Calculated Exchange Parameters Research Articles

Electronic structure, magnetism, and exchange integrals in transition-metal oxides: Role of the spin polarization of the functional in DFT+ U calculations

Density functional theory augmented with Hubbard-$U$ corrections (DFT+$U$) is currently one of the widely used methods for first-principles electronic structure modeling of insulating transition metal oxides (TMOs). Since $U$ is relatively large compared to band widths, the magnetic excitations in TMOs are expected to be well described by a Heisenberg model. However, in practice the calculated exchange parameters $J_{ij}$ depend on the magnetic configuration from which they are extracted and on the functional used to compute them. In this work we investigate how the spin polarization dependence of the underlying exchange-correlation functional influences the calculated magnetic exchange constants of TMOs. We perform a systematic study of the predictions of calculations based on the local density approximation plus $U$ (LDA+$U$) and the local spin density approximation plus $U$ (LSDA+$U$) for the electronic structures, total energies and magnetic exchange interactions $J_{ij}$'s extracted from ferromagnetic (FM) and antiferromagnetic (AFM) configurations of several transition metal oxide materials. We report that, for realistic choices of Hubbard $U$ and Hund's $J$ parameters, LSDA+$U$ and LDA+$U$ calculations result in different values of the magnetic exchange constants and band gap. The dependence of the band gap on the magnetic configuration is stronger in LDA+$U$ than in LSDA+$U$ and we argue that this is the main reason why the configuration dependence of the $J_{ij}$'s is found to be systematically more pronounced in LDA+$U$ than in LSDA+$U$ calculations. We report a very good correspondence between the computed total energies and the parameterized Heisenberg model for LDA+$U$ calculations, but not for LSDA+$U$, suggesting that LDA+$U$ is a more appropriate method for estimating exchange interactions.

Microscopic origin of ferro-antiferromagnetic transition upon non-magnetic substitution in Ru2(Mn1−xVx)Ge full Heusler alloys

On the basis of first-principle simulations of interatomic magnetic exchange interactions, we show that the transition from antiferromagnetic order in Ru2MnGe to ferromagnetic order in vanadium substituted Ru2Mn1−xVxGe is due to a progressive increase of the first-nearest neighbor (NN) ferromagnetic coupling between Mn atoms. The revealed mechanism is quite unusual since commonly one would expect, and indeed it has been proposed earlier, that the transition scenario is due to the suppression of some relevant interactions by the non-magnetic substitution or chemical disorder effects. Here, using our ab-initio calculated exchange parameters and performing finite temperature Monte Carlo statistical simulations on a disordered lattice, we describe the experimental magnetic phase diagram for the full range of vanadium concentrations, including the variation of the ordering temperature and the onset of finite magnetization in the ground state. Since the observed changes in the MnMn magnetic interactions are continuous with increasing V content, we argue that there is a threshold concentration of V substitutions where the critical fluctuations associated with frustration effects on the fcc lattice could be studied experimentally.

Polar Order and Frustrated Antiferromagnetism in Perovskite Pb2MnWO6 Single Crystals.

Single crystals of the multiferroic double-perovskite Pb2MnWO6 have been synthesized and their structural, thermal, magnetic and dielectric properties studied in detail. Pure perovskite-phase formation and stoichiometric chemical composition of the as-grown crystals are confirmed by X-ray single-crystal and powder diffraction techniques as well as energy-dispersive X-ray and inductively coupled plasma mass spectrometry. Detailed structural analyses reveal that the crystals experience a structural phase transition from the cubic space group (s.g.) Fm3̅m to an orthorhombic structure in s.g. Pn21a at about 460 K. Dielectric data suggest that a ferrielectric phase transition takes place at that same temperature, in contrast to earlier results on polycrystalline samples, which reported a transition to s.g. Pnma and an antiferroelectric low-temperature phase. Magnetic susceptibility measurements indicate that a frustrated antiferromagnetic phase emerges below 8 K. Density functional theory based calculations confirm that the cationic order between Mn and W is favorable. The lowest total energy was found for an antiferromagnetically ordered state. However, analyses of the calculated exchange parameters revealed strongly competing antiferromagnetic interactions. The large distance between the magnetic atoms, together with magnetic frustration, is shown to be the main reason for the low value of the ordering temperature observed experimentally. We discuss the structure-property relationships in Pb2MnWO6 and compare these observations to reported results on related Pb2BWO6 perovskites with different B cations.

First-principles calculations of exchange interactions, spin waves, and temperature dependence of magnetization in inverse-Heusler-based spin gapless semiconductors

Employing first-principles electronic-structure calculations in conjunction with the frozen-magnon method, we calculate exchange interactions, spin-wave dispersion, and spin-wave stiffness constants in inverse-Heusler-based spin gapless semiconductor (SGS) compounds ${\text{Mn}}_{2}\text{CoAl}, {\text{Ti}}_{2}\text{MnAl}, {\text{Cr}}_{2}\text{ZnSi}, {\text{Ti}}_{2}\text{CoSi}$, and ${\text{Ti}}_{2}\text{VAs}$. We find that their magnetic behavior is similar to the half-metallic ferromagnetic full-Heusler alloys, i.e., the intersublattice exchange interactions play an essential role in the formation of the magnetic ground state and in determining the Curie temperature ${T}_{\mathrm{c}}$. All compounds, except ${\text{Ti}}_{2}\text{CoSi}$, possess a ferrimagnetic ground state. Due to the finite energy gap in one spin channel, the exchange interactions decay sharply with the distance, and hence magnetism of these SGSs can be described considering only nearest- and next-nearest-neighbor exchange interactions. The calculated spin-wave dispersion curves are typical for ferrimagnets and ferromagnets. The spin-wave stiffness constants turn out to be larger than those of the elementary $3d$ ferromagnets. Calculated exchange parameters are used as input to determine the temperature dependence of the magnetization and ${T}_{\mathrm{c}}$ of the SGSs. We find that the ${T}_{\mathrm{c}}$ of all compounds is much above the room temperature. The calculated magnetization curve for ${\text{Mn}}_{2}\text{CoAl}$ as well as the Curie temperature are in very good agreement with available experimental data. This study is expected to pave the way for a deeper understanding of the magnetic properties of the inverse-Heusler-based SGSs and enhance the interest in these materials for application in spintronic and magnetoelectronic devices.

Exchange parameters of strongly correlated materials: Extraction from spin-polarized density functional theory plus dynamical mean-field theory

In this paper we present an accurate numerical scheme for extracting interatomic exchange parameters (${J}_{ij}$) of strongly correlated systems, based on first-principles full-potential electronic structure theory. The electronic structure is modeled with the help of a full-potential linear muffin-tin orbital method. The effects of strong electron correlations are considered within the charge self-consistent density functional theory plus dynamical mean-field theory. The exchange parameters are then extracted using the magnetic force theorem; hence all the calculations are performed within a single computational framework. The method allows us to investigate how the ${J}_{ij}$ parameters are affected by dynamical electron correlations. In addition to describing the formalism and details of the implementation, we also present magnetic properties of a few commonly discussed systems, characterized by different degrees of electron localization. In bcc Fe, treated as a moderately correlated metal, we found a minor renormalization of the ${J}_{ij}$ interactions once the dynamical correlations are introduced. However, generally, if the magnetic coupling has several competing contributions from different orbitals, the redistribution of the spectral weight and changes in the exchange splitting of these states can lead to a dramatic modification of the total interaction parameter. In NiO we found that both static and dynamical mean-field results provide an adequate description of the exchange interactions, which is somewhat surprising given the fact that these two methods result in quite different electronic structures. By employing the Hubbard-I approximation for the treatment of the $4f$ states in hcp Gd we reproduce the experimentally observed multiplet structure. The calculated exchange parameters result in being rather close to the ones obtained by treating the $4f$ electrons as noninteracting core states.

Theoretical studies on polynuclear {Cu(II)5Gd(III)n} clusters (n = 4, 2): towards understanding their large magnetocaloric effect.

Density functional theory (DFT) studies on two polynuclear clusters, [Cu(II)5Gd(III)4O2(OMe)4(teaH)4(O2CC(CH3)3)2(NO3)4] (1) and [Cu5Gd2(OH)4(Br)2-(H2L)2(H3L)2(NO3)2(OH2)4] (2), have been carried out to probe the origin of the large magnetocaloric effect (MCE). The magnetic exchange interactions for 1 and 2 via multiple pathways are estimated using DFT calculations. While the calculated exchange parameters deviate from previous experimental estimates obtained by fitting the magnetic data, the DFT parameter set is found to offer a striking match to the magnetic data for both complexes, highlighting the problem of overparameterization. Magnetostructural correlations for {Cu-Gd} pairs have been developed where both the Cu-O-Gd angles and Cu-O-Gd-O dihedral angles are found to significantly influence the magnitude and sign of the exchange constants. The magnitude of the MCE has been examined as a function of the exchange interactions, and clues on how the effect can be enhanced are discussed.

Electronic and magnetic structure of a possible iron based superconductor BaFe2Se3

We present results of LDA calculations (band structure, densities of states, Fermi surfaces) for possible iron based superconductor BaFe2Se3 (Ba123) in normal (paramagnetic) phase. Results are briefly compared with similar data on prototype BaFe2As2 and (K,Cs)Fe2Se2 superconductors. Without doping this system is antiferromagnetic with T_N^{exp}~250K and rather complicated magnetic structure. Neutron diffraction experiments indicated the possibility of two possible spin structures (antiferromagnetically ordered "plaquettes" or "zigzags"), indistinguishable by neutron scattering. Using LSDA calculated exchange parameters we estimate Neel temperatures for both spin structures within the molecular field approximation and show \tau_1 ("plaquettes") spin configuration to be more favorable than \tau_2 ("zigzags").

Ab-initio calculation of effective exchange interactions, spin waves, and Curie temperature in L21- and L12-type local moment ferromagnets

Employing first-principles electronic structure calculations in conjunction with the frozen-magnon method, we study the effective exchange interactions and spin waves in local moment ferromagnets. As prototypes we have chosen three L21-type full Heusler alloys Cu2MnAl, Ni2MnSn, and Pd2MnSn, and the L12-type XPt3 compounds with X = V, Cr, and Mn. We have also included CoPt3 which is a usual ferromagnet. In all compounds due to the large spatial separation (∼4 Å) of the magnetic transition-metal atoms, the 3d states belonging to different atoms overlap weakly and as a consequence the exchange coupling is indirect, mediated by the sp electrons. Calculated effective exchange parameters are long range and show RKKY-type oscillations. The spin-wave dispersion curves are in reasonable agreement with available experimental data. Using the calculated exchange parameters, we have estimated the Curie temperatures within both the mean-field and the random-phase approximations. In local moment ferromagents deviations of the estimated Curie temperature with respect to the available experimental data occur when the ground-state electronic structure calculations overestimate the values of the spin magnetic moments as in VPt3.

Magnetic moments and exchange interaction in Sm(Co, Fe)5 from first-principles

The electronic structure, magnetization and exchange interaction in Sm(Co1−xFex)5 with x=0–1 are studied from a first-principles density functional calculation. The dependence of the magnetization on Fe content shows a 3d-like Slater–Pauling relationship in these alloys. As the Fe content x increases from 0 to 1.0, the magnetization increases from 7.8μB to 10.6μB (x=0.8) and then decreases to 10.0μB (x=1). The effective exchange interaction parameters show a peak value around x=0.6, which is ascribed to the exchange parameters between Fe and Co being larger than those for Co–Co and Fe–Fe pairs. The estimated TC from the calculated exchange parameters range between 890K and 1357K in Sm(Co1−xFex)5 using a multi-sublattices mean field model.

Magnetic Exchange Interactions in a 2D Grid-like Copper(II) Polymer with Bridging End-on Cyanato and Pyrazine Ligands: A DFT Study

The structure of a 2D grid-like copper(II) complex [Cu<TEX>$(NCO)_2$</TEX>(pyz)](pyz=pyrazine) (1) consists of 1D chains of Cu-pyz units connected by double end-on (EO) cyanato bridges. Each Cu(II) ion has a distorted octahedral coordination, completed by the four EO cyanato and two pyrazine ligands. Magnetic interactions through EO cyanato and pyrazine bridges in 1 are discussed on the basis of DFT broken-symmetry calculations at the B3LYP level. For model dicopper(II) complexes I (bridged by cyanato) and II (bridged by pyrazine), electronic structure calculations reproduce very well the experimental couplings for the S = 1/2 ferromagnetic and antiferromagnetic exchange-coupled 2D system: the calculated exchange parameters J are +1.25 <TEX>$cm^{-1}$</TEX> and -3.07 <TEX>$cm^{-1}$</TEX> for I and II, respectively. The <TEX>$\sigma$</TEX> orbital interactions between the Cu <TEX>$x^2-y^2$</TEX> magnetic orbitals and the nitrogen lone-pair orbitals of pyrazine are analyzed from the viewpoint of through-bond interaction. The energy splitting of 0.106 eV between two SOMOs indicates that the superexchange interaction should be antiferromagnetic in II. On the other hand, there are no bridging orbitals that efficiently connect the two copper(II) magnetic orbitals in I because the HOMOs of the basal-apical NCO bridge do not play a role in the formation of overlap interaction pathway. The energy separation in the pair of SOMOs of I is calculated to be very small (0.054 eV). This result is consistent with the occurrence of weakly ferromagnetic properties in I.

Electronic structure and magnetic coupling in CaV2O5: 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.

Effect of Fe partial substitution for Co on the magnetic properties of Y(Co,Fe)5 from first-principles

The structure, magnetization and exchange interaction in Y(Co1−xFex)5 with x=0 to 0.3 are studied from a first-principles density functional calculation. The cohesive energy calculations indicate that Fe prefers to occupy the 3g site and the lattice constants increase with Fe Content. The magnetization increases from 7.50 to 8.97μB with increasing x from 0 to 0.3 as the calculations show that Fe has a much larger moment (about 2.4μB) than that of Co (about 1.5μB). The exchange parameters between Fe and Co are larger than those for Co–Co and Fe–Fe pairs, and are responsible for the higher TC of Y(Co1−xFex)5. The estimated TC from the calculated exchange parameters increases from about 1065 to 1298 K with increasing x from 0 to 0.3 using a multisublattices mean-field model.

Exchange energies, Curie temperatures and magnons in Heusler compounds

Heisenberg exchange parameters for various Heusler compounds with L21 structure were calculated using the Korringa–Kohn–Rostoker method and by employing the magnetic-force theorem to calculate the total energy changes associated with a local rotation of magnetization directions. Random occupation was treated within the coherent potential approximation. Further, the Curie temperatures were calculated in the mean-field approximation and have been found to be in good agreement with the experiment. A procedure for evaluating the spin-stiffness constants for the case of multiple magnetic sublattices is given and the results were compared with measured values. Magnon dispersion curves were obtained by Fourier transforming the calculated exchange parameters.

New binuclear metal chelate complexes of copper(II) chloride and acetate with bis(hetarylhydrazones) obtained by condensation of 2,6-diformyl-4-R-phenols with 2-hydrazinoquinoline

Bis(hetarylhydrazones) synthesized for the first time were used as ligands to obtain a number of binuclear copper(II) chelates from copper acetate and chloride. The physicochemical and, first of all, magnetic properties of the resulting complexes were studied. Analysis of the calculated exchange parameters showed that they differ significantly from those obtained previously for analogous binuclear metal chelates containing the identical set of donor atoms. Possible reasons for the differences in the magnetochemical behavior of the binuclear complexes obtained are discussed.

Properties of low-lying excited manifolds inMn12acetate

Most experimental data on the single-molecule magnet Mn$_{12}$ acetate have been successfully explained by the assumption that the Mn$_{12}$ acetate has an effective ground-state spin of S=10. However, the effect of the low-lying excited manifolds caused by interactions between Mn spins has not been well understood. To investigate the features of the low-lying excited manifolds, the intramolecular exchange interactions are calculated using density-functional theory (DFT). With the calculated exchange parameters, the energy gap between the S=10 ground-state and the first excited-state manifold is calculated by diagonalization of the Heisenberg Hamiltonian. The upper limit on the energy gap is about 40.5 K which is likely to be overestimated due to incomplete treatment of the Coulomb potential within DFT. It is found that there are several S=9 low-energy excited-state manifolds above the S=10 ground-state manifold. The magnetic anisotropy barriers for the low-lying spin excitations are calculated using DFT. Based on the calculations, it is found that the anisotropy barriers for the low-lying excited manifolds are approximately the same as that for the ground-state manifold, which is applicable to other single-molecule magnets such as Mn$_4$.

Exchange interaction in theYbCrBr93−mixed dimer: The origin of a strongYb3+−Cr3+exchange anisotropy

The superexchange interaction between ${\mathrm{Yb}}^{3+}$ and ${\mathrm{Cr}}^{3+}$ ions in the mixed ${\mathrm{YbCrBr}}_{9}^{3\ensuremath{-}}$ bioctahedral face-sharing dimer is quantitatively analyzed using a modified kinetic exchange theory, which is adapted to a realistic description of the electronic structure of lanthanide ions in solids. The general procedure of the calculation of the $4f\ensuremath{-}3d$ anisotropic exchange spin Hamiltonian is presented and applied to the ${\mathrm{YbCrBr}}_{9}^{3\ensuremath{-}}$ dimer. The spin-Hamiltonian of the ${\mathrm{Yb}}^{3+}\ensuremath{-}{\mathrm{Cr}}^{3+}$ exchange interaction is found to be extremely anisotropic, ${H=J}_{z}{S}_{\mathrm{Yb}}^{z}{S}_{\mathrm{Cr}}^{z}{+J}_{\ensuremath{\perp}}{(S}_{\mathrm{Yb}}^{x}{S}_{\mathrm{Cr}}^{x}{+S}_{\mathrm{Yb}}^{y}{S}_{\mathrm{Cr}}^{y}),$ with the antiferromagnetic ${J}_{z}$ and ferromagnetic ${J}_{\ensuremath{\perp}}$ parameters, where ${S}_{\mathrm{Yb}}^{\ensuremath{\mu}}$ and ${S}_{\mathrm{Cr}}^{\ensuremath{\mu}}$ $(\ensuremath{\mu}=x,y,z)$ are the components of the effective spin ${S}_{\mathrm{Yb}}=\frac{1}{2}$ of the ${\mathrm{Yb}}^{3+}$ ion (corresponding to the ground ${\ensuremath{\Gamma}}_{6}$ Kramers doublet) and the true spin ${S}_{\mathrm{Cr}}=\frac{3}{2}$ of the ${\mathrm{Cr}}^{3+}$ ion, respectively. The calculated exchange parameters are quite consistent with the experimental data ${(J}_{z}=\ensuremath{-}5.16{\mathrm{cm}}^{\ensuremath{-}1}$ and ${J}_{\ensuremath{\perp}}=+4.19{\mathrm{cm}}^{\ensuremath{-}1})$ at reasonable values of the $\mathrm{Yb}\ensuremath{\rightarrow}\mathrm{Cr}$ and $\mathrm{Yb}\ensuremath{\leftarrow}\mathrm{Cr}$ charge transfer energies. The contributions to the ${J}_{z}$ and ${J}_{\ensuremath{\perp}}$ exchange parameters from the individual states of the ${4f}^{12}{\ensuremath{-}3d}^{4}$ and ${4f}^{14}{\ensuremath{-}3d}^{2}$ charge transfer configurations are analyzed in detail and general regularities are established. Our results indicate that a very strong $4f\ensuremath{-}3d$ exchange anisotropy can appear even in the absence of the crystal-field anisotropy on the lanthanide ion.

Physicochemical Study of New Mono- and Binuclear Copper(II) Complexes with Sterically Hindered Acylhydrazones and Azomethines

Series of new binuclear copper(II) complexes with acylhydrazones and azomethines of substituted derivatives of salicylaldehyde containing bulky tert-butyl substituents were synthesized. The target dimerization of the monomeric fragments of the complexes caused by the steric factors was shown to predetermine the specific features of their magnetochemical behavior. The calculated exchange parameters for the complexes based on acylhydrazones range from –110 to –138 cm–1 and those for the complexes based on azomethines lie in the interval from –400 to –500 cm–1.

Four-spin interaction as an effective interaction in high-T c copper oxides

The lowest states of an undoped copper-oxide cluster are determined numerically and fitted by a spin Hamiltonian containing a cyclic 4-spin exchange interaction. The size of this interaction is found to be about a quarter of the size of the nearest-neighbor Heisenberg exchange. The 4-spin exchange leads to a renormalization of spin-wave properties and to extra features in magnetic Raman scattering. The calculated exchange parameters are consistent with the observed spin-wave velocity.

Compatibility of the two‐site exchange model and 1H NMR relaxation rates

We demonstrate a formalism for determining whether 1H longitudinal and transverse magnetic relaxation decay curves are compatible with a model of proton exchange between two sites with inherently different relaxation rates. We apply the method to published data in which both decay curves have been fit to normalized biexponential functions, a prediction of the simplest two-site exchange model. The analysis is applied to relaxation data of adsorbed water vapor on silica gel (J.R. Zimmerman and J.A. Lasater, J. Phys. Chem. 62, 1157 (1958] and to relaxation data reported in mycelia of Botrytis cinerea Persoon and pupae of the tobacco cutworm (M. Yoshida and K. Nose, Agric. Biol. Chem. 51, 3399 (1987]. Exchange parameters are calculated form these data sets and the compatibility of the two-site exchange model with the data is discussed for each case. The sensitivity of the calculated exchange parameters to errors in the bioexponential fitting parameters is treated in some detail.

Two-site exchange revisited: a new method for extracting exchange parameters in biological systems

A new analysis is presented which links real volume fractions, relaxation rates, and intracompartmental exchange rates directly with apparent volume fractions and relaxation rates obtained from biexponential fits of transverse magnetization decay curves. The analysis differs from previous methods in that measurements from two paramagnetic doping levels are used to close the two-site exchange equations. Both the new method and one previously described by Herbst and Goldstein (HG) have been applied to paramagnetically doped whole-blood data sets. Significant differences in the calculated exchange parameters are found between the two methods. A small dependence of the intracellular relaxation rate on extracellular paramagnetic agent concentration, assumed nonexistent with the HG method, is inferred from the new analysis. The analysis was also applied to published data on perfused rat hearts, and we obtained a limited assessment of two-site exchange in this system.