Spin-Wave Emission from Vortex Cores under Static Magnetic Bias Fields.

We studied the influence of a static in-plane magnetic field on the alternating-field-driven emission of nanoscale spin waves from magnetic vortex cores. Time-resolved scanning transmission X-ray microscopy was used to image spin waves in disk structures of synthetic ferrimagnets and single ferromagnetic layers. For both systems, it was found that an increasing magnetic bias field continuously displaces the wave-emitting vortex core from the center of the disk toward its edge without noticeably altering the spin-wave dispersion relation. In the case of the single-layer disk, an anisotropic lateral expansion of the core occurs at higher magnetic fields, which leads to a directional rather than radial-isotropic emission and propagation of waves. Micromagnetic simulations confirm these findings and further show that focusing effects occur in such systems, depending on the shape of the core and controlled by the static magnetic bias field.

Reconfigurable submicrometer spin-wave majority gate with electrical transducers.

Spin waves are excitations in ferromagnetic media that have been proposed as information carriers in hybrid spintronic devices with much lower operation power than conventional charge-based electronics. Their wave nature can be exploited in majority gates by using interference for computation. However, a scalable spin-wave majority gate that can be cointegrated alongside conventional electronics is still lacking. Here, we demonstrate a submicrometer inline spin-wave majority gate with fan-out. Time-resolved imaging of the magnetization dynamics by scanning transmission x-ray microscopy illustrates the device operation. All-electrical spin-wave spectroscopy further demonstrates majority gates with submicrometer dimensions, reconfigurable input and output ports, and frequency-division multiplexing. Challenges for hybrid spintronic computing systems based on spin-wave majority gates are discussed.

Single shot acquisition of spatially resolved spin wave dispersion relations using X-ray microscopy.

For understanding magnonic materials the fundamental characterization of their frequency response is essential. However, determining full dispersion relations and real space wavelength measurements are challenging and time-consuming tasks. We present an approach for spin wave excitation by a modified Sinc pulse, which combines a cosine signal with a conventional Sinc function. The resulting adjustable frequency bands lead to a broadband spin wave excitation at uniform power levels. Subsequently, time resolved scanning transmission X-ray microscopy is used for direct imaging of all excited spin waves in real space. To demonstrate the capabilities of this approach, a modified Sinc excitation of an ultra-thin yttrium-iron-garnet film is shown that simultaneously reveals phase, amplitude, and k-space information from a single measurement. Consequently, this approach allows a fast and thorough access to the full dispersion relation including spatial maps of the individual spin wave modes, enabling complete characterization of magnonic materials down to the nanoscale in real and reciprocal space.

Quantification of Competing Magnetic States and Switching Pathways in Curved Nanowires by Direct Dynamic Imaging.

For viable applications, spintronic devices based, for example, on domain wall motion need to be highly reliable with stable magnetization states and highly reproducible switching pathways transforming one state to another. The existence of multiple stable states and switching pathways in a system is a definitive barrier for device operation, yet rare and stochastic events are difficult to detect and understand. We demonstrate an approach to quantify competing magnetic states and stochastic switching pathways based on time-resolved scanning electron microscopy with polarization analysis, applied to the technologically relevant control of vortex domain wall chirality via field and curvature in curved wires. As a pump-probe technique, our analysis scheme nonetheless allows for the disentanglement of different occurring dynamic pathways, and we can even identify the rare events leading to changes from one magnetization switching pathway to another pathway via temperature- and geometry-dependent measurements. The experimental imaging is supported by micromagnetic simulations to reveal the mechanisms responsible for the change of the pathway. Together the results allow us to explain the origin and details of the domain wall chirality control and to quantify the frequency and the associated energy barriers of thermally activated changes of the states and switching pathways.

Understanding the Uniqueness of 2p Elements in Periodic Tables.

The Periodic Table, and the unique chemical behavior of the first element in a column (group), were discovered simultaneously one and a half centuries ago. Half a century ago, this unique chemistry of the light homologs was correlated to the then available atomic orbital (AO) radii. The radially nodeless 1s, 2p, 3d, 4f valence AOs are particularly compact. The similarity of r(2s)≈r(2p) leads to pronounced sp-hybrid bonding of the light p-block elements, whereas the heavier p elements with n≥3 exhibit r(ns) ≪ r(np) of approximately -20 to -30 %. Herein, a comprehensive physical explanation is presented in terms of kinetic radial and angular, as well as potential nuclear-attraction and electron-screening effects. For hydrogen-like atoms and all inner shells of the heavy atoms, r(2s) ≫ r(2p) by +20 to +30 %, whereas r(3s)≳r(3p)≳r(3d), since in Coulomb potentials radial motion is more radial orbital expanding than angular motion. However, the screening of nuclear attraction by inner core shells is more efficient for s than for p valence shells. The uniqueness of the 2p AO is explained by this differential shielding. Thereby, the present work paves the way for future physical explanations of the 3d, 4f, and 5g cases.

Toward a wavefunction-based treatment of strong electron correlation in extended systems by means of incremental methods.

Incremental expansions have been used in the past to make electron correlation energies of large molecules and solids accessible to a treatment with wavefunction-based quantum-chemical methods. For this purpose, the Hartree-Fock space of occupied orbitals is partitioned into groups of localized orbitals; these groups are then correlated separately, one at a time, and their correlation energies are added up to a first estimate of the total correlation energy; subsequently, this estimate is systematically improved by correlating pairs, triples, etc., of the localized groups simultaneously. This works well when dynamic correlation effects are predominant and correlation effects rapidly decrease with the distance of the localization centers. For strong static correlation, Hartree-Fock is no longer a good starting point, localization is less well effective, and the convergence of the incremental scheme deteriorates. Here, two ways of improvement are considered for the latter case: optimization of the localized orbitals at a higher level than Hartree-Fock and use of incremental expansions from more than one reference determinant. These improvements are illustrated for H10 rings and H12 sheets up to dissociation and for the transition between the intra-atomic and interatomic bonding regimes in Be6 rings.

Correspondence on "Core Electron Topologies in Chemical Compounds: Case Study of Carbon versus Silicon".

The conclusions of a recent Communication of Yoshida, Raebiger, Shudo, and Ohno published in this journal, that varying core orbital topologies with minuscule negative tails upon bond formation determine the different chemistries of carbon and silicon and affect ionization energies, excitation energies and bond properties of molecules, are now shown to be based on computational artifacts and oversimplified models. The all-electron wave function uniquely determines the observables, while its representation by one-electron orbital products depends on the details of the chosen approximation and therefore need to be considered with great care.

Toward fast and accurate ab initio calculation of magnetic exchange in polynuclear lanthanide complexes.

Ab initio calculations of the magnetic exchange in polynuclear lanthanide complexes are very challenging and often not feasible, due to large active spaces, the large number of required states or the necessity to include dynamical correlation into the calculations. We present an approach which allows for the computationally efficient calculation of exchange splittings in polynuclear lanthanide complexes including dynamical correlation. This is achieved by extending the local-density-fitted configuration-averaged Hartree-Fock (LDF-CAHF) method to systems with more than one group of open-shell orbitals (e.g. at different metal atoms) and combining it with linear-scaling many-state pair-natural-orbital complete active space perturbation theory of second order (PNO-CASPT2). In order to assess the performance of the method, we apply it to the asymmetric dinuclear complex [hqH2][Yb2(hq)4(NO3)3]·MeOH (hqH = 8-hydroxyquinoline).

Current-Induced Skyrmion Generation through Morphological Thermal Transitions in Chiral Ferromagnetic Heterostructures.

Magnetic skyrmions promise breakthroughs in future memory and computing devices due to their inherent stability and small size. Their creation and current driven motion have been recently observed at room temperature, but the key mechanisms of their formation are not yet well-understood. Here it is shown that in heavy metal/ferromagnet heterostructures, pulsed currents can drive morphological transitions between labyrinth-like, stripe-like, and skyrmionic states. Using high-resolution X-ray microscopy, the spin texture evolution with temperature and magnetic field is imaged and it is demonstrated that with transient Joule heating, topological charges can be injected into the system, driving it across the stripe-skyrmion boundary. The observations are explained through atomistic spin dynamic and micromagnetic simulations that reveal a crossover to a global skyrmionic ground state above a threshold magnetic field, which is found to decrease with increasing temperature. It is demonstrated how by tuning the phase stability, one can reliably generate skyrmions by short current pulses and stabilize them at zero field, providing new means to create and manipulate spin textures in engineered chiral ferromagnets.

Exchange coupling and single molecule magnetism in redox-active tetraoxolene-bridged dilanthanide complexes.

Tetraoxolene radical-bridged lanthanide SMM systems were prepared for the first time by reduction of the respective neutral compounds. Magnetic measurements reveal the profound influence of the radical center on magnetic behavior. Strong magnetic couplings are revealed in the radical species, which switch on SMM behavior under zero applied field for DyIII and TbIII compounds. HFEPR spectra unravel the contributions of the magnetic coupling and the magnetic anisotropy. For GdIII this results in much more accurate magnetic coupling parameters with respect to bulk magnetic measurements.

Dealing with the exponential wall in electronic structure calculations.

An alternative to the density functional theory is the use of wavefunction based electronic structure calculations for solids. In order to perform them, the Exponential Wall (EW) problem has to be resolved. It is caused by an exponential increase of the number of configurations with increasing electron number N. There are different routes one may follow. One is to characterize a many-electron wavefunction by a vector in Liouville space with a cumulant metric rather than in Hilbert space. This removes the EW problem. Another is to model the solid by an impurity or fragment embedded in a bath which is treated at a much lower level than the former. This is the case in the Density Matrix Embedding Theory (DMET) or the Density Embedding Theory (DET). The latter two are closely related to a Schmidt decomposition of a system and to the determination of the associated entanglement. We show here the connection between the two approaches. It turns out that the DMET (or DET) has an identical active space as a previously used Local Ansatz, based on a projection and partitioning approach. Yet, the EW problem is resolved differently in the two cases. By studying a H10 ring, these differences are analyzed with the help of the method of increments.

Orbital breathing effects in the computation of x-ray d-ion spectra in solids by ab initio wave-function-based methods.

In existing theoretical approaches to core-level excitations of transition-metal ions in solids relaxation and polarization effects due to the inner core hole are often ignored or described phenomenologically. Here we set up an ab initio computational scheme that explicitly accounts for such physics in the calculation of x-ray absorption and resonant inelastic x-ray scattering spectra. Good agreement is found with experimental transition-metal L-edge data for the strongly correlated d 9 cuprate Li2CuO2, for which we determine the absolute scattering intensities. The newly developed methodology opens the way for the investigation of even more complex d n electronic structures of group VI B to VIII B correlated oxide compounds.

Three-dimensional Character of the Magnetization Dynamics in Magnetic Vortex Structures: Hybridization of Flexure Gyromodes with Spin Waves.

Three-dimensional linear spin-wave eigenmodes of a vortex-state Permalloy disk are studied by micromagnetic simulations based on the Landau-Lifshitz-Gilbert equation. The simulations confirm that the increase of the disk thickness leads to the appearance of additional exchange-dominated so-called gyrotropic flexure modes having nodes along the disk thickness, and eigenfrequencies that decrease when the thickness is increased. We observe the formation of a gap in the mode spectrum caused by the hybridization of the first flexure mode with one of the azimuthal spin-wave modes of the disk. A qualitative change of the transverse profile of this azimuthal mode is found, demonstrating that in a thick vortex-state disk the influence of the "transverse" and the "azimuthal" coordinates cannot be separated. The three-dimensional character of the eigenmodes is essential to explain the recently observed asymmetries in an experimentally obtained phase diagram of vortex-core reversal in relatively thick Permalloy disks.

Strongly frustrated triangular spin lattice emerging from triplet dimer formation in honeycomb Li2IrO3.

Iridium oxides with a honeycomb lattice have been identified as platforms for the much anticipated Kitaev topological spin liquid: the spin-orbit entangled states of Ir(4+) in principle generate precisely the required type of anisotropic exchange. However, other magnetic couplings can drive the system away from the spin-liquid phase. With this in mind, here we disentangle the different magnetic interactions in Li2IrO3, a honeycomb iridate with two crystallographically inequivalent sets of adjacent Ir sites. Our ab initio many-body calculations show that, while both Heisenberg and Kitaev nearest-neighbour couplings are present, on one set of Ir-Ir bonds the former dominates, resulting in the formation of spin-triplet dimers. The triplet dimers frame a strongly frustrated triangular lattice and by exact cluster diagonalization we show that they remain protected in a wide region of the phase diagram.

Enhanced Nonadiabaticity in Vortex Cores due to the Emergent Hall Effect.

We present a combined theoretical and experimental study, investigating the origin of the enhanced nonadiabaticity of magnetic vortex cores. Scanning transmission x-ray microscopy is used to image the vortex core gyration dynamically to measure the nonadiabaticity with high precision, including a high confidence upper bound. We show theoretically, that the large nonadiabaticity parameter observed experimentally can be explained by the presence of local spin currents arising from a texture induced emergent Hall effect. This study demonstrates that the magnetic damping α and nonadiabaticity parameter ß are very sensitive to the topology of the magnetic textures, resulting in an enhanced ratio (ß/α>1) in magnetic vortex cores or Skyrmions.

Transferability and accuracy by combining dispersionless density functional and incremental post-Hartree-Fock theories: Noble gases adsorption on coronene/graphene/graphite surfaces.

The accuracy and transferability of the electronic structure approach combining dispersionless density functional theory (DFT) [K. Pernal et al., Phys. Rev. Lett. 103, 263201 (2009)] with the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)], are validated for the interaction between the noble-gas Ne, Ar, Kr, and Xe atoms and coronene/graphene/graphite surfaces. This approach uses the method of increments for surface cluster models to extract intermonomer dispersion-like (2- and 3-body) correlation terms at coupled cluster singles and doubles and perturbative triples level, while periodic dispersionless density functionals calculations are performed to estimate the sum of Hartree-Fock and intramonomer correlation contributions. Dispersion energy contributions are also obtained using DFT-based symmetry-adapted perturbation theory [SAPT(DFT)]. An analysis of the structure of the X/surface (X = Ne, Ar, Kr, and Xe) interaction energies shows the excellent transferability properties of the leading intermonomer correlation contributions across the sequence of noble-gas atoms, which are also discussed using the Drude oscillator model. We further compare these results with van der Waals-(vdW)-corrected DFT-based approaches. As a test of accuracy, the energies of the low-lying nuclear bound states supported by the laterally averaged X/graphite potentials (X = (3)He, (4)He, Ne, Ar, Kr, and Xe) are calculated and compared with the best estimations from experimental measurements and an atom-bond potential model using the ab initio-assisted fine-tuning of semiempirical parameters. The bound-state energies determined differ by less than 6-7 meV (6%) from the atom-bond potential model. The crucial importance of including incremental 3-body dispersion-type terms is clearly demonstrated, showing that the SAPT(DFT) approach effectively account for these terms. With the deviations from the best experimental-based estimations smaller than 2.3 meV (1.9%), the accuracy of the combined DFT and post-HF incremental scheme is established for all the noble-gas atoms. With relative deviations smaller than 4% and 11%, good agreement is also achieved by applying the vdW-corrected DFT treatments PBE-D3 and vdW-DF2 for noble-gas atoms heavier than neon.

Strong magnetic frustration and anti-site disorder causing spin-glass behavior in honeycomb Li2RhO3.

With large spin-orbit coupling, the electron configuration in d-metal oxides is prone to highly anisotropic exchange interactions and exotic magnetic properties. In 5d(5) iridates, given the existing variety of crystal structures, the magnetic anisotropy can be tuned from antisymmetric to symmetric Kitaev-type, with interaction strengths that outsize the isotropic terms. By many-body electronic-structure calculations we here address the nature of the magnetic exchange and the intriguing spin-glass behavior of Li2RhO3, a 4d(5) honeycomb oxide. For pristine crystals without Rh-Li site inversion, we predict a dimerized ground state as in the isostructural 5d(5) iridate Li2IrO3, with triplet spin dimers effectively placed on a frustrated triangular lattice. With Rh-Li anti-site disorder, we explain the observed spin-glass phase as a superposition of different, nearly degenerate symmetry-broken configurations.

Combining density functional and incremental post-Hartree-Fock approaches for van der Waals dominated adsorbate-surface interactions: Ag2/graphene.

A combined density functional (DFT) and incremental post-Hartree-Fock (post-HF) approach, proven earlier to calculate He-surface potential energy surfaces [de Lara-Castells et al., J. Chem. Phys. 141, 151102 (2014)], is applied to describe the van der Waals dominated Ag2/graphene interaction. It extends the dispersionless density functional theory developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] by including periodic boundary conditions while the dispersion is parametrized via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. Starting with the elementary cluster unit of the target surface (benzene), continuing through the realistic cluster model (coronene), and ending with the periodic model of the extended system, modern ab initio methodologies for intermolecular interactions as well as state-of-the-art van der Waals-corrected density functional-based approaches are put together both to assess the accuracy of the composite scheme and to better characterize the Ag2/graphene interaction. The present work illustrates how the combination of DFT and post-HF perspectives may be efficient to design simple and reliable ab initio-based schemes in extended systems for surface science applications.

Communication: unraveling the (4)He droplet-mediated soft-landing from ab initio-assisted and time-resolved density functional simulations: Au@(4)He300/TiO2(110).

An ab-initio-based methodological scheme for He-surface interactions and zero-temperature time-dependent density functional theory for superfluid (4)He droplets motion are combined to follow the short-time collision dynamics of the Au@(4)He300 system with the TiO2(110) surface. This composite approach demonstrates the (4)He droplet-assisted sticking of the metal species to the surface at low landing energy (below 0.15 eV/atom), thus providing the first theoretical evidence of the experimentally observed (4)He droplet-mediated soft-landing deposition of metal nanoparticles on solid surfaces [Mozhayskiy et al., J. Chem. Phys. 127, 094701 (2007) and Loginov et al., J. Phys. Chem. A 115, 7199 (2011)].

Communication: A combined periodic density functional and incremental wave-function-based approach for the dispersion-accounting time-resolved dynamics of 4He nanodroplets on surfaces: 4He/graphene.

In this work we propose a general strategy to calculate accurate He-surface interaction potentials. It extends the dispersionless density functional approach recently developed by Pernal et al. [Phys. Rev. Lett. 103, 263201 (2009)] to adsorbate-surface interactions by including periodic boundary conditions. We also introduce a scheme to parametrize the dispersion interaction by calculating two- and three-body dispersion terms at coupled cluster singles and doubles and perturbative triples (CCSD(T)) level via the method of increments [H. Stoll, J. Chem. Phys. 97, 8449 (1992)]. The performance of the composite approach is tested on (4)He/graphene by determining the energies of the low-lying selective adsorption states, finding an excellent agreement with the best available theoretical data. Second, the capability of the approach to describe dispersionless correlation effects realistically is used to extract dispersion effects in time-dependent density functional simulations on the collision of (4)He droplets with a single graphene sheet. It is found that dispersion effects play a key role in the fast spreading of the (4)He nanodroplet, the evaporation-like process of helium atoms, and the formation of solid-like helium structures. These characteristics are expected to be quite general and highly relevant to explain experimental measurements with the newly developed helium droplet mediated deposition technique.