Effective Heisenberg Exchange Research Articles

A potential all-electronic route to the charge-density-wave phase in monolayer vanadium diselenide

The transition metal dichalcogenides offer significant promise for the tunable realisation and application of correlated electronic phases. However, tuning their properties requires an understanding of the physical mechanisms underlying their experimentally observed ordered phases, and in particular the extent to which lattice vibrations are a necessary ingredient. Here we present a potential mechanism for charge-density-wave formation in monolayers of vanadium diselenide in which the key role at low energies is played by a combination of electron–electron interactions and nesting. There is a competition between superconducting and density-wave fluctuations as sections of the Fermi surface are tuned to perfect nesting. This competition leads to charge-density-wave order when the effective Heisenberg exchange interaction is comparable to the effective Coulomb repulsion. When all effective interactions are purely repulsive, it results instead in d-wave superconductivity. We discuss the possible role of lattice vibrations in enhancing the effective Heisenberg exchange during the earlier stages of the renormalisation group flow.

Strong phonon-magnon coupling of an O/Fe(001) surface

Using density functional calculations, we elucidate the interaction between magnons and phonons on Fe(001) and O/Fe(001) surfaces. The effective Heisenberg exchange parameters between neighbor sites ( J i ) were derived by fitting the ab initio spin spiral dispersion relation to a classical Heisenberg model. In bulk Fe, J 5 b has a larger amplitude than J 2 b - J 4 b . Surface magnons were softer on the Fe(001) surface than in bulk, but were strengthened on the O/Fe(001) surface through strong interactions between the O and Fe atoms. The four calculated high-energy phonon modes of O/Fe(001) excellently agreed with the experimental measurements. The J 1 in O/Fe(001) decreased significantly with increasing phonon amplitude. Phonon-magnon coupling occurred more easily on O/Fe(001) than on Fe(001). The softening of the magnon on the O/Fe(001) with phonon amplitude was attributed to the reduced amplitude of longitudinal excitations. Magnetic moment of the Fe atom of the second layer (Fe2) was especially sensitive to phonon amplitude, regardless of the motion direction of the Fe2 atoms.

Enhanced nematic fluctuations near an antiferromagnetic Mott insulator and possible application to high-Tc cuprates

Motivated by the widespread experimental observations of nematicity in strongly underdoped cuprate superconductors, we investigate the possibility of enhanced nematic fluctuations in the vicinity of a Mott insulator that displays Néel-type antiferromagnetic order. By performing a strong-coupling expansion of an effective model that contains both Cu-d and O-p orbitals on the square lattice, we demonstrate that quadrupolar fluctuations in the p-orbitals inevitably generate a biquadratic coupling between the spins of the d-orbitals. The key point revealed by our classical Monte-Carlo simulations and large-N calculations is that the biquadratic term favors local stripe-like magnetic fluctuations, which result in an enhanced nematic susceptibility that onsets at a temperature scale determined by the effective Heisenberg exchange J. We discuss the impact of this type of nematic order on the magnetic spectrum and outline possible implications on our understanding of nematicity in the cuprates.

Dzyaloshinsky-Moriya interaction in -(Zn, Cr)S(111) surface: First principle calculations

According to density functional theory calculations, we elucidate the atomic and electronic structure of -(Zn, Cr)S(111) surface. The magnetic interaction between Cr atoms is via S atoms close to the Cr layer. This interaction is shown by the analysis of spin charge contour plot and partial density of states (DOS) of each atom. The DOSs of other S atoms are non magnetic and have no magnetic exchange with the Cr layer. E(q) and E(-q) are the dispersions between energy E and wave vector q of spin spiral in the opposite directions. They are calculated with generalized Bloch equations and all the magnetic moments of Cr atoms are arranged in the plane perpendicular to the -(Zn, Cr)S(111) film. The differences between E(q) and E(-q) are caused by the interface of -(Zn, Cr)S(111), where the symmetry of space perpendicular to the film is broken. Effective Heisenberg exchange interaction (HBI) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors (Ji and di) are derived by well fitting the ab initio spin spiral dispersion E(q) to HBI with DMI model and E(q)-E(-q) to DMI model, respectively. The J2 plays a major role with a large negative value of -9.04 meV. The J1 is about 2/5 of J2, and J3 is about 1/4 of J2 with positive value. The DMI d1 is -0.53 meV, and d2 is 0.07 meV. With these HBI parameters, E(0) is the largest one at which -(Zn, Cr)S(111) has no ferromagnetic interface. The E(q) has its lowest energy with the q at M=b1/2 in the first Brillouin zone. Hence, -(Zn, Cr)S(111) is an M-type antiferromagnetic (AFM) material. In this type of AFM configuration, magnetic moments of Cr atom in a line along b2 are parallel to each other, and antiparallel to the magnetic moments in adjacent lines. The E(q) at K=b1/2+ b2/2 is almost as large as that at point. The value of DMI parameter d1 is about 1/5 of that on Co/Pt3 interface and 1/2 of Co/graphene. However, it is a negative number, which shows the clockwise chirality. The -(Zn, Cr)S(111) interface has obvious DMI, and skyrmion may be formed at this transition-metal/semiconductor (TM/S) interface. It is a good option to search for DMI in different kinds of TM/S heterojunctions. The material that combines the advantage of heterojunction, and DMI may have new magnetic phenomenon, which is usefulfor the magnetic storage. This paper enriches the research on DMI.

First principle study of weak Dzyaloshinsky-Moriya interaction in Co/BN surface

Based on density functional theory calculations, we elucidate the atomic and electronic structures of Co atom of hexgonal BN (Co/h-BN). The interaction between magnetic moments of Co atoms is realized through Co-N_-B_ grid, which is indicated by the analysis of spin charge contour plot and partial density of states of each atom, where and denote the site of B or N atom close to and away from Co atom, respectively. Then the dispersion relations E(q) and E(-q) (q denotes the direction vector of spin spiral) between energy and wave vector of spin spiral in the opposite directions are calculated with generalized Bloch equations. In the incommensurate spin spiral calculations, all the magnetic moments of Co atom are arranged in the same plane that is perpendicular to the Co/h-BN film. The difference between E(q) and E(-q) is caused by the interface of Co/h-BN, where the symmetry of space perpendicular to the film is broken. Moreover, the effective Heisenberg exchange interaction (HBI) and Dzyaloshinsky-Moriya interaction (DMI) parameters between different neighbors (Ji and di) are derived by well fitting the ab initio magnon dispersion E(q) to HBI with DMI model and E(q)-E(-q) to DMI model, respectively. The J1 has a negative value and plays a major role, J3 is one order of magnitude smaller than J1, and other parameters are close to zero. Hence, Co/h-BN is triangular antiferromagnetic material with the q at k point in the first Brillouin zone. However, the spin spiral with the q at M point is only 2 meV larger than the basic state with the only negative J1 and smaller positive J2. The DMI is not shown in this interface with d1 and d2 close to zero. Based on the non DMI character and its stability in air, h-BN can be capped on other DMI interfaces. The reason that the DMI in Co/h-BN is much smaller than in Co/Gra is much larger height between Co and h-BN. It is 0.192 nm for h-BN but it is 0.156 nm for Co/Gra. We may reduce the height to enhance the DMI by other ways, such as adding electrical and magnetic fields in the future.

Volume dependence of magnetic properties in [formula omitted] (Y=Ti-Ni) Heusler alloys: A first-principles study

The magnetic properties tuning and volume dependence in the series of quaternary full Heusler alloys with formula Co2Cr1−xYxGa (Y=Ti, V, Mn, Fe, Co, Ni) were studied with a detailed first-principles exploration. We employ the density functional KKR method with the coherent potential approximation, estimating effective Heisenberg exchange constants via the magnetic force theorem together with mean-field Curie temperature (TC) and magnetic moment for compositions in the whole concentration range. The volumetric dependency of these magnetic properties is studied, particularly the pressure derivatives of TC at equilibrium. Our ternary alloy calculations show good agreement with local-density and generalized gradient approximations in the literature. The quaternary alloys show a wide range of tunable magnetic properties, where magnetic moments range from 0.8 to 4.9μB, TC from 130K to 1250K, and dTC/dV values range from −7 to +6.3KÅ−3.

Dynamical exchange interaction from time-dependent spin density functional theory

We report on {\it ab initio} time-dependent spin dynamics simulations for a two-center magnetic molecular complex based on time-dependent non-collinear spin density functional theory. In particular, we discuss how the dynamical behavior of the {\it ab initio} spin-density in the time-domain can be mapped onto a model Hamiltonian based on the classical Heisenberg spin-spin interaction $J\vcr{S}_1\cdot \vcr{S}_2$. By analyzing individual localized-spin trajectories, extracted from the spin-density evolution, we demonstrate a novel method for evaluating the effective Heisenberg exchange coupling constant, $J$, from first principles simulations. We find that $J$, extracted in such a new dynamical way, agrees quantitatively to that calculated by the standard density functional theory broken-symmetry scheme.

Effective Heisenberg exchange integrals of diluted magnetic semiconductors determined within realistic multi-band tight-binding models

Diluted magnetic semiconductors (DMS) like Ga1−x Mn x As are described by a realistic tight-binding model (TBM) for the (valence) bands of GaAs, by a Zener (J-)term modeling the coupling of the localized Mn-spins to the spins of the valence band electrons, and by an additional potential scattering (V-) term due to the Mn-impurities. We calculate the effective (Heisenberg) exchange interaction between two Mn-moments mediated by the valence electrons. The influence of the number of bands taken into account (6-band or 8-band TBM) and of the potential (impurity) scattering V-term is investigated. We find that for realistic values of the parameters the indirect exchange integrals show a long-range, oscillating (RKKY-like) behavior, if the V-term is neglected, probably leading to spin-glass behavior rather than magnetic order. But by including a V-term of a realistic magnitude the exchange couplings become short ranged and mainly positive allowing for the possibility of ferromagnetic order. Our results are in good agreement with available results of ab initio treatments.

Performance of the tau-dependent functionals in predicting the magnetic coupling of ionic antiferromagnetic insulators.

The performance of some kinetic energy density (tau) dependent functionals in predicting the effective Heisenberg exchange has been explored using the KNiF3 and K2NiF4 insulators as case examples. Our results show that this new generation of functionals represents an important improvement with respect to the current local and gradient corrected functionals yielding a semi-quantitative description of the antiferromagnetic coupling without the need of hybrid approaches thus avoiding the calculation of exact, Hartree-Fock exchange. This feature opens a wide field of application especially in solid state.

Temperature-dependent electronic structure and magnetic stability of thin ferromagnetic films

We study correlation effects and temperature dependencies in the electronic structure of thin ferromagnetic local-moment films. In a first step the Kondo-lattice model is investigated as a candidate for a proper representation of local-moment ferromagnets. Magnetic and electronic key quantities as the Curie temperature and the quasiparticle density of states are derived with previously tested many-body procedures. It is shown that the magnetic properties can be interpreted exclusively in terms of the temperature-dependent electronic quasiparticle structure. An extended RKKY theory leads to effective Heisenberg exchange integrals, which turn out to be functionals of the conduction electron self-energy, getting therewith a remarkable temperature and band occupation dependence. In a second step, the model studies are combined with tight-binding-LMTO bandstructure calculations in order to get for real ferromagnetic films quasiparticle densities of states and quasiparticle bandstructures. The proposed method avoids the double-counting of relevant interactions and takes into account the correct symmetry of the atomic orbitals. Special results are given for thin ferromagnetic EuO (1 0 0) films. The Curie temperature T C of the EuO film turns out to be strongly thickness-dependent, starting from a very low value (≃15 K) for the monolayer and reaching the bulk value at about 30 layers. For a 20-layer film we predict the existence of a surface state, the temperature behaviour of which can lead to a surface halfmetal–insulator transition.

Nature of the Magnetic Interaction in Organic Radical Crystals. 5. Magnetic Interaction in Mixed Radical Ion Crystals

The nature and magnitude of the spin exchange interaction within the half-filled band of 1-D stacks of mixed radical ion crystals (MRIC) consisting of two hydrocarbons H1 and H2 with different ionization potentials and electron affinities have been investigated theoretically. In a fully reduced or oxidized 1-D crystal, each elementary unit is an anion radical or a cation radical: (H1 ...H2)•- - - or - - (H1 ...H2)•+ - -. In contrast to organic radical cation (anion) crystals which consist of identical polycyclic hydrocarbons −(Hδ···Hδ)•+− or −(Hδ···Hδ)•-− with a metalic or semiconducting ground state, the ground state of some classes of MRICs is a magnetic one. The band theory of magnetic interaction in many electron π-systems is applied to calculate the different contributions of the effective Heisenberg exchange integral.

Magnetic exchange interaction between π-electron radicals adsorbed on α-boron-nitride surfaces

The magnetic interactions between organic π-radicals adsorbed on 1D and 2D α-boron-nitride (α-BN) crystals are investigated theoretically. As in the case of analogous systems with graphite surfaces [N. Tyutyulkov, F. Dietz, K. Müllen, Chem. Phys. 255 (2000) 223], an intramolecular exchange interaction between the π-electrons within a narrow half-filled band occurs, with the main component from the Coulomb (Hund) exchange. Compared to graphite the values of the effective Heisenberg exchange integral are smaller in the case of α-BN. The energy spectrum, and the magnetic and thermodynamic characteristics of Ising models consisting of methyl radicals adsorbed on 1D and 2D α-BN surfaces are discussed based on the analytically solved equations.

Structure and properties of non-classical polymers.: Part XII: A new family of high-spin polycyclic 1-D systems

The magnetic properties of a new class of 1-D high-spin polycyclic aromatic polymers were studied theoretically. It was found that the electrons within the half-filled band of non-bonding MOs (NBMO) are ferromagnetically coupled. The direct (Coulomb) exchange determined by the topology of the polymers is the main component of the effective Heisenberg exchange integral. A new concept for viewing high-spin π-systems in terms of point defects (vacancies) in quasi 1-D graphites and polycyclic hydrocarbons was developed. The NBMOs can be considered as surface or Tamm states.

Structures and Ground State Spin Multiplicities of Poly-Radical-Ions of Homo- and Heteronuclear Dendralenes

The ground state spin multiplicity and the geometry of the reductively and oxidatively doped homo- and heteronuclear dendralenes were investigated by means of ab initio calculations. The results were compared with the calculated effective Heisenberg exchange integral for doped infinite dendralenes.

Polaron effects in the nearly atomic limit of the Hubbard model

The Hubbard Model of electron correlation effects in solids is unified with Holstein's molecular crystal model for small polarons as a first step in studying electron-phonon coupling in π-bonded organic solids. Some implications of the electron-lattice coupling on both the single particle excitation spectrum and the effective Heisenberg exchange energy are discussed.

Two-Electron Heisenberg Exchange Interaction between Neighboring Atoms

The method of Nesbet is applied to the model investigated by Freeman and Watson to describe the Heisenberg exchange interaction between neighboring transition metal atoms. Pairs of atomic Hartree-Fock $d$ orbitals obtained from calculations on ${\mathrm{Co}}^{++}$ and Co are used; the nuclei and the remaining electrons are represented by two point charges at the nearest neighbor internuclear separation of Co atoms in the metal. Nuclear charges, $Z$, of one and ten are used to examine the effect of changing the assumed potential. The effective Heisenberg exchange parameter is large and negative for all values of the parameters used here. The present results agree in sign with the earlier results of Freeman and Watson, who used the Heitler-London method without the ionic configuration, but differ by an order of magnitude for $Z=1$, and are somewhat closer for $Z=10$. The discrepancy is probably due to this omission, since the present formalism takes all configurations into account for a system described by two basis orbitals. Since the observed exchange parameter for metallic cobalt is positive (ferromagnetic), and since previous investigations suggest that additional effects (due to including the remaining electrons of the ions) will not substantially alter the computed value, it appears that the ferromagnetic coupling must be explained by some mechanism other than the two-atom Heisenberg exchange interaction between localized $d$ orbitals.