Effective Heisenberg Model and Exchange Interaction for Strongly Correlated Systems.

We consider the extended Hubbard model and introduce a corresponding Heisenberg-like problem written in terms of spin operators. The derived formalism is reminiscent of Anderson's idea of the effective exchange interaction and takes into account nonlocal correlation effects. The results for the exchange interaction and spin susceptibility in the magnetic phase are expressed in terms of single-particle quantities. This fact not only can be used for realistic calculations of multiband systems but also allows us to reconsider a general description of many-body effects in the most interesting physical regimes, where the physical properties of the system are dominated by collective (bosonic) fluctuations. In the strongly spin-polarized limit, when the local magnetic moment is well defined, the exchange interaction reduces to a standard expression of the density functional theory that has been successfully used in practical calculations of magnetic properties of real materials.

Excitonic Instability and Pseudogap Formation in Nodal Line Semimetal ZrSiS.

Electron correlation effects are studied in ZrSiS using a combination of first-principles and model approaches. We show that basic electronic properties of ZrSiS can be described within a two-dimensional lattice model of two nested square lattices. A high degree of electron-hole symmetry characteristic for ZrSiS is one of the key features of this model. Having determined model parameters from first-principles calculations, we then explicitly take electron-electron interactions into account and show that, at moderately low temperatures, ZrSiS exhibits excitonic instability, leading to the formation of a pseudogap in the electronic spectrum. The results can be understood in terms of Coulomb-interaction-assisted pairing of electrons and holes reminiscent of that of an excitonic insulator. Our finding allows us to provide a physical interpretation of the unusual mass enhancement of charge carriers in ZrSiS recently observed experimentally.

Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators.

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

Erratum: The Bethe-Slater curve revisited; new insights from electronic structure theory.

A correction to this article has been published and is linked from the HTML version of this paper. The error has been fixed in the paper.

Magnetic character of holmium atom adsorbed on platinum surface.

We address a recent controversy concerning the magnetic state of holmium adatom on platinum surface. Within a combination of the density functional theory (DFT) with the exact diagonalization (ED) of Anderson impurity model, the 〈J z 〉 = 0 paramagnetic ground state |J = 8, J z = ±8〉 is found. In an external magnetic field, this state is transformed to a spin-polarized state with 〈J z 〉 ≈ 6.7. We emphasize the role of 5d-4f interorbital exchange polarization in modification of the 4f shell energy spectrum.

The Bethe-Slater curve revisited; new insights from electronic structure theory.

The Bethe-Slater (BS) curve describes the relation between the exchange coupling and interatomic distance. Based on a simple argument of orbital overlaps, it successfully predicts the transition from antiferromagnetism to ferromagnetism, when traversing the 3d series. In a previous article [Phys. Rev. Lett. 116, 217202 (2016)] we reported that the dominant nearestneighbour (NN) interaction for 3d metals in the bcc structure indeed follows the BS curve, but the trends through the series showed a richer underlying physics than was initially assumed. The orbital decomposition of the inter-site exchange couplings revealed that various orbitals contribute to the exchange interactions in a highly non-trivial and sometimes competitive way. In this communication we perform a deeper analysis by comparing 3d metals in the bcc and fcc structures. We find that there is no coupling between the E g orbitals of one atom and T 2g orbitals of its NNs, for both cubic phases. We demonstrate that these couplings are forbidden by symmetry and formulate a general rule allowing to predict when a similar situation is going to happen. In γ-Fe, as in α-Fe, we find a strong competition in the symmetry-resolved orbital contributions and analyse the differences between the high-spin and low-spin solutions.

Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.

By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.

Racah materials: role of atomic multiplets in intermediate valence systems.

We address the long-standing mystery of the nonmagnetic insulating state of the intermediate valence compound SmB6. Within a combination of the local density approximation (LDA) and an exact diagonalization (ED) of an effective discrete Anderson impurity model, the intermediate valence ground state with the f-shell occupation 〈n4f〉 = 5.6 is found for the Sm atom in SmB6. This ground state is a singlet, and the first excited triplet state ~3 meV higher in the energy. SmB6 is a narrow band insulator already in LDA, with the direct band gap of ~10 meV. The electron correlations increase the band gap which now becomes indirect. Thus, the many-body effects are relevant to form the indirect band gap, crucial for the idea of "topological Kondo insulator" in SmB6. Also, an actinide analog PuB6 is considered, and the intermediate valence singlet ground state is found for the Pu atom. We propose that [Sm, Pu]B6 belong to a new class of the intermediate valence materials with the multi-orbital "Kondo-like" singlet ground-state. Crucial role of complex spin-orbital f( n)-f ( n+1) multiplet structure differently hybridized with ligand states in such Racah materials is discussed.

Tuning emergent magnetism in a Hund's impurity.

The recently proposed concept of a Hund's metal--a metal in which electron correlations are driven by Hund's rule coupling-can be used to explain the exotic magnetic and electronic behaviour of strongly correlated electron systems of multi-orbital metallic materials. Tuning the abundance of parameters that determine these materials is, however, experimentally challenging. Here, we show that the basic constituent of a Hund's metal--a Hund's impurity--can be realized using a single iron atom adsorbed on a platinum surface, a system that comprises a magnetic moment in the presence of strong charge fluctuations. The magnetic properties can be controlled by using the tip of a scanning tunnelling microscope to change the binding site and degree of hydrogenation of the 3d transition-metal atom. We are able to experimentally explore a regime of four almost degenerate energy scales (Zeeman energy, temperature, Kondo temperature and magnetic anisotropy) and probe the magnetic excitations with the microscope tip. The regime of our Hund's impurity can be tuned from an emergent magnetic moment to a multi-orbital Kondo state, and the system could be used to test predictions of advanced many-body theories for non-Fermi liquids in quantum magnets or unconventional superconductors.

Correlation-Driven Charge and Spin Fluctuations in LaCoO_{3}.

The spin transition in LaCoO_{3} has been investigated using density-functional theory in combination with dynamical mean-field theory employing continuous time quantum Monte Carlo and exact diagonalization impurity solvers. Calculations on the experimental rhombohedral atomic structure with two Co sites per unit cell show that an independent treatment of the Co atoms results in a ground state with strong charge fluctuations induced by electronic correlations. Each atom shows a contribution from either a d^{5} or a d^{7} state in addition to the main d^{6} state. These states play a relevant role in the spin transition which can be understood as a low spin-high spin (LS-HS) transition with significant contributions (~10%) to the LS and HS states of d^{5} and d^{7} states, respectively. We report spectra as well as optical conductivity data for all cases. A thermodynamic analysis reveals a significant kinetic energy gain through introduction of charge fluctuations, which in addition to the potential energy reduction lowers the total energy of the system.

Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion.

We study the charge-density dynamics within the two-dimensional extended Hubbard model in the presence of long-range Coulomb interaction across the metal-insulator transition point. To take into account strong correlations we start from self-consistent extended dynamical mean-field theory and include nonlocal dynamical vertex corrections through a ladder approximation to the polarization operator. This is necessary to fulfill charge conservation and to describe plasmons in the correlated state. The calculated plasmon spectra are qualitatively different from those in the random-phase approximation: they exhibit a spectral density transfer and a renormalized dispersion with enhanced deviation from the canonical √q behavior. Both features are reminiscent of interaction induced changes found in single-electron spectra of strongly correlated systems.

Magnetic anisotropy energy and effective exchange interactions in Co intercalated graphene on Ir(1 1 1).

The electronic structure, magnetic moments, effective exchange interaction parameter and the magnetic anisotropy energy of [monolayer Co]/Ir(1 1 1) and Co intercalated graphene on Ir(1 1 1) are studied making use of the first-principles density functional theory calculations. A large positive magnetic anisotropy of 1.24 meV/Co is found for [monolayer Co]/Ir(1 1 1), and a high Curie temperature of 1190 K is estimated. These findings show the Co/Ir(1 1 1) system is a promising candidate for perpendicular ultra-high density magnetic recording applications. The magnetic moments, exchange interactions and the magnetic anisotropy are strongly affected by graphene. Reduction of the magnetic anisotropy and the Curie temperature are found for graphene/[monolayer Co]/Ir(1 1 1). It is shown that for graphene placed in the hollow-hexagonal positions over the monolayer Co, the magnetic anisotropy remains positive, while for the placements with one of the C atoms on the top of Co it becomes negative. These findings may be important for assessing the use of graphene for magnetic recording and magnetoelectronic applications.

Electronic correlations determine the phase stability of iron up to the melting temperature.

We present theoretical results on the high-temperature phase stability and phonon spectra of paramagnetic bcc iron which explicitly take into account many-body effects. Several peculiarities, including a pronounced softening of the [110] transverse (T1) mode and a dynamical instability of the bcc lattice in harmonic approximation are identified. We relate these features to the α-to-γ and γ-to-δ phase transformations in iron. The high-temperature bcc phase is found to be highly anharmonic and appears to be stabilized by the lattice entropy.

Optimal Hubbard models for materials with nonlocal Coulomb interactions: graphene, silicene, and benzene.

To understand how nonlocal Coulomb interactions affect the phase diagram of correlated electron materials, we report on a method to approximate a correlated lattice model with nonlocal interactions by an effective Hubbard model with on-site interactions U(*) only. The effective model is defined by the Peierls-Feynman-Bogoliubov variational principle. We find that the local part of the interaction U is reduced according to U(*)=U-V[over ¯], where V[over ¯] is a weighted average of nonlocal interactions. For graphene, silicene, and benzene we show that the nonlocal Coulomb interaction can decrease the effective local interaction by more than a factor of 2 in a wide doping range.

Excitation spectra of transition-metal atoms on the Ag (100) surface controlled by Hund's exchange.

We report photoemission experiments revealing the valence electron spectral function of Mn, Fe, Co, and Ni atoms on the Ag (100) surface. The series of spectra shows splittings of higher energy features which decrease with the filling of the 3d shell and a highly nonmonotonic evolution of spectral weight near the Fermi edge. First principles calculations demonstrate that two manifestations of Hund's exchange J are responsible for this evolution. First, there is a monotonic reduction of the effective exchange splittings with increasing filling of the 3d shell. Second, the amount of charge fluctuations and, thus, the weight of quasiparticle peaks at the Fermi level varies nonmonotonically through this 3d series due to a distinct occupancy dependence of effective charging energies U(eff).

Adatoms and clusters of 3d transition metals on graphene: electronic and magnetic configurations.

We investigate the electronic and magnetic properties of single Fe, Co, and Ni atoms and clusters on monolayer graphene (MLG) on SiC(0001) by means of scanning tunneling microscopy (STM), x-ray absorption spectroscopy, x-ray magnetic circular dichroism (XMCD), and ab initio calculations. STM reveals different adsorption sites for Ni and Co adatoms. XMCD proves Fe and Co adatoms to be paramagnetic and to exhibit an out-of-plane easy axis in agreement with theory. In contrast, we experimentally find a nonmagnetic ground state for Ni monomers while an increasing cluster size leads to sizeable magnetic moments. These observations are well reproduced by our calculations and reveal the importance of hybridization effects and intra-atomic charge transfer for the properties of adatoms and clusters on MLG.

Enhanced screening in chemically functionalized graphene.

Resonant scatterers such as hydrogen adatoms can strongly enhance the low-energy density of states in graphene. Here, we study the impact of these impurities on electronic screening. We find a two-faced behavior: Kubo formula calculations reveal an increased dielectric function ε upon creation of midgap states but no metallic divergence of the static ε at small momentum transfer q→0. This bad metal behavior manifests also in the dynamic polarization function and can be directly measured by means of electron energy loss spectroscopy. A new length scale l(c) beyond which screening is suppressed emerges, which we identify with the Anderson localization length.

Local gating of an Ir(111) surface resonance by graphene islands.

The influence of graphene islands on the electronic structure of the Ir(111) surface is investigated. Scanning tunneling spectroscopy (STS) indicates the presence of a two-dimensional electron gas with a binding energy of -160 meV and an effective mass of -0.18me underneath single-layer graphene on the Ir(111) surface. Density functional calculations reveal that the STS features are predominantly due to a holelike surface resonance of the Ir(111) substrate. Nanometer-sized graphene islands act as local gates, which shift and confine the surface resonance.

In-plane magnetic anisotropy of Fe atoms on Bi2Se3(111).

The robustness of the gapless topological surface state hosted by a 3D topological insulator against perturbations of magnetic origin has been the focus of recent investigations. We present a comprehensive study of the magnetic properties of Fe impurities on the prototypical 3D topological insulator Bi(2)Se(3) using local low-temperature scanning tunneling spectroscopy and integral x-ray magnetic circular dichroism techniques. Single Fe adatoms on the Bi(2)Se(3) surface, in the coverage range ≈ 1% of a monolayer, are heavily relaxed into the surface and exhibit a magnetic easy axis within the surface plane, contrary to what was assumed in recent investigations on the supposed opening of a gap. Using ab initio approaches, we demonstrate that an in-plane easy axis arises from the combination of the crystal field and dynamic hybridization effects.

Strong-coupling d-wave superconductivity in PuCoGa5 probed by point-contact spectroscopy.

Superconductivity is due to an attractive interaction between electrons that, below a critical temperature, drives them to form Cooper pairs and to condense into a ground state separated by an energy gap from the unpaired states. In the simplest cases, the pairing is mediated by lattice vibrations and the wavefunction of the pairs is isotropic. Less conventional pairing mechanisms can favour more exotic symmetries of the Cooper pairs. Here, we report on point-contact spectroscopy measurements in PuCoGa(5), a moderate heavy-fermion superconductor with a record high critical temperature T(c)=18.5 K. The results prove that the wavefunction of the paired electrons has a d-wave symmetry, with four lobes and nodes, and show that the pairing is likely to be mediated by spin fluctuations. Electronic structure calculations, which take into account the full structure of the f-orbital multiplets of Pu, provide a hint of the possible origin of these fluctuations.