Noncollinear density functional theory having proper invariance and local torque properties

Bulik, Ireneusz W.; Scalmani, Giovanni; Frisch, Michael J.; Scuseria, Gustavo E.

doi:10.1103/physrevb.87.035117

Cited by 67 publications

(63 citation statements)

References 47 publications

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“…The noncollinear DFT (ncDFT) [72][73][74][75] coupled to nonequilibrium density matrix [47] offers an algorithm to compute spin torque in arbitrary device geometry at vanishing or finite bias voltage. The single-particle spin-dependent Kohn-Sham (KS) Hamiltonian in ncDFT takes the form…”

Section: How To Model Spin Torque Using Nonequilibrium Density Mamentioning

confidence: 99%

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

Nikolić¹,

Dolui²,

Petrović³

et al. 2018

Handbook of Materials Modeling

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We review a unified approach for computing: (i) spin-transfer torque in magnetic trilayers like spin-valves and magnetic tunnel junction, where injected charge current flows perpendicularly to interfaces; and (ii) spin-orbit torque in magnetic bilayers of the type ferromagnet/spin-orbit-coupledmaterial, where injected charge current flows parallel to the interface. The experimentally explored and technologically relevant spin-orbit-coupled-materials include 5d heavy metals, topological insulators, Weyl semimetals and transition metal dichalcogenides. Our approach requires to construct the torque operator for a given Hamiltonian of the device and the steady-state nonequilibrium density matrix, where the latter is expressed in terms of the nonequilibrium Green's functions and split into three contributions. Tracing these contributions with the torque operator automatically yields field-like and damping-like components of spin-transfer torque or spin-orbit torque vector, which is particularly advantageous for spin-orbit torque where the direction of these components depends on the unknown-in-advance orientation of the current-driven nonequilibrium spin density in the presence of spin-orbit coupling. We provide illustrative examples by computing spin-transfer torque in a one-dimensional toy model of a magnetic tunnel junction and realistic Co/Cu/Co spin-valve, both of which are described by first-principles Hamiltonians obtained from noncollinear density functional theory calculations; as well as spin-orbit torque in a ferromagnetic layer described by a tight-binding Hamiltonian which includes spin-orbit proximity effect within ferromagnetic monolayers assumed to be generated by the adjacent monolayer transition metal dichalcogenide. In addition, we show how spin-orbit proximity effect, quantified by computing (via first-principles retarded Green's function) spectral functions and spin textures on monolayers of realistic ferromagnetic material like Co in contact with heavy metal or monolayer transition metal dichalcogenide, can be tailored to enhance the magnitude of spin-orbit torque. We also quantify errors made in the calculation of spin-transfer torque when using Hamiltonian from collinear density functional theory, with rigidly rotated magnetic moments to create noncollinear magnetization configurations, instead of proper (but computationally more expensive) self-consistent Hamiltonian obtained from noncollinear density functional theory. * bnikolic@udel.edu 1 For easy navigation, we provide a list of abbreviations used throughout the Chapter: 1D-Particle Current z y x Co Lead Co Lead Cu(a) (b) M free fixed M Co Pt θ θ M free MoS 2 Co M free θ (c) FIG. 2. Schematic view of: (a) FM/NM/FM trilayer for calculations of STT in spin-valves; (b) FM/HM bilayer for calculations of SOT in the presence of the spin Hall current along the z-axis generated by the HM layer; and (c) FM/monolayer-TMD for calculations of SOT in the absence of any spin Hall current. The semi-infinite FM layers in (a) are chosen as Co (0001), and t...

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Section: How To Model Spin Torque Using Nonequilibrium Density Mamentioning

confidence: 99%

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

Nikolić¹,

Dolui²,

Petrović³

et al. 2018

Handbook of Materials Modeling

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“…In this contribution, we choose to rely on the latter approach, with the spin‐orbit interaction based on a two‐component Hamiltonian . This Hamiltonian can be used within the framework of DFT provided the functional dependence is adapted to accommodate the fact that two‐component densities can in general be noncollinear; ie, the orientation of the spin magnetization vector may vary with the position in space . Transition densities and properties can be then calculated by performing a two‐component time‐dependent DFT (2c‐TDDFT) calculation starting from the single‐determinant 2c‐DFT reference or, as an alternative, through a real‐time propagation of the two‐component Hamiltonian .…”

Section: Theorymentioning

confidence: 99%

“…[30][31][32][33][34][35][36][37][38][39][40][41] This Hamiltonian can be used within the framework of DFT provided the functional dependence is adapted to accommodate the fact that two-component densities can in general be noncollinear; ie, the orientation of the spin magnetization vector may vary with the position in space. [42][43][44][45][46] Transition densities and properties can be then calculated by performing a twocomponent time-dependent DFT (2c-TDDFT) calculation starting from the single-determinant 2c-DFT reference 40,46 or, as an alternative, through a real-time propagation of the two-component Hamiltonian. 47 Here, we choose the first option, from which we can determine the singletto-triplet transition densities by solving the response equation through an iterative Davidson algorithm as previously described.…”

Section: Spin-orbit Couplingsmentioning

confidence: 99%

Computational simulation of vibrationally resolved spectra for spin‐forbidden transitions

et al. 2018

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In this computational study, we illustrate a method for computing phosphorescence and circularly polarized phosphorescence spectra of molecular systems, which takes into account vibronic effects including both Franck-Condon and Herzberg-Teller contributions. The singlet and triplet states involved in the phosphorescent emission are described within the harmonic approximation, and the method fully takes mode-mixing effects into account when evaluating Franck-Condon integrals. Spin-orbit couplings, which are responsible for these otherwise forbidden phenomena, are accounted for by means of a relativistic two-component time-dependent density functional theory method. The model is applied to two types of chiral systems: camphorquinone, a rigid organic system that allows for an extensive benchmark, and some members of a class of iridium complexes. The merits and shortcomings of the methods are discussed, and some perspectives for future developments are offered.

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“…While some work has been done for the development of truly noncollinear density functionals, the most common approach is to find ways to adapt common density functionals developed for collinear densities to the general case. Over the past decades, numerous collinear density functionals have been developed and benchmarked against a variety of molecular properties, therefore the ability to use them for noncollinear cases with minimal modifications is highly desirable, and much work has been done in this respect, particularly in the context of relativistic two‐component methods . One feature that is expected from the exact functional is a nonvanishing local magnetic exchange‐correlation torque acting on the spin magnetization .…”

Section: Noncollinear Dftmentioning

confidence: 99%

“…This is a point that has been very clearly brought to the quantum chemical community in recent years by the Scuseria group (see Refs. [ ] and citations therein). Because symmetry breaking is the by‐product of a mean‐field description, it can be considered artifactual.…”

Section: Introductionmentioning

confidence: 99%

Current development of noncollinear electronic structure theory

Goings

Egidi

2017

Int J of Quantum Chemistry

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In this Perspective, we review recent developments in noncollinear electronic structure theory.After a brief historical overview of studies into broken symmetry wave functions, we show that noncollinear wave functions are necessary for studying spin and magnetic phenomena on account of spin-symmetry breaking terms in the Hamiltonian. Recent developments applying noncollinear electronic structure theory to magnetization dynamics, spin dynamics, and spin-orbit coupling in excited state properties are showcased. We also discuss some recent developments in noncollinear density functional theory. Finally, we comment on the future of noncollinear electronic structure theory.noncollinear spin, relativistic electronic structure theory, symmetry breaking, time-dependent electronic structure theory, two-component method 1 | I N TR ODU C TI ON Mean-field, and self-consistent field (SCF), methods are the backbone of modern electronic structure theory. Since the introduction of the singledeterminant ansatz by Hartree and Fock, there has been a great deal of work on understanding the nature of the Hartree-Fock (HF) solutions as well as how to improve their utility in the description of atoms and molecules. It was recognized early on that the solution of the HF equations required a balance between two (sometimes competing) goals. [1][2][3][4][5] The first was that the HF equations would be at a variational minimum: the best SCF solution would be the lowest energy single-determinant approximation to the full configuration interaction (FCI) equations (for a given basis).Solutions of the HF equations would always seek to find the lowest possible energy solution, so as to satisfy the variational principle. Conversely, it was known that the underlying electronic Hamiltonian is invariant to several unitary transformations, most notably spin rotations. This invariance expresses itself as a conservation law, and the conserved quantity is total spin angular momentum S 2 as well as the spin projection along an arbitrary axis, S z . Surely a physically meaningful solution of the HF approximation would also have good quantum numbers, so invariance to rotations in the spin manifold was built-in to the HF equations as a constraint in the single determinantal expression. For example, the restricted Hartree-Fock (RHF) equations contain only paired electrons in orbitals, yielding solutions with good spin quantum numbers.Unfortunately, it was quickly found that there are many cases where insisting that the HF solution be a spin eigenstate yields energies that are higher than they would otherwise be if spin symmetry constraints were relaxed. For example, in the classic example of the dissociation of H 2 one finds that when the bond is stretched to a certain distance (the Coulson-Fischer point) an RHF to UHF instability forms and qualitatively correct dissociation curve are obtained only in the spin symmetry broken state. The spin symmetry breaking arises when the solutions approach a (near) degeneracy. Hartree-Fock solutions are unstable...

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Noncollinear density functional theory having proper invariance and local torque properties

Cited by 67 publications

References 47 publications

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

Computational simulation of vibrationally resolved spectra for spin‐forbidden transitions

Current development of noncollinear electronic structure theory

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