Noncollinear Spin Density Functional Theory Research Articles

Erratum: Constructing semilocal approximations for noncollinear spin density functional theory featuring exchange-correlation torques [Phys. Rev. B 107 , 165111 (2023)

Erratum: Constructing semilocal approximations for noncollinear spin density functional theory featuring exchange-correlation torques [Phys. Rev. B <b>107</b> , 165111 (2023)

Magnetic interaction induced splitting of bands in hexagonal RMnO3 (R = Lu, Y, and Sc) compounds

In this work, calculations using non-collinear spin density functional theory were performed to study the electronic band structures for different antiferromagnetic orders in hexagonal RMnO3 (R = Lu, Y, and Sc) compounds. These are an important class of multifunctional materials with interesting properties for various applications. By comparing the band structure of different magnetic configurations, it is observed that some of them exhibit band splitting that can be attributed to ferromagnetic interplane coupling. The energy splitting is significantly larger (331 meV) for the ScMnO3 compound, which probably has a higher interplane magnetic interaction. In addition, we report that the spin–orbit coupling also induces a splitting of bands in some regions of the Brillouin zone for those magnetic configurations with a weak magnetic moment along the hexagonal c-axis. These findings offer an intriguing insight into the topological characteristics of hexagonal manganites’ band structure, which was previously unexplored in existing literature. This discovery opens avenues for future investigations in this field.

Constructing semilocal approximations for noncollinear spin density functional theory featuring exchange-correlation torques

We present a semilocal exchange-correlation energy functional for noncollinear spin density functional theory based on short-range expansions of the spin-resolved exchange hole and the two-body density matrix. Our functional is explicitly derived for noncollinear magnetism, is U(1) and SU(2) gauge invariant, and gives rise to nonvanishing exchange-correlation torques. Testing the functional for frustrated antiferromagnetic chromium clusters, the exchange part is shown to perform favorably compared with the far more expensive Slater and optimized effective potentials, and a delicate interplay between exchange and correlation torques is uncovered.

Low-rank approximations for accelerating plane-wave hybrid functional calculations in unrestricted and noncollinear spin density functional theory.

The adaptively compressed exchange (ACE) operator combined with interpolative separable density fitting (ISDF) decomposition has been utilized to accelerate plane-wave hybrid functional calculations for restricted Kohn-Sham density functional theory (DFT), but the neglect of spin degree of freedom has limited its application in the exploration of systems where the spin property of the electron is critical. Herein, we derive the ACE-ISDF formulation for hybrid functional calculations in both unrestricted and noncollinear spin DFT with plane waves and periodic boundary conditions. We proposed an improved ISDF algorithm for the sum of Kohn-Sham orbital pairs to further reduce the computational cost for the spin-noncollinear case. Numerical results demonstrate that these improved ACE-ISDF low-rank approximations can not only significantly reduce the computational time by two orders of magnitude compared with conventional plane-wave hybrid functional calculations but also lead to a good convergence behavior when a moderate rank parameter is set, even for complex periodic magnetic systems. By using these ACE-ISDF approximations, we investigate the electronic and magnetic properties of two-dimensional periodic ferromagnetic semiconductors consisting of triangular zigzag graphene quantum dots and transition metal atoms. Our computational results showcase that hybrid functional calculations in spin DFT can provide not only accurate electronic structures but also accurate magnetic order temperature of ferromagnetic semiconductors compared to local or semilocal functional calculations.

Photoferroic prospective of multiferroic HoMnO3 compound, evaluated on the base of the DFT study of its magnetic, electronic, and optical properties

In this work, non-collinear spin density functional theory based all-electron full-potential linearized augmented plane wave electronic structure method have been employed to study magnetic, electronic, and optical properties of multiferroic HoMnO3 compound in order to evaluate its potential to be used in photovoltaic applications. Exchange and correlation effects of the Ho 4f- and Mn 3d-electrons were treated on the base of the local spin density approximation including effective Hubbard (Ueff) correction. We concluded that the ground state magnetic structure should be described by Γ3 irreducible representation of the P63cm space group, for both the Mn and the Ho magnetic sub-lattices. The calculated indirect and direct band gaps, corresponding to the transition from the O 2p-to the Mn 3d-states, are found to be 1.25 eV and 1.4 eV, respectively, in very good agreement with the experimental findings. Calculated dielectric tensor spectra are found to be in satisfactory agreement with the experiment as well. On the base of these results, we investigated photoferroic properties of the HoMnO3 by calculating its absorption coefficient spectrum and the effective mass tensor of the photogenerated electrons and holes. By comparing results with those of isostructural LuMnO3 and the YMnO3 multiferroics, we concluded that the HoMnO3 exhibits similar photoferroic properties, a fact that classifies it as a material suitable for photovoltaic applications.

Effects of tensile strain on the electronic, optical and ferroelectric properties of a multifunctional R3c InFeO3 compound

The search for materials with appropriate ferroelectric and photovoltaic properties is an intense field of research. The main objective of these studies is to obtain efficient materials for solar cell applications. In this work, non-collinear spin density functional theory calculations are performed to describe the electronic, optical, and ferroelectric properties of a multiferroic R3c InFeO3 compound under tensile strain. Our studies reveal that under conditions of tensile strain, this material had ideal fundamental properties for photovoltaic applications. Under 9% tensile strain of the R3c InFeO3 unit cell volume (a = 5.536 Å and c = 13.808 Å), a direct energy band gap of 1.74 eV was found. With this energy band gap, the material absorbs the entire range of visible light, and for a film thickness of up to 100 nm it reaches a maximum photoconversion efficiency of 20%, a higher value than observed in some semiconductors that are used in practice. Furthermore, the effective mass of charge carriers (m*), and the exciton binding energy (Eb) are significantly decreased (m* < 0.4 m0 and Eb < 1.0 meV), which likely to lead to better charge mobility and easier separation of the electron-hole pair in the process of photoabsorption. Under this level of strain, the spontaneous electric polarization was reduced to 77.6 µC/cm2, a value that is still higher than other ferroelectric-photovoltaic materials.

The structural, magnetic and electronic properties of the ground state of the hexagonal LuMnO3 multiferroic

Non-collinear spin density functional theory calculations were employed to study structural, magnetic, and electronic properties of the hexagonal LuMnO3 compound in its ferroelectric phase. For that purpose, it was utilized full-potential linearized augmented plane wave plus local orbitals method, for the first time. The exchange and correlation effects were treated in the frame of the local spin density approximation (LSDA) including effective Hubbard (Ueff) correction. The principal objective of the work was to determine three properties of the LuMnO3 ground state: (1) the crystallographic space group (P63cm or P63), (2) the non-collinear magnetic configuration of the Mn spin moments (Γ1, Γ2, Γ3, Γ4, Γ1 + Γ2 or Γ3 + Γ4), and (3) the electronic structure. The results reveal that the P63cm structure with the Γ3 + Γ4 spin configuration (with ϕ = 80°) should be the ground state. The calculated indirect bandgap of 1.19 eV agrees well with the gap determined from optical conductivity measurements. Analysis of the details of the calculated electronic structure made it possible to interpret the origin of the most pronounced 1.7 eV peak in the optical conductivity spectrum, as well as to explain why it is registered only for the incident light polarized perpendicularly to the c-axis.

Optical properties, energy band gap and the charge carriers’ effective masses of the R3c BiFeO3 magnetoelectric compound

Calculations based on collinear and non-collinear spin density functional theory (DFT) were used to investigate the complex dielectric function spectrum, energy band gap, electronic band structure and the effective mass of the charge carriers of the R3c BiFeO3 magnetoelectric compound. Exchange and correlation electronic effects were taken into account using the local spin density approximation (LSDA), including the effective Hubbard (Ueff) correction (LSDA + Ueff). With Ueff = 6.0 eV and using the non-collinear spin DFT, the calculated complex dielectric function spectrum agrees very well with the experimental data from the literature. The optical absorption edge is estimated to be 2.2 eV, which according to the calculated electronic band structure corresponds to an indirect energy band gap. The electronic band structures also revealed that the aforementioned material has a direct band gap of 2.6 eV, which agrees with some experimental predictions. In addition, the hole and electron effective masses of the R3c BiFeO3 compound were computed. The smallest hole effective mass eigenvalue (0.38 m0) agrees with previous DFT calculations (0.67 m0). However, the smallest electron effective mass eigenvalue (0.39 m0) was one order of magnitude smaller than that reported in an earlier study (3.06 m0).

Non-collinear spin DFT study of the ground state magnetic structure, optical and electronic properties of the hexagonal LuFeO3 multiferroic

Hexagonal LuFeO3 compound is a multiferroic material whose ground state magnetic structure, band gap, and optical absorption spectra are matters of debate in the literature. In the present paper, these properties have been investigated by the employment of the calculations based on non-collinear spin density functional theory, with the exchange and correlation effects treated by local spin density approximation (LSDA) including effective Hubbard (Ueff) correction (LSDA + Ueff). It was concluded that the results with Ueff = 4.0 eV correlate to the experimental facts in the best manner. The ground state magnetic configuration is found to be Γ1 + Γ2, characterized by weak ferromagnetism along the c-axis (0.07 μB/Fe-atom). The calculated band gap is found to be 1.03 eV, supporting those experimental works which conclude that the gap value should be ∼1.1 eV. The optical absorption spectrum is computed and found to be in reasonable agreement with experimental data. Its edge (up to 5 eV) is generated by electronic transitions between the occupied and unoccupied Fe 3d- and the O 2p-states, with energy transfer occurring within the basal planes of the hexagonal crystal structure. The controversial lowest energy peak (centered between 1 and 2 eV) is generated by absorption of the light polarized perpendicularly to the hexagonal c-axis.

Implementation of non-collinear spin-constrained DFT calculations in SIESTA with a fully relativistic Hamiltonian

An accurate and efficient general method to constrain the magnetization of individual atoms or groups of atoms within a fully relativistic non-collinear spin density functional theory formalism is presented and implemented within the SIESTA code. This approach can be applied to study a variety of complex magnetic configurations and to build effective magnetic Hamiltonians for multiscaling micromagnetic simulations. As an example, the method is applied to obtain constrained magnetic states for a Fe3 structure, and for a S = 1/2 kagome layer (vanadium oxyfluoride V7O6F18). Of paramount importance in spintronics is the control and manipulation of magnetic interactions between constituent species, characterized mainly by the pair-wise magnetic exchange tensor . By constraining the atomic magnetizations of an infinite Fe linear chain, the total selfconsistent energy values are mapped to a generalized Heisenberg model, obtaining not only the diagonal terms of but also the off-diagonal contributions due to the explicit presence of the spin–orbit coupling in the formalism. The diagonal values of promote short ranged ferromagnetic alignment whilst the non-zero off-diagonal values can lead to the formation of the spiral states in the chain, as expected from theory.

Ground-state magnetic structure of hexagonal YMnO3 compound: A non-collinear spin density functional theory study

With objective to determine ground state magnetic structure of multiferroic hexagonal YMnO3 we performed systematic non-collinear spin density-functional-theory (DFT) study of six possible magnetic configurations of Mn ions, treating exchange and correlation effects by standard local-spin-density approximation (LSDA), by LSDA including Hubbard correction (LSDA+U), and taking into account the spin-orbit interaction. We found that P63 and P6´3 configurations are the most stable ones, with very small energy difference between them. This result substantiates conclusions of latest neutron-diffraction studies. Both configurations are characterized by canting of Mn spins that produces weak ferro- (P63) or anti-ferromagnetism (P6′3) along the hexagonal c-axis. The calculated Mn magnetic moments are found to be in good agreement with experiment, and electronic structure generally agrees with previous non-collinear spin DFT studies that used different basis sets and exchange and correlation functionals.

Magnetization Dynamics from Time-Dependent Noncollinear Spin Density Functional Theory Calculations.

A computational scheme, based on a time-dependent extension of noncollinear spin density functional theory, for the simultaneous simulation of charge and magnetization dynamics in molecular systems is presented. We employ a second-order Magnus propagator combined with an efficient predictor-corrector scheme that allows us to treat large molecular systems over long simulation periods. The method is benchmarked against the low-frequency dynamics of the H-He-H molecule where the magnetization dynamics can be modeled by the simple classical magnetization precession of a Heisenberg-Dirac-van Vleck Hamiltonian. Furthermore, the magnetic exchange couplings of the bimetallic complex [Cu(bpy)(H2O)(NO3)2(μ-C2O4)] (BISDOW) are extracted from its low-frequency spin precession dynamics showing good agreement with the coupling obtained from ground state energy differences. Our approach opens the possibility to perform real-time simulation of spin-related phenomena using time-dependent density functional theory in realistic molecular systems.

First-principles analysis of a homochiral cycloidal magnetic structure in a monolayer Cr on W(110)

The magnetic structure of a Cr monolayer on a W(110) substrate is investigated by means of first-principles calculations based on noncollinear spin density functional theory (DFT). As magnetic ground state we find a long-period homochiral left-rotating spin spiral on top of an atomic-scale antiferromagnetic order of nearest-neighbor atoms. The rotation angle of the magnetic moment changes inhomogeneously from atom to atom across the spiral. We predict a propagation direction along the crystallographic $[001]$ direction with a period length of $|\ensuremath{\lambda}|=14.3\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$, which is in excellent agreement with a modulation of the local antiferromagnetic contrast observed in spin-polarized scanning tunneling microscope experiments by Santos et al. [New J. Phys. 10, 013005 (2008)]. We identify the Dzyaloshinskii-Moriya interaction as the origin of the homochiral magnetic structure, competing with the Heisenberg-type exchange interaction and magnetocrystalline anisotropy energy. From DFT calculations we extract parameters for a micromagnetic model and thereby determine a considerable inhomogeneity of the spin spiral, increasing the period length by 6% compared to homogeneous spin spirals. The results are compared to the behavior of a Mn and Fe monolayer and Fe double layer on a W(110) substrate.

Electrically Controlled Eight‐Spin‐Qubit Entangled‐State Generation in a Molecular Break Junction

The generation of spin-based multi-qubit entangled states in the presence of an electric field is one of the most challenging tasks in current quantum-computing research. Such examples are still elusive. By using non-equilibrium Green's function-based quantum-transport calculations in combination with non-collinear spin density functional theory, we report that an eight-spin-qubit entangled state can be generated with the high-spin state of a dinuclear Fe(II) complex when the system is placed in a molecular break junction. The possible gate operation scheme, gating time, and decoherence issues have been carefully addressed. Furthermore, our calculations reveal that the preservation of the high spin state of this complex is possible if the experimentalists keep the electric-field strength below 0.78 V nm(-1). In brief, the present study offers a unique way to realize the first example of a multi-qubit entangled state by electrical means only.

Non-collinear spin DFT for lanthanide ions in doped hexagonal NaYF4

Trivalent lanthanide ions (Ln3+) doped in hexagonal (β)-NaYF4 nanocrystals (Na24Y23Ln1F96, Ln = La, Ce, Pr, Nd, Pm, Sm, Eu, Gd) were systematically studied by density functional theory (DFT) with a perturbative account for spin–orbit coupling. The simulated results, including the optimised molecular structures, electronic and magnetic properties, are compared to previous spin-polarised DFT studies in the same system. The spin–orbit coupling effects become significant with the increase in the number of unpaired 4f electrons in the doped lanthanide ions, particularly for the Sm3+-, Eu3+- and Gd3+-doped nanocrystals. Abnormal behaviour of Eu3+-doped nanocrystals was observed due to the Wybourne–Downer mechanism. A ‘sandwich-like’ 2p–4f–4d,5d electronic structure for Na24Y23Ln1F96 and the energies of the highest occupied 4f electrons from Ce3+ to Gd3+ are consistent with Dorenbos's relationship. The energy difference between the first and second Russell–Saunders terms (2S+1L) of the lanthanide dopant is consistent with Carnall's experimental results and with earlier spin-polarised DFT calculations.

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.

A New Approach to Noncollinear Spin Density Functional Theory beyond the Local Density Approximation.

The application of density functional theory to heavy elements and magnetic materials requires the generalization of existing functionals to the case of noncollinear spins. This letter describes a new idea to achieve such a generalization which, unlike previous efforts in this direction, (i) affords a nonvanishing local magnetic torque, (ii) is invariant with respect to spin-rotations, (iii) is free from numerical instabilities in regions of small magnetization, and (iv) reduces to the proper collinear limit.

Itinerant and localized magnetic moments in ferrimagnetic Mn2CoGa thin films probed by x-ray magnetic linear dichroism: Experiment andab initiotheory

Epitaxial thin films of the half-metallic ${X}_{a}$ compound Mn${}_{2}$CoGa (Hg${}_{2}$CuTi prototype) were prepared by dc magnetron co-sputtering with different heat treatments on MgO (001) substrates. High-quality films with a bulk magnetization of $1.95(5)\phantom{\rule{0.16em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ per unit cell were obtained. The ${L}_{3,2}$ x-ray magnetic circular dichroism spectra agree with calculations based on density functional theory (DFT) and reveal the antiparallel alignment of the two inequivalent Mn moments. X-ray magnetic linear dichroism, in good agreement with theory as well, allows us to distinguish between itinerant and local Mn moments. Based on noncollinear spin DFT, it is shown that one of the two Mn moments has local character, whereas the other Mn moment and the Co moment are itinerant.

Negative Tunneling Magnetoresistance by Canted Magnetization inMgO/NiOTunnel Barriers

The influence of the insertion of an ultrathin NiO layer between the MgO barrier and the ferromagnetic electrodes in magnetic tunnel junctions has been investigated from measurements of the tunneling magnetoresistance and via x-ray magnetic circular dichroism (XMCD). The magnetoresistance shows a high asymmetry with respect to bias voltage, giving rise to a negative value of up to -16% at 2.8 K. We attribute this effect to the formation of noncollinear spin structures at the interface of the NiO layer as inferred from XMCD measurements. The magnetic moments of the interface Ni atoms tilt from their easy axis due to exchange coupling with the neighboring ferromagnetic electrode, and the tilting angle decreases with increasing NiO thickness. The experimental observations are further supported by noncollinear spin density functional calculations.

Overhauser’s spin-density wave in exact-exchange spin-density functional theory

The spin density wave (SDW) state of the uniform electron gas is investigated in the exact exchange approximation of noncollinear spin density functional theory (DFT). Unlike in HartreeFock theory, where the uniform paramagnetic state of the electron gas is unstable against formation of the spin density wave for all densities, in exact-exchange spin-DFT this instability occurs only for densities lower than a critical value. It is also shown that, although in a suitable density range it is possible to find a non-interacting SDW ground state Slater determinant with energy lower than the corresponding paramagnetic state, this Slater determinant is not a self-consistent solution of the Optimized Effective Potential (OEP) integral equations of noncollinear spin-DFT. A selfconsistent solution of the OEP equations which gives an even lower energy can be found using an excited-state Slater determinant where only orbitals with single-particle energies in the lower of two bands are occupied while orbitals in the second band remain unoccupied even if their energies are below the Fermi energy.