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.

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 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).

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.

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.

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.

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.

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.

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.

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)].

Electronic structure of low-dimensional 4d(5) oxides: interplay of ligand distortions, overall lattice anisotropy, and spin-orbit interactions.

The electronic structure of the low-dimensional 4d(5) oxides Sr2RhO4 and Ca3CoRhO6 is herein investigated by embedded-cluster quantum chemistry calculations. A negative tetragonal-like t2g splitting is computed in Sr2RhO4 and a negative trigonal-like splitting is predicted for Ca3CoRhO6, in spite of having positive tetragonal distortions in the former material and cubic oxygen octahedra in the latter. Our findings bring to the foreground the role of longer-range crystalline anisotropy in generating noncubic potentials that compete with local distortions of the ligand cage, an issue not addressed in standard textbooks on crystal-field theory. We also show that sizable t2g(5)-t2g(4)eg(1) couplings via spin-orbit interactions produce in Sr2RhO4 ⟨Z⟩ = ⟨Σ(i)l(i)·s(i)⟩ ground-state expectation values significantly larger than 1, quite similar to theoretical and experimental data for 5d(5) spin-orbit-driven oxides such as Sr2IrO4. On the other hand, in Ca3CoRhO6, the ⟨Z⟩ values are lower because of larger t2g-eg splittings. Future X-ray magnetic circular dichroism experiments on these 4d oxides will constitute a direct test for the ⟨Z⟩ values that we predict here, the importance of many-body t2g-eg couplings mediated by spin-orbit interactions, and the role of low-symmetry fields associated with the extended surroundings.

Assessing the performance of dispersionless and dispersion-accounting methods: helium interaction with cluster models of the TiO2(110) surface.

As a prototypical dispersion-dominated physisorption problem, we analyze here the performance of dispersionless and dispersion-accounting methodologies on the helium interaction with cluster models of the TiO2(110) surface. A special focus has been given to the dispersionless density functional dlDF and the dlDF+Das construction for the total interaction energy (K. Pernal, R. Podeswa, K. Patkowski, and K. Szalewicz, Phys. Rev. Lett. 2009, 109, 263201), where Das is an effective interatomic pairwise functional form for the dispersion. Likewise, the performance of symmetry-adapted perturbation theory (SAPT) method is evaluated, where the interacting monomers are described by density functional theory (DFT) with the dlDF, PBE, and PBE0 functionals. Our benchmarks include CCSD(T)-F12b calculations and comparative analysis on the nuclear bound states supported by the He-cluster potentials. Moreover, intra- and intermonomer correlation contributions to the physisorption interaction are analyzed through the method of increments (H. Stoll, J. Chem. Phys. 1992, 97, 8449) at the CCSD(T) level of theory. This method is further applied in conjunction with a partitioning of the Hartree-Fock interaction energy to estimate individual interaction energy components, comparing them with those obtained using the different SAPT(DFT) approaches. The cluster size evolution of dispersionless and dispersion-accounting energy components is then discussed, revealing the reduced role of the dispersionless interaction and intramonomer correlation when the extended nature of the surface is better accounted for. On the contrary, both post-Hartree-Fock and SAPT(DFT) results clearly demonstrate the high-transferability character of the effective pairwise dispersion interaction whatever the cluster model is. Our contribution also illustrates how the method of increments can be used as a valuable tool not only to achieve the accuracy of CCSD(T) calculations using large cluster models but also to evaluate the performance of SAPT(DFT) methods for the physically well-defined contributions to the total interaction energy. Overall, our work indicates the excellent performance of a dlDF+Das approach in which the parameters are optimized using the smallest cluster model of the target surface to treat van der Waals adsorbate-surface interactions.

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.

Comment on "Going beyond the frozen core approximation: development of coordinate-dependent pseudopotentials and application to Na2(+)" [J. Chem. Phys. 138, 054110 (2013)].

The new coordinate-dependent pseudopotential for Na2(+) by Kahros and Schwartz [J. Chem. Phys. 138, 054110 (2013)] is assessed and compared to the pseudopotential approach by Fuentealba et al. [Chem. Phys. Lett. 89, 418 (1982)] which incorporates the coordinate-dependent core-polarization potential by Müller and Meyer [J. Chem. Phys. 80, 3311 (1984)]. In contrast to the latter approach, the one by Kahros and Schwartz does not reproduce the accurately known experimental data and∕or high level theoretical results for Na2(+). The treatment of core polarization by Kahros and Schwartz neglects the dynamic polarization of atomic cores which is much more important for Na2(+) than the static one. On the other hand, the Kahros and Schwartz method heavily overestimates frozen-core corrections at the Hartree-Fock level by compounding them with artifacts of a superposition of non-norm-conserving pseudopotentials.

The use of explicitly correlated methods on XeF6 predicts a C3v minimum with a sterically active, free valence electron pair on Xe.

Explicitly correlated CCSD(T)-F12b calculations show that the lowest energy conformer of XeF(6) is the C(3v) structure with a stereoactive lone pair. The C(3v) structure is 1.08 kcal/mol below the C(2v) structure and 1.80 kcal/mol below the O(h) structure without vibrational corrections. The C(2v) conformer is a transition state connecting the different C(3v) minima on the pseudorotation potential energy surface, and the O(h) structure is a higher-order saddle point leading to the C(2v) transition states. The calculated vibrational frequencies for the C(3v) structure best fit the experimental frequencies. The calculated heats of formation for XeF(6), -62.1 ± 1.4 kcal/mol at 0 K and -64.0 ± 1.4 kcal/mol at 298 K, are the best available values and show that there are serious issues with the experimental values. The results show that the explicitly correlated CCSD(T)-F12b method can be used to address important electronic structure issues with smaller basis sets.

Approaching the bulk limit with finite cluster calculations using local increments: the case of LiH.

Finite-cluster calculations employing high-level wavefunction-based ab initio methods and extended atomic-orbital basis sets are used to determine local energy increments for bulk LiH. It is shown that these increments can be converged with respect to cluster size and point-charge embedding so as to yield bulk cohesive energies with an accuracy of better than 1 mE(h), both at the Hartree-Fock and at correlated levels. Instrumental for the efficiency of the scheme is the introduction of non-orthogonal orbitals, at an intermediate stage.

Coupled vortex oscillations in spatially separated permalloy squares.

We experimentally study the magnetization dynamics of pairs of micron-sized permalloy squares coupled via their stray fields. The trajectories of the vortex cores in the Landau-domain patterns of the squares are mapped in real space using time-resolved scanning transmission x-ray microscopy. After excitation of one of the vortex cores with a short magnetic-field pulse, the system behaves like coupled harmonic oscillators. The coupling strength depends on the separation between the squares and the configuration of the vortex-core polarizations. Considering the excitation via a rotating in-plane magnetic field, it can be understood that only a weak response of the second vortex core is observed for equal core polarizations.

An incremental correlation approach to excited state energies based on natural transition/localized orbitals.

A new incremental approach to the computation of vertical excitation energies is presented. The method works based on the definition of a dominant occupied orbital where the excitation takes place (natural transition orbital) and by localizing the remaining occupied space. The use of a reduced two-body expansion leads to a linear number of terms to be computed. A series of benchmark calculations have been carried out on small to medium sized photoactive systems. The results compare well to the full calculations, with maximum deviations of 0.3 eV, and an average absolute deviation of about 0.08 eV. In addition, a energy decomposition analysis is made on the basis of orbital distances to the chromophore region. First results indicate that orbitals beyond a relatively small radius can be safely neglected, leading to further drastic savings in the calculations.

Magnetic antivortex-core reversal by circular-rotational spin currents.

Topological singularities occur as antivortices in ferromagnetic thin-film microstructures. Antivortices behave as two-dimensional oscillators with a gyrotropic eigenmode which can be excited resonantly by spin currents and magnetic fields. We show that the two excitation types couple in an opposing sense of rotation in the case of resonant antivortex excitation with circular-rotational currents. If the sense of rotation of the current coincides with the intrinsic sense of gyration of the antivortex, the coupling to the Oersted fields is suppressed and only the spin-torque contribution locks into the gyrotropic eigenmode. We report on the experimental observation of purely spin-torque induced antivortex-core reversal. The dynamic response of an isolated antivortex is imaged by time-resolved scanning transmission x-ray microscopy on its genuine time and length scale.