Orbital Polarization Correction Research Articles

Electron Correlation Enhances Orbital Polarization at a Ferromagnetic Metal/Insulator Interface: Depth-Resolved X-ray Magnetic Circular Dichroism and First-Principles Study

The Fe(CoB)/MgO interface is vital to spintronics as it exhibits the tunneling magnetoresistance (TMR) effect and interfacial perpendicular magnetic anisotropy (PMA) simultaneously. To further enhance TMR and PMA for the development of high-density magnetoresistive random access memory, it is essential to clarify the behavior of Fe atoms interfaced with MgO. This study reveals that the spin and orbital magnetic moments of Fe are enhanced at the Fe/MgO interface. The enhancement in the orbital magnetic moment is much more significant than that predicted by the standard density functional theory. Theoretical calculations based on the orbital polarization correction reproduce this enhancement, the origin of which is attributed to the electron–electron correlation resulting from electron localization at the Fe/MgO interface. The present findings highlight the importance of electron–electron correlation at ferromagnet/oxide interfaces, which has often been disregarded in spintronics.

Giant Magnetoelectric Coupling in Multiferroic PbTi1-x V x O3 from Density Functional Calculations.

Giant magnetoelectric coupling is a very rare phenomenon that has gained much attention in the past few decades due to fundamental interest as well as practical applications. Here, we have successfully achieved giant magnetoelectric coupling in PbTi1–xVxO3 (x = 0–1) using a series of generalized gradient-corrected GGA (generalized gradient approximation), including on-site Coulomb repulsion (U)-corrected spin-polarized calculations based on accurate density functional theory. Our total energy calculations show that PbTi1–xVxO3 stabilizes in C-type antiferromagnetic ground state for x > 0.123. With the substitution of V into PbTiO3, the tetragonal distortion is highly enhanced accompanied by a linear increase in polarization. In addition, our band structure analysis shows that for lower x values, the tendency to form two-dimensional magnetism of PbTi1–xVxO3 decreases. The orbital magnetic polarization was calculated with self-consistent field method by including orbital polarization correction in the calculation as well as from the computed X-ray magnetic dichroism spectra. A nonmagnetic metallic ground state is observed for the paraelectric phase for V concentration (x) = 1 competing with a volume change of 10% showing a large magnetovolume effect. Our orbital-projected density of states as well as orbital ordering analysis suggest that the orbital ordering plays a major role in the magnetic-to-nonmagnetic transition when going from ferroelectric to paraelectric phase. The calculated magnetic anisotropic energy shows that the direction [110] is the easy axis of magnetization for x = 1 composition. The partial polarization analysis shows that the Ti/V–O hybridization majorly contributes to the total electrical polarization. The present study adds a new series of compounds to the magnetoelectric family with rarely existing giant coupling between electric- and magnetic-order parameters. These results show that such kind of materials can be used for novel practical applications where one can change the magnetic properties drastically (magnetic to nonmagnetic, as shown here) with external electric field and vice versa.

Spin and orbital magnetism in phthalocyanine functionalized with 3d transition metals: A relativistic density functional theory study

The structural, magnetic, and electronic properties of 3d transition metal phthalocyanines, TMPc (TM = Sc-Ni, Cu), were studied by a full potential local orbital method in the framework of relativistic density functional theory. Binding energies, charge transfers, spin and orbital magnetic moments, and magnetic anisotropy energies were determined. Spin-orbit coupling in full relativistic regime together with orbital polarization correction to the exchange-correlation functional added a notable orbital contribution to magnetic moments of the individual 3d transition metals. In the presence of orbital polarization correction, significant in-plane orbital magnetic moments of 1.38 μB and 1.03 μB were found for vanadium atom in VPc and cobalt atom in CoPc, respectively. Besides, VPc showed planar magnetic anisotropy with 51.5 meV energy gain. Our calculations revealed that FePc has an out-of-plane easy axis.

Effect of Coulomb repulsion on spin and orbital magnetism of cobalt–benzene complex: A relativistic density functional study

We have demonstrated electronic configurations and magnetic properties of single Co adatom on benzene (Bz) molecule in the framework of relativistic density functional theory. A sequence of fixed spin moment (FSM) calculations were carried out with and without Coulomb repulsion (U). We have investigated that varying the strength of Coulomb repulsion results to different equilibrium positions for the Co adatom on benzene molecule. It was shown that inclusion of the on-site Coulomb repulsion in the Co 3d orbitals affects significantly the geometry of Co–Bz complex. We also found two stable low-spin and high-spin multiplicities for the complex. The nature of the high-spin configuration was explained according to the Hubbard electron–electron correlation in 3d shell of the Co adatom. Our FSM results indicate that the high-spin state is a global minimum in the presence of Hubbard parameter U. The relativistic spin–orbit coupling and using orbital polarization correction induce considerable orbital magnetism in both low and high spin states of the Co–Bz complex. We have also calculated magnetic anisotropy energies for two spin states and we found out that an out-of-plane magnetic orientation of Co adatom is more favorable in the low spin state whereas the Coulomb repulsion (U = 2 eV and U = 4 eV) predicts an in-plane magnetic orientation for Co adatom. Our findings can be implicitly taken into account for the extended system of added single Co atom on graphene.

Electronic structures and magnetic properties of 3d magnetic atoms adsorbed on olympicene molecule: A density functional theory study

The adsorption characteristics of transition metal (TM) adatoms on olympicene, a graphene-like molecule consisting of five rings of which four are benzene-like rings, are analyzed by means of first-principles calculations. The electronic structures and magnetic properties of 3d transition metals on olympicene were investigated in the framework of generalized-gradient approximation using relativistic density functional theory. Our calculations were based on full-potential local orbital (FPLO) method. Stable structure and total energies were obtained. Relaxed TM@Olympicene molecules, unlike the pure organic olympicene, were partially buckled. Binding energy calculations showed high stability for Ni@Olympicene whereas Mn did not bind to olympicene surface. Electronic charge transfers were consistent with Pauling electronegativities. The related HOMO-LUMO gaps decreased with respect to pure olympicene. Our calculated total and TM spin magnetic moments indicated that TM@Olympicene were strongly magnetized. Orbital polarization correction (OPC) were also used in order to get an upper estimation for orbital magnetic moment of all 3d atoms. Fe@Olympicene shows highest orbital moment of 0.18 μB. The Atoms in Molecules (AIM) approach was used to analyze the nature of TMC bonds in TM@Olympicene complexes. The results show the TMC bonds have a degree of covalency in their interactions.

Correlation effects and orbital magnetism of Co clusters

Recent experiments on isolated Co clusters have shown huge orbital magnetic moments in comparison with their bulk and surface counterparts. These clusters hence provide the unique possibility to study the evolution of the orbital magnetic moment with respect to the cluster size and how competing interactions contribute to the quenching of orbital magnetism. We investigate here different theoretical methods to calculate the spin and orbital moments of Co clusters, and assess the performances of the methods in comparison with experiments. It is shown that density functional theory in conventional local density or generalized gradient approximations, or even with a hybrid functional, severely underestimates the orbital moment. As natural extensions/corrections we considered the orbital polarization correction, the LDA+U approximation as well as the LDA+DMFT method. Our theory shows that of the considered methods, only the LDA+DMFT method provides orbital moments in agreement with experiment, thus emphasizing the importance of dynamic correlations effects for determining fundamental magnetic properties of magnets in the nano-size regime.

Relativistic first-principles study on spin and orbital magnetism of mattagamite (CoTe2)

We have demonstrated electronic and magnetic properties of CoTe2 compound in the framework of relativistic density functional theory using generalized gradient approximation (GGA). The spin and orbital magnetic moments of Co and Te atoms were obtained using full-potential local orbitals band structure scheme. We have found a partially quenched orbital moment of 0.096μB for Co atom in the local spin density approximation. In order to improve the intrinsic deficiency of local density approximation for describing orbital magnetism, an orbital polarization correction was applied to CoTe2 and a significant orbital moment of 0.153μB was found for Co atom in this compound.

Electronic structure and Fermi surface of paramagnetic and antiferromagnetic UPt2Si2

We report density functional theory-based calculations of the electronic structure and Fermi surface properties of the intermetallic uranium compound UPt${}_{2}$Si${}_{2}$, which orders antiferromagnetically at ${T}_{N}=32$ K with a total magnetic moment of 2${\ensuremath{\mu}}_{B}$/U-atom and exhibits a moderate mass enhancement in the specific-heat coefficient. Our investigation is carried out using relativistic, full-potential band-structure methods within the framework of the local spin density approximation (LSDA), the LSDA with orbital polarization correction (LSDA+OPC), and the LSDA supplemented with an additional Hubbard $U$ (LSDA+$U$). We find that the LSDA+OPC scheme predicts the total magnetic moment in best agreement with experiment; from this we infer that the $5f$ electrons in UPt${}_{2}$Si${}_{2}$ are orbitally polarized, mostly itinerant, and exhibit only a slight tendency toward localization. Our total energy calculations predict UPt${}_{2}$Si${}_{2}$ to form in the CaBe${}_{2}$Si${}_{2}$ ($P4/nmm$) structure, in contrast to URu${}_{2}$Si${}_{2}$ (ThCr${}_{2}$Si${}_{2}$: $I4/mmm$). The theoretical Fermi surfaces are also studied for the nonmagnetic and antiferromagnetic phases with the employed computational schemes and are found to be quasi-two-dimensional. At the antiferromagnetic transition, the Fermi surface is found to become more two-dimensional with small regions of gapping.

X-ray photoemission spectrum, electronic structure, and magnetism of UCu 2Si 2

The room temperature X-ray photoemission spectrum of the ferromagnetic compound UCu 2Si 2 ( T C = 100 K) was measured using an Al K α source. Related theoretical spectra were computed from densities of electronic states obtained in the local density approximation (LDA), the generalized gradient approximation (GGA), and using the GGA + U method. The calculated spectrum is in a good agreement with the experimental one. The spin polarized calculations based on the GGA + U approach as well as GGA/LSDA with orbital polarization (OP) corrections taken into account provide values of the total magnetic moment in reasonable agreement with the experimental values ranging between 1.6 and 2.0 μ B/U atom.

First principles study on spin and orbital magnetism of 3d transition metal monatomicnanowires (Mn, Fe and Co)

We have demonstrated the electronic structure and magnetic properties of 3d transitionmetal nanowires (Mn, Fe and Co) in the framework of relativistic density functionaltheory. The equilibrium bond lengths were optimized using the generalized gradientapproximation. In a full relativistic regime individual spin and orbital moments inducedfrom spin polarization via spin–orbit coupling were calculated. In order to get an upperestimate for orbital moments, we used an orbital polarization correction to ourexchange–correlation functional. We found that the orbital magnetic moments of Fe and Colinear chains are strongly enhanced in the presence of an orbital polarization correction. Wehave calculated the exchange coupling parameters between two nearest-neighbormagnetic atoms according to a Heisenberg-like model in the presence of the orbitalpolarization correction. We found that the Co and Fe nanowires behave like aferromagnetic linear chain whereas a Mn monatomic nanowire remains antiferromagnetic.

First principles study on spin and orbital magnetism in CuFeSb and CuCoSb alloys with C1 b structure

In this work the effect of spin–orbit coupling and orbital polarization (OP) corrections on the spin and orbital magnetism of two half-Heusler alloys (CuFeSb and CuCoSb) is investigated by means of local spin density calculations. It is demonstrated that OP corrections predict large orbital moments for Fe and Co individual atoms in the considered compounds. It is found that the Heusler alloys with C1 b structure are potential candidates to show large orbital magnetism.

Electronic structure and Fermi surface ofUNZ(Z=Seand Te) byab initiocalculations

The electronic structures of ferromagnetic (FM) UNTe and its nonmagnetically ordered (NMO) isostructural (tetragonal $P4/nmm$) and isoelectronic counterpart, UNSe, have been calculated from first principles in the framework of the fully relativistic and full-potential local-orbital band-structure code within local-spin density approximation (LSDA) including also an orbital polarization correction by Eriksson, Brooks, and Johansson (OPB). The results predict that both ternaries have a covalently metallic character and solely uranium atoms, located in (001) planes, form a metallic bond due to the $\text{U}\text{ }5f\text{\ensuremath{-}}6d$ electrons. The $\text{U}\text{ }5f$ electrons contribute also to a covalent bond with the ligand N and Te or Se atoms and they reveal a dual character, i.e., partly localized and itinerant. Contrary to UNSe, UNTe is a collinear FM with the magnetic moment alignment along the $c$ axis, as observed experimentally in the past and now is well reproduced by the $\text{LSDA}+\text{OPB}$ calculations. In NMO states of both systems, band pseudogaps are opening merely $\ensuremath{\sim}0.25\text{ }\text{eV}$ below the Fermi level, which cause an instability of the metallic state under small perturbations leading to a semiconducting behavior. The two-band Fermi surfaces (FSs) of both compounds (in NMO state) have similar quasi-two-dimensional (Q2D) properties with nesting vectors along the [100] direction. In turn, UNTe in the FM state possesses three-band FS with also Q2D properties and nesting features along the [100] and [110] directions, being important, e.g., in arising such collective phenomena as superconductivity.

Ensemble interpretation ofL(S)DA+U

We propose an ensemble interpretation of the $\text{L}(\text{S})\text{DA}+U$ functional aiming at the construction of a well-defined rigorous scheme as a reference point for further investigations of the functional. An explicit ensemble state, which realizes the conventional $\text{L}(\text{S})\text{DA}+U$ interaction term proportional to the product of the orbital-occupation numbers, is presented. It cannot, however, represent the correct interaction in the general case as it produces spurious self-interaction. We propose to consider the interaction term as resulting from a variational problem and present a method for its solution. As a functional of orbital occupations the interaction term results in piecewise constant corrections to the orbital potentials. The double-counting term is treated as the value of the interaction term for a spherically symmetric atomic configuration. The resulting expression is related to the so-called atomic limit for the double-counting term. It completely cancels the isotropic part (corresponding to the parameter $U$ of the Hubbard model) of the interaction term, so that only the anisotropic part responsible for the so-called orbital polarization correction remains.

Electronic structure and Fermi surface of strongly ferromagneticU2N2Z-type(Z=Sb,Te,Bi)compounds from first principles

The electronic structures of the uranium ternaries of the ${\text{U}}_{2}{\text{N}}_{2}Z$-type $(Z=\text{Sb},\text{Te},\text{Bi})$, crystallizing in the tetragonal $I4/mmm$ structure and having among uranium systems relatively high values of both their ferromagnetic (FM) transition temperatures and ordered magnetic moments (mms), have been investigated ab initio. They were calculated employing the local-spin density-functional theory with different versions of the orbital polarization correction (OPC) applied within the fully relativistic and full potential local-orbital band-structure code. The obtained results predict all these materials to be metallic both in the ferromagnetically ordered and nonmagnetically ordered (NMO) states. However, the bottoms of their conduction bands in the NMO states occur merely about 0.3 eV below the Fermi level, ${\text{E}}_{\text{F}}$, and a pronounced gap in ${\text{U}}_{2}{\text{N}}_{2}\text{Te}$ or pseudogaps in the two remaining compounds are opening just below these bands, which makes such a metallic state unstable. The considerable reduction in these gap or pseudogaps in the FM states cause a stabilization of a metallic behavior. A covalently metallic bonding character of these ternaries has been obtained in all calculations. It appeared that the only uranium atoms create predominantly metallic bonding due to a fairly strong hybridization between the U $5f$ and U $6d$ electrons. The U $5f$ electrons contributing also to the covalent bonding have somewhat dual character, i.e., partly localized and itinerant. Contrary to the Sb- and Bi-based ternaries ordered along the $c$ axis, as deduced from previous neutron powder diffraction studies, ${\text{U}}_{2}{\text{N}}_{2}\text{Te}$ has a canted FM structure with its mms tilted from the $c$ axis by about $70\ifmmode^\circ\else\textdegree\fi{}$. This fact has also been revealed by the present theoretical results. These data also point to the fact that the telluride, unlike the two other compounds, exhibits an almost half-metallic behavior. For all three ternaries, using the OPXC version of OPC the computed mms are in accord with the published experimental data. In turn, the Fermi surfaces of investigated ternaries have quasi-two-dimensional properties and quite unique nesting features along directions of their easy magnetization axes.

Transition metal dimers as potential molecular magnets: A challenge to computational chemistry

Dimers are the smallest chemical objects that show magnetic anisotropy. We focus on 3d and 4d transition metal dimers that have magnetic ground states in most cases. Some of these magnetic dimers have a considerable barrier against re-orientation of their magnetization, the so-called magnetic anisotropy energy, MAE. The height of this barrier is important for technological applications, as it determines, e.g., the stability of information stored in magnetic memory devices. It can be estimated by means of relativistic density functional calculations. Our approach is based on a full-potential local-orbital method (FPLO) in a four-component Dirac-Kohn-Sham implementation. Orbital polarization corrections to the local density approximation are employed. They are discussed in the broader context of orbital dependent density functionals. Ground state properties (spin multiplicity, bond length, harmonic vibrational frequency, spin- and orbital magnetic moment, and MAE) of the 3d and 4d transition metal dimers are evaluated and compared with available experimental and theoretical data. We find exceptionally high values of MAE, close to 0.2 eV, for four particular dimers: Fe(2), Co(2), Ni(2), and Rh(2).

Spin and orbital magnetism of FeBr2: a density functional theory study

The electronic and magnetic properties ofFeBr2 have been studied in the framework of the local spin-density approximation (LSDA).In order to improve the intrinsic deficiency of the LSDA in describing orbitalmagnetism, two different orbital polarization corrections have been applied to Feions. The spin and orbital magnetic moments on the Fe and Br sites have beenevaluated using the fully relativistic version of the full-potential local orbitalsminimum basis method and the full-potential linearized augmented plane-wave+ local orbitals method. We found a partially quenched orbital moment on the Fe ion and asmall spin moment on the p states of the Br ion.

Spin and orbital magnetism in full Heusler alloys: A density functional theory study ofCo2YZ(Y=Mn,Fe;Z=Al,Si,Ga,Ge)

The effect of spin-orbit coupling and orbital polarization (OP) corrections on the spin and orbital magnetism of full Heusler alloys is investigated by means of local spin-density calculations. It is demonstrated that OP corrections are needed to explain the experimental orbital moments ${M}_{l}$. Model calculations employing one ligand field parameter yield the correct order of magnitude of ${M}_{l}$, but do not account for its quantitative composition dependence. Spin-orbit coupling reduces the degree of spin polarization of the density of states at Fermi level by a few percent. We provide arguments that ${\mathrm{Co}}_{2}\mathrm{Mn}\mathrm{Ga}$ and the ${\mathrm{Co}}_{2}YZ$ compounds with $Y=\mathrm{Fe}$ might not be half metals as suggested by recent experiments for $Z=\mathrm{Si}$.

Spin and orbital magnetism of Au3Co: Density functional calculations

AbstractThe metastable L12 compound Au3Co has been considered as a model for high Co impurity concentration in gold. The spin and orbital moments of this compound have been calculated in the framework of local spin density approximation (LSDA) with and without orbital polarization corrections, using the relativistic version of the full‐potential local orbital minimum basis code. We also calculated the magnetocrystalline anisotropy energy. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

LSDA+U Calculations of UIrAl and UPtAl

Ternary uranium compounds UPtAl and UIrAl both crystallize in the layered ZrNiAl structure. Despite of the same structure and the fact that Pt and Ir are neighbors in periodic table, these compounds display rather different magnetic properties. By electronic structure calculations in the framework of density-functional theory (DFT) with LSDA+U exchange-correlation functional, we reproduced uranium magnetic moments and improved the agreement between calculated equilibrium volume and experiment for both compounds in comparison to existing calculations based on relativistic LSDA with or without orbital-polarization corrections.

Symmetry and magnetism ofUFe5Al7

We report symmetry analysis and first-principles density-functional-theory (DFT) calculations of the magnetic structure in ${\mathrm{UFe}}_{5}{\mathrm{Al}}_{7}.$ Two results can be considered as most significant. First, we show that the magnetic structure of ${\mathrm{UFe}}_{5}{\mathrm{Al}}_{7}$ is noncollinear. This is an important modification of the magnetic phase diagram suggested previously. The noncollinearity is a consequence of the interplay between the symmetry of the magnetic crystal and the spin-orbit coupling. Second, we show that the DFT reproduces a drastic difference in the magnetic structure of ${\mathrm{UFe}}_{5}{\mathrm{Al}}_{7}$ and ${\mathrm{UFe}}_{4}{\mathrm{Al}}_{8}$ compounds. This difference appears mainly as a result of a strong variation of the angle between the crystallographic b axis and the $8f$ Fe moments under the influence of the replacement of one of the Al atoms by the Fe atom. The influence of the orbital polarization correction is discussed.