilibrium, non-spin-polarized electrons generated in the Au layer.

Terahertz spin current pulses controlled by magnetic heterostructures

In spin-based electronics, information is encoded by the spin state of electron bunches. Processing this information requires the controlled transport of spin angular momentum through a solid, preferably at frequencies reaching the so far unexplored terahertz regime. Here, we demonstrate, by experiment and theory, that the temporal shape of femtosecond spin current bursts can be manipulated by using specifically designed magnetic heterostructures. A laser pulse is used to drive spins from a ferromagnetic iron thin film into a non-magnetic cap layer that has either low (ruthenium) or high (gold) electron mobility. The resulting transient spin current is detected by means of an ultrafast, contactless amperemeter based on the inverse spin Hall effect, which converts the spin flow into a terahertz electromagnetic pulse. We find that the ruthenium cap layer yields a considerably longer spin current pulse because electrons are injected into ruthenium d states, which have a much lower mobility than gold sp states. Thus, spin current pulses and the resulting terahertz transients can be shaped by tailoring magnetic heterostructures, which opens the door to engineering high-speed spintronic devices and, potentially, broadband terahertz emitters.

Pressure and temperature control of spin-switchable metal-organic coordination polymers from ab initio calculations

We explore a combination of density-functional theory with supplemented Coulomb U (DFT+U) and ab initio molecular dynamics simulations to investigate the spin-crossover (SCO) phenomenon in coordination polymers. We demonstrate the applicability of the method for the case of bimetallic metal-organic framework Fe(2)[Nb(CN)(8)]·(4-pyridinealdoxime)(8)·2H(2)O [see S. Ohkoshi et al. Nat. Chem. 3, 564 (2011)]. Our study shows that this approach is capable of capturing the SCO transitions driven by pressure as well as temperature. In addition to discovering novel spin-state transitions, magnetic states involving changes in the long-range magnetic ordering pattern are achieved, thereby offering the tunability of spin states as well as the long-range order of the spins. We compare the SCO transition in the Fe-based framework with a computer designed Mn-based variant.

An advanced multi-orbital impurity solver for dynamical mean field theory based on the equation of motion approach

We propose an improved fast multi-orbital impurity solver for the dynamical mean field theory based on equations of motion (EOM) for Green's functions and a decoupling scheme. In this scheme the inter-orbital Coulomb interactions are treated fully self-consistently, and involve the inter-orbital fluctuations. As an example of the use of the derived multi-orbital impurity solver, the two-orbital Hubbard model is studied for various cases. Comparisons are made between numerical results obtained with our EOM scheme and those obtained with quantum Monte Carlo and numerical renormalization group methods. The comparison shows a good agreement, but also reveals a dissimilarity of the behaviors of the densities of states which is caused by inter-site inter-orbital hopping effects and on-site inter-orbital fluctuation effects, thus corroborating the assertion of the value of the EOM method for the study of multi-orbital strongly correlated systems.

Ab Initio investigation of the Elliott-Yafet electron-phonon mechanism in laser-induced ultrafast demagnetization

The spin-flip (SF) Eliashberg function is calculated from first principles for ferromagnetic Ni to accurately establish the contribution of Elliott-Yafet electron-phonon SF scattering to Ni's femtosecond laser-driven demagnetization. This is used to compute the SF probability and demagnetization rate for laser-created thermalized as well as nonequilibrium electron distributions. Increased SF probabilities are found for thermalized electrons, but the induced demagnetization rate is extremely small. A larger demagnetization rate is obtained for nonequilibrium electron distributions, but its contribution is too small to account for femtosecond demagnetization.

Superdiffusive spin transport as a mechanism of ultrafast demagnetization

We propose a semiclassical model for femtosecond laser-induced demagnetization due to spin-polarized excited electron diffusion in the superdiffusive regime. Our approach treats the finite elapsed time and transport in space between multiple electronic collisions exactly, as well as the presence of several metal films in the sample. Solving the derived transport equation numerically we show that this mechanism accounts for the experimentally observed demagnetization within 200 fs in Ni, without the need to invoke any angular momentum dissipation channel.

Quadratic X-ray magneto-optical effect upon reflection in a near-normal-incidence configuration at the M edges of 3d-transition metals

We have observed a quadratic x-ray magneto-optical effect in near-normal-incidence reflection at the M edges of iron. The effect appears as the magnetically induced rotation of approximately 0.1 degrees of the polarization plane of linearly polarized x-ray radiation upon reflection. A comparison of the measured rotation spectrum with results from x-ray magnetic linear dichroism data demonstrates that this is the first observation of the Schäfer-Hubert effect in the x-ray regime. Ab initio density-functional theory calculations reveal that hybridization effects of the 3p core states necessarily need to be considered when interpreting experimental data. The discovered magneto-x-ray effect holds promise for future ultrafast and element-selective studies of ferromagnetic as well as antiferromagnetic materials.

The electronic structure of UCoGe by ab initio calculations and XPS experiment

The crystal and electronic structures of the orthorhombic compound UCoGe are presented and discussed. It has been either refined by the x-ray diffraction on a single crystal or computed within the local spin density functional theory, employing the fully relativistic version of the full-potential local-orbital band structure code, respectively. We particularly give our attention to investigating the Fermi surface and de Haas-van Alphen quantities of UCoGe. The calculated electronic density is then examined by x-ray photoelectron spectroscopy (XPS). Fairly good agreement is achieved between theoretical and experimental XPS results in the paramagnetic state. A small difference in the position (in energy scale) of the U 5f bands is caused by the electron localization effect observed in the experimental XPS. There is also some discrepancy for the Co 3d electron contributions below E(F). The Fermi surface in the non-magnetic state is of a semimetallic type while that in the ferromagnetic state, with the ordered moment of -0.47 μ(B)/f.u. along the c axis, is more metallic, with nesting properties that may favour superconductivity.

Hidden order in URu2Si2 originates from Fermi surface gapping induced by dynamic symmetry breaking

Spontaneous, collective ordering of electronic degrees of freedom leads to second-order phase transitions that are characterized by an order parameter driving the transition. The notion of a 'hidden order' has recently been used for a variety of materials where a clear phase transition occurs without a known order parameter. The prototype example is the heavy-fermion compound URu(2)Si(2), where a mysterious hidden-order transition occurs at 17.5 K. For more than twenty years this system has been studied theoretically and experimentally without a firm grasp of the underlying physics. Here, we provide a microscopic explanation of the hidden order using density-functional theory calculations. We identify the Fermi surface 'hot spots' where degeneracy induces a Fermi surface instability and quantify how symmetry breaking lifts the degeneracy, causing a surprisingly large Fermi surface gapping. As the mechanism for the hidden order, we deduce spontaneous symmetry breaking through a dynamic mode of antiferromagnetic moment excitations.

Magnetic circular dichroism in two-photon photoemission

We report the observation of magnetic circular dichroism (MCD) in two-photon photoemission (2PPE). The Heusler alloys Ni2MnGa and Co2FeSi were investigated by excitation with femtosecond laser light, showing MCD asymmetries of A=(3.5+/-0.5)x10;{-3} for Ni2MnGa and of A=(2.1+/-1.0)x10;{-3} for Co2FeSi, respectively. A theoretical explanation is provided based on local spin-density calculations for the magnetic dichroic response; the computed 2PPE MCD agrees well with the experiment. The observed 2PPE magnetic contrast represents an interesting alternative for future time-resolved photoemission studies on surface magnetism practicable in the laboratory.

Tailoring the nature of magnetic coupling of Fe-porphyrin molecules to ferromagnetic substrates

We demonstrate that an antiferromagnetic coupling between paramagnetic Fe-porphyrin molecules and ultrathin Co and Ni magnetic films on Cu(100) substrates can be established by an intermediate layer of atomic oxygen. The coupling energies have been determined from the temperature dependence of x-ray magnetic circular dichroism measurements. By density functional theory+U calculations the coupling mechanism is shown to be superexchange between the Fe center of the molecules and Co surface-atoms, mediated by oxygen.

Calculated magneto-optical Kerr spectra of the half-Heusler compounds AuMnX (X = In, Sn, Sb)

The ferromagnetic ground states of the half-Heusler compounds AuMnX (X = In, Sn, Sb) have been calculated in the framework of the local spin-density approximation (LSDA) to density functional theory (DFT). AuMnSn is computed to be a half-metallic ferromagnet, whereas AuMnIn and AuMnSb are not half-metallic, due to their different band filling. The computed relativistic electronic structures served as inputs to calculate the magneto-optical Kerr rotations and ellipticities for all three materials. In the case of AuMnSn the largest, zero-temperature, polar Kerr rotation has been found to be -0.45° at about 1 eV photon energy. The computed MOKE spectra of AuMnSn are in qualitative agreement with recent experiments. The largest Kerr rotations of AuMnIn and AuMnSb have been calculated to be +0.64° at 4.3 eV and -0.85° at 0.9 eV, respectively.

Substrate-induced magnetic ordering and switching of iron porphyrin molecules

To realize molecular spintronic devices, it is important to externally control the magnetization of a molecular magnet. One class of materials particularly promising as building blocks for molecular electronic devices is the paramagnetic porphyrin molecule in contact with a metallic substrate. Here, we study the structural orientation and the magnetic coupling of in-situ-sublimated Fe porphyrin molecules on ferromagnetic Ni and Co films on Cu(100). Our studies involve X-ray absorption spectroscopy and X-ray magnetic circular dichroism experiments. In a combined experimental and computational study we demonstrate that owing to an indirect, superexchange interaction between Fe atoms in the molecules and atoms in the substrate (Co or Ni) the paramagnetic molecules can be made to order ferromagnetically. The Fe magnetic moment can be rotated along directions in plane as well as out of plane by a magnetization reversal of the substrate, thereby opening up an avenue for spin-dependent molecular electronics.

Superconductivity caused by the pairing of plutonium 5f Eelectrons in PuCoGa5

On the basis of electronic structure calculations we identify the superconductivity in the novel, high-temperature superconductor PuCoGa5 to be caused by the pairing of Pu 5f electrons. Assuming delocalized Pu 5f states, we compute theoretical crystallographic constants very near to the experimental ones, and the calculated specific heat coefficient compares reasonably to the measured coefficient. The theoretical Fermi surface is quasi-two-dimensional and the material appears to be close to a magnetic phase instability.

Observation of minority spin character of the new electron doped manganite La0.7Ce0.3MnO3 from tunneling magnetoresistance

We report the magnetotransport characteristics of a trilayer ferromagnetic tunnel junction built of an electron doped manganite (La0.7Ce0.3MnO3) and a hole doped manganite (La0.7Ca0.3MnO3). At low temperatures the junction exhibits a large positive tunneling magnetoresistance (TMR), irrespective of the bias voltage. At intermediate temperatures below T(C) the sign of the TMR is dependent on the bias voltage across the junction. The magnetoresistive characteristics of the junction strongly suggest that La0.7Ce0.3MnO3 is a minority spin carrier ferromagnet with a high degree of spin polarization, i.e., a transport half-metal.

Observation of the x-ray magneto-optical Voigt effect

The existence of the x-ray magneto-optical Voigt effect is demonstrated. By means of polarization analysis the Voigt rotation and ellipticity of linearly polarized synchrotron radiation are measured at the Co L3 edge upon transmission through an amorphous Co film. The observed x-ray Voigt rotation is about 7.5 degrees /microm. On the basis of ab initio calculations it is shown that the x-ray Voigt effect follows sensitively the amount of spin polarization of the 2p core states. Therefore it provides a unique measure of the spin splitting of the core states.

The frequency of seeing square wave density modulations in random dot patterns

A theoretical and experimental study on the detection of a square wave pattern of random dots is presented. Our theory applies to two-alternative forced choice experiments as well as to "seen"-"not seen" discrimination experiments. In our experiments we used the forced choice method. The theory provides a good description of the psychometric function of the percentage of correct decisions versus contrast. From these frequency of seeing (FOS) curves the apparent signal-to-noise ratio of the detection mechanism of human subjects can be derived. It is found that this ratio can have values of up to 100% and that it decreases with the number of dots in the stimulus and with the number of periods of the square wave. It is shown that a more precise description of the human performance can be obtained from the mid-points of the FOS-curves (i.e. the thresholds) rather than from the slopes.