Magnetism in systems with reduced dimensionality and chemical disorder: The local environment effects

We study influence of the local chemical environment, the so-called local environment effects, on the electronic structure and properties of magnetic systems with reduced dimensionality and chemical disorder, and show that they play a crucial role in a vicinity of magnetic instability. As a model, we consider Fe–Ni Invar. We present results obtained from ab initio calculations of the electronic structure, magnetic moments, and exchange interactions in random fcc Fe–Ni alloy, for a single monolayer alloy film on a Cu (0 0 1) substrate as well as in the bulk. We analyze the difference between the film and the bulk magnetization, which is found to be most pronounced for dilute alloys. We also analyze a sensitivity of the individual magnetic moments and effective exchange parameters to the local chemical environment of the atoms.     

Exchange Interactions at Surfaces of Fe, Co, and Gd

Magnetic exchange interactions at low-index surfaces of bcc iron, hcp cobalt, and hcp gadolinium are studied using ab initio electronic structure calculations. Interlayer exchange couplings derived from total-energy differences are enhanced at the surfaces over their bulk counterparts. This trend is in contrast to a surface reduction of on-site exchange parameters formulated within a classical Heisenberg model. A particular attention is paid to the sensitivity of exchange interactions at a Gd(0001) surface to relaxation of interlayer distances. The calculated results do not provide support for recently observed surface enhancement of the Curie temperature of the Gd metal.     

Lattice simulations for light nuclei: Chiral effective field theory at leading order

We discuss lattice simulations of light nuclei at leading order in the chiral effective field theory. Using lattice pion fields and auxiliary fields, we include the physics of instantaneous one-pion exchange and the leading-order S-wave contact interactions. We also consider higher-derivative contact interactions which adjust the S-wave scattering amplitude at higher momenta. By construction our lattice path integral is positive definite in the limit of exact Wigner SU(4) symmetry for any even number of nucleons. This SU(4) positivity and the approximate SU(4) symmetry of the low-energy interactions play an important role in suppressing sign and phase oscillations in Monte Carlo simulations. We assess the computational scaling of the lattice algorithm for light nuclei with up to eight nucleons and analyze in detail calculations of the deuteron, triton, and helium-4.     

Exact matrix elements for general two-body central-force interactions,expressed as sums of products

ABSTRACT

In a manner similar to but distinct from concurrent tensor efforts in electronic structure, it is shown that the Laplace transform can serve as a generator for a sum-of-products (SOP) form that allows one to write essentially any function of distance between two particles (i.e. any central force potential) as an exact two-body matrix. In particular, exact expressions for the Coulomb, Yukawa and long-range Ewald two-body operators are evaluated in a band-limited (Sinc function) basis. The resultant exact, full-basis, SOP representations for these interaction potentials – acting in conjunction with an external harmonic confining field – are validated via comparison with energy eigenstate solutions obtained via an independent calculation based on separation of variables. The new two-body matrix representations may have substantial impact in any of the many disciplines in which pair-wise central force interactions are relevant – especially, electronic structure and dynamics.     

Mixed spin ladders with exotic ground states

We study the “mixed spin” isotropic ladder system having S=1 spins on one leg and S=1/2 spins on the other, with general-type exchange interactions between spins on neighboring rungs. A set of model Hamiltonians with exact ground states in the form of a certain matrix product wave function is obtained. We show that sufficiently strong frustration can lead to exotic singlet ground states with infinite (exponential) degeneracy. We also list a couple of rather simple models with nontrivial ground states, including a model with only bilinear exchange. Received: 2 December 1997 / Accepted: 28 January 1998     

Electronic quasiparticle structure of ferromagnetic bcc iron

We investigate the influence of electron correlations on the temperature-dependence of the electronic structure of ferromagnetic bcc iron by use of a manybody evaluation of a generalized model of magnetism. The single-particle part of the model-Hamiltonian is taken from an LDA band structure calculation. The manybody interactions are described by only two parameters, an intraband Coulomb interactionU and an interband exchangeJ. WithU=1.8 eV andJ=0.2 eV the self-consistent model solution yields aT=0 moment of about 2.04 µ_B and a Curie-temperature of 1044K. Details of the magnetic behaviour of Fe can be traced back to a striking temperature variation of the quasiparticle density of states. A novel explanation for the experimentally-observed non-collapsing exchange splitting is demonstrated in terms of the temperature-dependent spectral density for wave-vectors near the -point. Typical differences in the magnetic behaviour of Fe and Ni are worked out.     

Electronic, magnetic, and vibrational properties of the molecular magnet Mn4 monomer and dimer

A new type of the single-molecule magnet [Mn₄O₃Cl₄(O₂CEt)₃(py)₃] forms dimers. Recent magnetic hysteresis measurements on this single-molecular magnet revealed interesting phenomena: an absence of quantum tunneling at zero magnetic field and tunneling before magnetic field reversal. This is attributed to a significant antiferromagnetic exchange interaction between different monomers. To investigate this system, we calculate the electronic structure, magnetic properties, intramolecular and intermolecular exchange interactions using density-functional theory within the generalized-gradient approximation. Our calculations agree with experiment. We find that the calculated threefold symmetric structure is vibrationally stable. We also calculate vibrational infrared absorption and Raman scattering intensities for the monomer which can be tested experimentally.     

Oxygen vacancy induced ferromagnetism in rutile TiO2–x

First‐principles LDA + U calculations have been performed to study the effects of oxygen vacancies (V_O) on the electronic structure and magnetism in undoped rutile TiO_2–x . Instead of treated as an adjustive parameter, the value of U was determined by constrained‐density‐functional calculations. The calculated electronic structure reveals that the valence electrons released by V_O would occupy mainly the neighboring Ti:3d orbital which then becomes spin‐polarized due to intra‐atomic exchange interaction, thereby giving rise to the half‐metallic ferromagnetism. The magnetization induced by V_O in rutile TiO_2–x is almost proportional to the V_O concentration (x) for x > 0.0625, and becomes 0 for x ≤ 0.0417. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of all-order density-functional perturbation theory, using the second order and the strong-correlation limit

To boost the accuracy of electronic structure calculations, the exchange-correlation energy may be constructed from the Kohn-Sham orbitals. A formally exact construction is the density-functional perturbation series, which appears to diverge for many real systems. We predict the radius of convergence and resum this series, using only exact exchange and second-order correlation plus explicit density functionals for the strong-interaction limit. Our new correlation functional, along with exact exchange, predicts atomization energies with competitive accuracy and without the usual error cancellation.     

The Girardeau's fermion-boson procedure in the light of the composite-boson many-body theory

We reconsider the procedure developed for atoms a few decades ago by Girardeau, in the light of the composite-boson many-body theory we recently proposed. The Girardeau's procedure makes use of a so called “unitary Fock-Tani operator” which in an exact way transforms one composite bound atom into one bosonic “ideal” atom. When used to transform the Hamiltonian of interacting atoms, this operator generates an extremely complex set of effective scatterings between ideal bosonic atoms and free fermions which makes the transformed Hamiltonian impossible to write explicitly, in this way forcing to some truncation. The scatterings restricted to the ideal-atom subspace are shown to read rather simply in terms of the two elementary scatterings of the composite-boson many-body theory, namely, the energy-like direct interaction scatterings — which describe fermion interactions without fermion exchange — and the dimensionless Pauli scatterings — which describe fermion exchanges without fermion interaction. We here show that, due to a fundamental difference in the scalar products of elementary and composite bosons, the Hamiltonian expectation value for N ground state atoms obtained by staying in the ideal-atom subspace and working with boson operators only, differ from the exact ones even for N = 2 and a mapping to the ideal-atom subspace performed, as advocated, from the fully antisymmetrical atomic state, i.e., the state which obeys the so-called “subsidiary condition”. This shows that, within this Girardeau's procedure too, we cannot completely forget the underlying fermionic components of the particles if we want to correctly describe their interactions.     

Magnetic interactions in strongly correlated systems: Spin and orbital contributions

We present a technique to map an electronic model with local interactions (a generalized multi-orbital Hubbard model) onto an effective model of interacting classical spins, by requiring that the thermodynamic potentials associated to spin rotations in the two systems are equivalent up to second order in the rotation angles, when the electronic system is in a symmetry-broken phase. This allows to determine the parameters of relativistic and non-relativistic magnetic interactions in the effective spin model in terms of equilibrium Green’s functions of the electronic model. The Hamiltonian of the electronic system includes, in addition to the non-relativistic part, relativistic single-particle terms such as the Zeeman coupling to an external magnetic field, spin–orbit coupling, and arbitrary magnetic anisotropies; the orbital degrees of freedom of the electrons are explicitly taken into account. We determine the complete relativistic exchange tensors, accounting for anisotropic exchange, Dzyaloshinskii–Moriya interactions, as well as additional non-diagonal symmetric terms (which may include dipole–dipole interaction). The expressions of all these magnetic interactions are determined in a unified framework, including previously disregarded features such as the vertices of two-particle Green’s functions and non-local self-energies. We do not assume any smallness in spin–orbit coupling, so our treatment is in this sense exact. Finally, we show how to distinguish and address separately the spin, orbital and spin–orbital contributions to magnetism, providing expressions that can be computed within a tight-binding Dynamical Mean Field Theory.     

An exact formulation of the Blume-Emery-Griffiths model on a two-fold Cayley tree model

A two-fold Cayley tree graph with fully q-coordinated sites is constructed and the spin-1 Ising Blume-Emery-Griffiths model on the constructed graph is solved exactly using the exact recursion equations for the coordination number q = 3. The exact phase diagrams in (kT/J, K/J ) and (kT/J, D/J) planes are obtained for various values of constants D/J and K/J, respectively, and the tricritical behavior is found. It is observed that when the negative biquadratic exchange (K) and the positive crystal-field (D) interactions are large enough, the tricritical point disappears in the (kT/J, K/J) plane. On the other hand, the system always exhibits a tricritical behavior in the phase diagram of (kT/J, D/J) plane. Received 8 June 2001 and Received in final form 28 September 2001     

First-principle study on electronic structure and magnetic properties of molecular-based antiferromagnet: (2-amino-5-chloropyridinium)2CuBr4

The electronic structure and magnetic properties of the (2-amino-5-chloropyridinium)₂CuBr₄ compound were studied using the full potential augmented plane wave plus local-orbitals method (FP-APW+lo) within density functional theory. The Cu atoms are the magnetic centers, magnetic moments originate mainly from the Cu 3d and Br 4p states, leading to a total magnetic moment of 1.00 μ_B per molecule. There is an important hybridization between the Cu 3d and Br 4p states, which causes the magnetic interactions between the Cu centers to pass through the Br p-orbitals near the Cu atoms. According to the self-consistent total energies, it was found that in the ground state there exist antiferromagnetic interactions for both intraplanar and interplanar magnetic exchange, but the latter is much weaker than the former.     

Electronic structure and magnetic coupling in CaV<Subscript>2</Subscript>O<Subscript>5</Subscript>: spin dimer versus spin ladder

The electronic structure and magnetic exchange interactions of the ladder vanadate CaV₂O₅ have been studied by ab initio electronic structure calculations based on density functional theory (DFT). Geometry optimization and electronic structure calculations are performed using spin-polarized generalized gradient approximation (GGA) exchange-correlation functionals for four possible spin-ordered states. The experimentally observed insulating behavior has been reproduced successfully in the framework of the band theory by considering the magnetic ordering. Calculated results reveal that the true magnetic ground state of CaV₂O₅ is the antiferromagnetic (AFM) state with AFM exchange interactions both inside the rungs and along the ladder legs. Calculated exchange parameters indicate that the ladder structural vanadate CaV₂O₅ should be described as weakly coupled dimer system rather than as spin ladder compound. The AFM interactions inside the dimer are crucial to the insulating ground state and magnetic characteristics of CaV₂O₅.     

Practical failures from the inclusion of exact exchange: how much exact exchange is appropriate?

The influence of exact exchange incorporated into exchange—correlation functionals on the predictions of relative energies, structures, electronic states, and vibrational spectra is examined numerically. Failures of widely used hybrid exchange—correlation functionals due to either the physical unacceptability of including exact exchange or an unbalanced mixing of exact exchange are considered. One set of examples involves tetraatomic chalcogen clusters and charge transfer complexes between diatomic chalcogens and diatomic oxygen. Poor energetic predictions from Hartree-Fock rule against the inclusion of exact exchange into the exchange—correlation functionals for these systems with significant left—right electron correlation effects. The energies of the conformers of [10]annulene are considered from an unusual viewpoint, namely, the empirical adjustment of the admixture of exact exchange to match the predictions of very high level theoretical methods. For this annulene with insignificant left-right electron correlation effects, a greater (50%) percentage of exact exchange should be included. The relationship of symmetry breaking to the inclusion of exact exchange is examined for seven linear radicals, OXO (X = B, Al, Ga, In, TI). AIOS, and OAIS. exchange—correlation functionals generate symmetry adapted solutions at the expense of an unusual ordering of the Kohn-Sham orbitals, which can cause uncharacteristic electronic states, incorrect vibrational spectra, and poorer predictions of energetics. These effects are greater when exact exchange is included. In all the examples considered, the appropriate focus for a detailed discussion of molecular properties involves consideration of the effects of exact exchange.     

Compensation temperatures,magnetic susceptibilities and phase diagrams of a mixed ferrimagnetic ternary system on the Bethe lattice

Compensation behaviors, magnetic susceptibilities and the phase diagrams of the ternary system of the type ABC consisting of Ising spins σ = 1/2, S = 3/2 and m = 5/2 in the presence of a single-ion anisotropy are studied on the Bethe lattice within the framework of the exact recursion relations. Both ferromagnetic and antiferromagnetic exchange interactions are considered. The exact expressions for sublattice magnetizations and magnetic susceptibilities are obtained, and then thermal behaviors of the sublattice magnetizations, total magnetization, magnetic sublattice susceptibilities and total susceptibility are investigated. We find that the system only undergoes a second order phase transition for the different and same bilinear nearest-neighbor exchange interaction parameters, but displays compensation behaviors for only different bilinear interaction parameters. We also present the phase diagrams for the different and same bilinear nearest-neighbor exchange interaction parameters. A comparison is made with the other ternary system of the type ABC consisting of different spin values.     

Investigations of “soft-landed” Cd surface atoms via nuclear methods: hyperfine-field sign determination

Using refined preparation techniques, cadmium guest atoms have been positioned at different sites on the surfaces of nickel crystals. The magnetic hyperfine fields and the electric field gradients at the Cd nuclei were measured by time-dependent perturbed angular correlation (TDPAC) spectroscopy of the emitted gamma radiations. By measuring the combined interactions, electric field gradients and magnetic hyperfine fields can be unambiguously attributed to each surface site. The signs of the magnetic hyperfine fields are determined by applying an external magnetic field and choosing the appropriate γ-ray detector configuration. The measured fields correlate with the number of neighbouring host atoms. Band structure calculations confirm this finding and predict magnetic fields for various sp elements from the band structure of the s-like conduction electrons. The quadrupolar interactions are manifestations of the balance in the occupation of the guest p-sublevels. These results provide new information on the structure and formation of electronic configurations of sp elements in different local environments and will contribute to understanding electronic effects on surfaces.     

Exchange interactions,spin waves,and transition temperatures in itinerant magnets

This contribution reviews an ab initio two-step procedure to determine exchange interactions, spin-wave spectra, and thermodynamic properties of itinerant magnets. In the first step, the self-consistent electronic structure of a system is calculated for a collinear spin structure at zero temperature. In the second step, parameters of an effective classical Heisenberg Hamiltonian are determined using the magnetic force theorem and the one-electron Green functions. The Heisenberg Hamiltonian and methods of statistical physics are employed in subsequent evaluation of magnon dispersion laws, spin-wave stiffness constants, and Curie/Néel temperatures. The applicability of the developed scheme is illustrated by selected properties of various systems such as transition and rare-earth metals, disordered alloys including diluted magnetic semiconductors, ultrathin films, and surfaces. A comparison to other ab initio approaches is presented as well.     

Defect-induced ferromagnetism in fullerenes

Based on the ab initio electronic structure calculations the picture of ferromagnetism in polimerized C₆₀ is proposed which seems to explain the whole set of controversial experimental data. We have demonstrated that, in contrast with cubic fullerene, in rhombohedral C₆₀ the segregation of iron atoms is energetically unfavorable which is a strong argument in favor of intrinsic character of carbon ferromagnetism which can be caused by vacancies with unpaired magnetic electrons. It is shown that: (i) energy formation of the vacancies in the rhombohedral phase of C₆₀ is essentially smaller than in the cubic phase, (ii) there is a strong ferromagnetic exchange interactions between carbon cages containing the vacancies, (iii) presence of iron impurities can diminish essentially the formation energy of intrinsic defects, and (iv) the fusion of the magnetic single vacancies into nonmagnetic bivacancies is energetically favorable. The latter can explain a fragility of the ferromagnetism.     

“W = 0” pairing in Cu-O clusters and in the plane

The Cu-O plane and the clusters that possess the same C_4v symmetry around a Cu ion have 2-hole eigenstates of the kinetic energy with vanishing on-site repulsion (W=0 pairs). Cluster calculations by exact diagonalisation show that these are the quasiparticles that lead to a paired ground state, and have superconducting flux-quantisation properties. Here, we extend the theory to the full plane, and show that the W=0 quasiparticles are again the natural explanation of superconducting flux-quantisation. Moreover, by a new approach which is exact in principle, we calculate the effective interaction between two holes added to the ground state of the repulsive three-band Hubbard model. To explain how a noninteracting electron gas becomes a superconductor when switching the local Coulomb interaction, we obtain a closed-form analytic expression including the effects of all virtual transitions to 4-body intermediate states (exchange of an electron-hole pair). Our scheme is ready to include other interactions which are not considered in the Hubbard model but may be important. In the plane, the W=0 pairs have ¹ B ₂ and ¹ A ₂ symmetry. The effective interaction in these channels is attractive and leads to a Cooper-like instability of the Fermi liquid, while it is repulsive for triplet pairs. From , we derive an integral equation for the pair eigenfunction; the binding energy of the pairs is in the range of tens of meV. However, our symmetry-based method is far more general than the model. Received 18 December 1998