Introduction To Noncollinear Spin
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- Introduction to noncollinear spin
- Atomic Scale Materials Modeling
- Introduction to Atomic-Scale Materials Modeling
- Key Takeaways
- 1. What is Atomic-Scale Materials Modeling?
- Definition
- Key Characteristics
- 2. The Foundation: Atoms, Interactions, and Energy
- Atoms as Building Blocks
- How Atoms Interact
- Total Energy: The Central Concept
- The Potential Energy Surface
- Finding Equilibrium: Energy Minimization
- The Many-Body Challenge
- 3. Two Fundamental Approaches
- 3.1 Force Fields
- 3.2 Density Functional Theory (DFT)
- 4. The Materials Modeling Hierarchy
- Scale Bridging in Materials Science
- Understanding the Hierarchy
- Where Atomic-Scale Modeling Fits
- 5. When to Use Atomic-Scale Modeling
- Primary Use Cases
- Force Fields & Molecular Dynamics
- 1. From Quantum Complexity to Classical Approximation
- What Do We Gain?
- What Do We Lose?
- The Fundamental Trade-off
- 2. Classical Force Fields: Mathematical Description
- What is a Force Field?
- 2.1 Bonded Force Fields
- 2.2 Metallic Force Fields
- 2.3 Covalent/Semiconductor Force Fields
- 2.4 Ionic Force Fields
- Force Field Parameters
- 3. Introduction to Molecular Dynamics (MD)
- What is Molecular Dynamics?
- The MD Algorithm: Step by Step
- Understanding MD Output: The Trajectory
- 4. Material Properties from MD Simulations
- What Can We Calculate?
- 5. Simple Application Example: Thermal Expansion of Aluminum
- The Problem
- The Simulation Approach
- Expected Results
- Extending the Example
- 1. From Quantum Complexity to Classical Approximation
- Electronic Structure: Density Functional Theory
- 1. Introduction: What is Electronic Structure?
- From Force Fields to Electrons
- Why Electrons Matter
- Electronic Structure: The Electron Distribution
- From Classical to Quantum
- Why Calculate Electronic Structure?
- 2. The Quantum Mechanical Many-Body Problem
- The Schrödinger Equation
- Key Approximations
- DFT: The Practical Solution
- 3. What Can DFT Calculate?
- 4. DFT Workflow and Best Practices
- Typical DFT Calculation Workflow
- 5. DFT vs. Force Fields: Making the Choice
- Comparison Table
- 6. Brief Introduction to SemiEmpirical Methods
- 1. Introduction: What is Electronic Structure?
- Introduction to Atomic-Scale Materials Modeling
- Getting started with QuantumATK
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- Prerequisites
- Importing Structures from the NanoLab Database
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- Band Structure, Projected Density of States and Effective Mass Calculations
- Prerequisites
- Setting up Band Structure Calculation Workflow
- Analyzing Band Structure Results
- Restarting to Obtain Projected Density of States
- Analyzing Projected Density of State Results
- Calculation of Effective Masses
- References
- Optical Property Calculations
- Prerequisites
- Setting up an Optical Property Calculation Workflow
- Analyzing Results
- Outlook
- References
- Molecular Dynamics Simulations for Generating Amorphous Structures
- Prerequisites
- Setting-Up Molecular Dynamics Simulations
- Analyzing Molecular Dynamics Simulations
- References
- NEGF Simulations of Electron Transport in Devices
- Prerequisites
- Building Si p-n Junction Device
- Setting up Electron Transport Simulations for the Si p-n Junction at 0 V Bias
- Analyzing Results at 0 V Bias
- Setting up Electron Transport Simulations for the Si p-n Junction at Finite Bias
- Analyzing Results at Finite Bias
- Summary and Outlook
- References
- Geometry Optimization
- Feature List
- Referencing QuantumATK
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- Create atomistic structure
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- Introduction
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- The Workflow Builder overview
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- Creating a simple workflow
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- Using Tables in the Workflow Builder
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- Ethanol molecule
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- Introduction
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- Phosphorene and its bandstructure
- Bandstructure
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- Training and Finetuning of MACE models
- Training a MACE model from scratch
- Naive Finetuning of foundation MACE models
- Multihead Finetuning of foundation MACE models
- Small study with additional models trained from scratch
- Validation of trained models
- Impact of important parameters
- General remarks
- Loading custom MACE models into QuantumATK
- Summary
- References
- 2D Database and potentials
- Importing a Structure from the 2D Materials Database
- Creating and Setting a Calculator from a 2D Potential Set
- Phonon Bandstructure calculation
- References
- Moment Tensor Potential (MTP) Training for Crystal and Amorphous Structures
- Prerequisites
- Overview of the MTP Training Workflow
- Crystal Training Data
- Amorphous Active Learning
- Final MTP Fitting
- Submitting the MTP Training Calculation
- Analyzing MTP Training Results
- MTP Validation for Crystals
- MTP Validation for Amorphous
- Summary and Outlook
- References
- MRAM workflow in QuantumATK: Study of STT-MRAM free layer stability
- Video
- Introduction
- Workflow for calculating the free layer stability in a STT-MRAM MTJ structure
- Vampire
- References
- Generating A Magnetoresistive RAM (MRAM) Stack using the MRAM-Builder
- Introduction
- Workflow to generate the MgO-FeCo-MgO MRAM structure
- Generating A High-k Metal Gate Stack Using the HKMG-Builder
- Introduction
- Workflow
- How to select the right calculator
- The Calculator types
- The DFT Calculators (LCAO and Plane Wave)
- The Semi Empirical Calculator
- The Force Field Calculator
- Using Thermochemistry Analyzer to Compare Chemical Reactions
- Background
- Getting started
- Understanding the Thermochemistry Analyzer GUI
- Example: Temperature Window for Thermal Atomic Layer Etching of HfO2 and ZrO2
- General Uses
- Electronic Properties of Phase Change Material Ge2Sb2Te5
- Geometry
- Bandgap Calculation
- Lattice Parameters
- Cohesive Energies
- Neutral Vacancy Formation Energies
- Total DOS With and Without Ge Vacancy
- STM simulations of tunneling anisotropic magneto resistance (TAMR)
- Introduction
- Setting up the 2LFe/W(110) structure
- Local Density of States calculations
- Analyzing the results
- Co adatom on 2LFe/W(110)
- COSMICS project
- References
- Bulk Magnetic Anisotropy Energy
- Introduction
- Theory
- MAE of FePt
- TotalEnergy calculations
- Convergence of results
- COSMICS project
- Magnetic Anisotropy Energy of Fe-MgO-Fe MTJ structure
- Introduction
- Fe-MgO-Fe MTJ structure
- MagneticAnisotropyEnergy calculation
- What causes the PMA?
- COSMICS project
- Heisenberg exchange coupling of iron and cobalt
- Introduction
- Theory
- Setting up calculations
- Analyzing the results
- COSMICS project
- References
- Building an model of an epoxy thermoset material
- Theory
- Building the thermoset model
- Analyzing the Thermoset Reaction
- Conclusions
- Analyzing the thermo-mechanical properties of a polymer material
- Glass Transition Temperature
- Young’s Modulus and Poisson Ratio
- Conclusions
- Generating A Moment Tensor Potential for HfO2 Using Active Learning
- Background
- Getting Started
- Workflow
- Step 1: Prepare Initial Reference Configurations
- Step 2: Compute Reference Data and Setup Active Learning
- Step 3: Find an MTP with Lowest Error
- Validation MD Simulation
- References
- FAQ Section
- Simulating Si Deposition using Silane
- Background
- Getting started
- Step 1: Reference Calculations
- Step 2: Adsorption and Dissociation of SiH4
- Step 3: Formation and Desorption of H2
- Conclusions
- References
- Electronic structure of NiO with DFT+U
- Prerequisites
- Introduction
- The electronic structure of NiO calculated with DFT
- DFT+U calculation for the NiO crystal
- DFT + Ab initio U calculation for the NiO crystal
- References
- Training and Finetuning of MACE models
- Semiconductors
- Phonon-limited mobility in graphene using the Boltzmann transport equation
- Geometry and electronic structure of graphene
- Phonons in Graphene
- Mobility of graphene
- Convergence of q- and k-point sampling
- Theory section
- References
- Effective mass of electrons in silicon
- Introduction
- Background
- Set up the calculation
- Analyze the results
- Going further
- References
- Spin-orbit splitting of semiconductor band structures
- Relavistic effects in Kohn-Sham DFT
- Silicon band splitting with ATK-DFT
- SO+MGGA band gap
- GaAs band structure with ATK-SE and SO coupling
- References
- Silicon p-n junction
- Silicon bulk: Slater-Koster vs DFT-MGGA
- Silicon device
- Analyzing the results
- References
- Optical Properties of Silicon
- Introduction
- Electronic structure and optical properties of silicon
- References
- NiSi2–Si interface
- Create the NiSi2/Si device
- Set-up the calculation for the undoped device
- Dope the device
- Analysis of the results
- Finite-bias calculations
- References
- Bi2Se3 topological insulator
- Build the Bi2Se3 crystal
- Bi2Se3 bulk band structure
- Bi2Se3 surface: Spin-orbit band structure
- DOS analysis: Dirac cone finger print
- Penetration depth of surface states
- Fermi surface and spin directions
- Topological Invariants
- References
- Effective band structure of random alloy InGaAs
- Methodology
- Band structures of InAs
- In0.53Ga0.47As random alloy
- Finite broadening
- Final comments
- References
- Complex band structure of Si(100)
- Background
- Si crystal cleaved in (100) direction
- Complex band structure calculation
- Analysing the results
- 3D visualizations
- References
- InAs p-i-n junction
- Setting up the device geometry
- Running the calculations
- Defining the work function of the metal gate
- Performing a gate scan
- References
- Inelastic current in a silicon p-n junction
- Creating the silicon p-n junction
- Transmission calculation without electron-phonon interactions
- Transmission calculation with electron-phonon interactions
- Speeding up the calculations
- References
- Elastic scattering, mean free path, mobility: Impurity scattering in a silicon nanowire
- Introduction
- Defected silicon nanowires
- Elastic scattering mean free path
- Fermi levels in doped nanowires
- Doping dependent mobility
- Summary and discussion
- Appendix: Building the nanowires
- References
- Virtual Crystal Approximation for InGaAs random alloy simulations
- Introduction
- Setting up the VCA calculations for InxGa1-xAs
- Analyzing the results for VCA with InxGa1-xAs
- Calculating effective masses
- Summary and discussion
- References
- DFT-1/2 and DFT-PPS density functional methods for electronic structure calculations
- DFT-1/2 methods
- DFT-PPS method
- References
- Electrical characteristics of devices using the IVCharacteristics study object
- Prerequisites
- Calculation and analysis of the \(\mathrm{I_{ds}-V_{gs}}\) curve for the FET on-state
- Extending the range of the \(\mathrm{I_{ds}-V_{gs}}\) curve to the FET off-state
- Analysis of the \(\mathrm{I_{ds}-V_{gs}}\) curve in the subthreshold region
- Calculating the drain-induced barrier lowering
- References
- Formation energies and transition levels of charged defects
- Procedure for calculating the formation energy
- Setting up the calculation
- Analyzing the results
- Discussion and summary
- Appendix
- References
- Introduction
- Methods
- HSE
- Nomenclature
- Pseudopotential Projector-Shift
- Silicon
- Summary
- Convergence
- Timing
- Results
- Appendix
- References
- Germanium
- Summary
- Convergence
- Timing
- Results
- Appendix
- Si0.5Ge0.5
- Summary
- Convergence
- Timing
- Results
- Appendix
- References
- Phonon-limited mobility in graphene using the Boltzmann transport equation
- Batteries & Energy Storage
- Li-air battery interface
- Li2O2 bulk and surface structures
- Li2CO3 bulk and surface structures
- The Li2O2/Li2CO3 interface
- References
- Li-ion diffusion in LiFePO4 for battery applications
- Import LiFePO4 bulk structure
- Optimize LiFePO4 lattice parameters
- Create the Li\(_{1-x}\)FePO4 structures
- Optimize initial and final configurations
- Create initial NEB trajectories
- Optimize Li diffusion path
- Calculate the reaction rates using harmonic transition state theory
- References
- Open-circuit voltage profile of a Li-S battery: ReaxFF molecular dynamics
- Amorphous Li0.4S compound
- Simulated annealing
- Open-circuit voltage
- Full open-circuit voltage profile
- Radial distribution functions
- References
- Photocurrent in a silicon p-n junction
- Device ground state
- Photocurrent
- References
- Li-air battery interface
- Complex Interfaces
- Building an interface between Ag(100) and Au(111)
- Import silver and gold crystals
- Building the Ag(100) and Au(111) crystals
- Building the interface
- Building the device configuration
- Advanced device relaxation - manual workflow
- Introduction
- Preparations
- Electrode relaxation
- Central region relaxation
- 1DMIN optimization of the interface using 2-probe calculations
- Relaxation of devices using the OptimizeDeviceConfiguration study object
- Introduction
- Unrelaxed Ag(100)|Ag(111) device
- Set up and run the device geometry optimization
- Relaxed device structures
- Appendix
- Atomic-scale capacitance
- Build the parallel plate capacitor
- Calculations
- Analysis
- Bias-dependent capacitance
- Dielectric spacer material
- Graphene–Nickel interface
- Creating the structure
- More configurations
- Building a Si-Si3N4 Interface
- Preparations: Two crystals
- Building the interface
- Final adjustment
- Doubling down: Buried layer model
- Interface as a device model
- NiSi2–Si interface
- Create the NiSi2/Si device
- Set-up the calculation for the undoped device
- Dope the device
- Analysis of the results
- Finite-bias calculations
- References
- Determination of low strain interfaces via geometric matching
- Method description
- Input and output description
- Example 1: Lattice match between two bulk systems
- Example 2: Lattice match between a bulk system with a predefined surface
- References
- Generating A High-k Metal Gate Stack Using the HKMG-Builder
- Introduction
- Workflow
- Generating A Magnetoresistive RAM (MRAM) Stack using the MRAM-Builder
- Introduction
- Workflow to generate the MgO-FeCo-MgO MRAM structure
- Modeling metal–semiconductor contacts: The Ag–Si interface
- Creating the device
- Projected local density of states
- Finite-bias calculations
- Note on the variation of the current
- References
- Resistivity calculations using the MD-Landauer method
- 1. Theory and numerical procedure
- 2. Calculation setup
- 3. Data analysis
- References
- Electron transport calculations with electron-phonon coupling included via the special thermal displacement method - STD-Landauer
- Building the device
- Calculations
- Analysis and discussion
- References
- Building an interface between Ag(100) and Au(111)
- 1D Nanostructures
- Transport in graphene nanoribbons
- Introduction
- Band structure of 2D graphene
- Band structure of an armchair ribbon
- Transport properties of a zigzag nanoribbon
- Transmission spectrum of a spin-polarized atomic chain
- Building the 1D carbon chain
- Spin-parallel transmission spectrum
- Spin anti-parallel transmission spectrum
- Introduction to noncollinear spin
- From collinear to noncollinear spin
- Getting started
- Spin rotation of 120°
- Analysis
- Spin-orbit interactions
- Carbon Nanotube Junctions
- Setting up the geometry
- Capping a carbon nanotube
- Build an extended (5,5) carbon nanotube
- Cut the fullerene in half
- Capping the tube
- Finalizing the geometry
- Simple carbon nanotube device
- Build and geometry optimize a short CNT
- CNT device configuration
- Thermoelectric effects in a CNT with isotope doping
- CNT device with tags for 14C doping
- Phonon transmission
- Electron transmission
- Thermoelectric transport properties
- References
- Graphene nanoribbon device: Electric properties
- Electron transmission spectrum
- Effect of the Gate Potential
- I–V characteristics
- When is the linear response approximation valid?
- Further analysis with ATK-SE
- Temperature dependent conductance
- Comparison to results for a longer device
- References
- Silicon nanowire field-effect transistor
- Introduction
- Band structure of a Si(100) nanowire
- Setting up and running the calculations
- Si(100) nanowire FET device
- Zero gate voltage calculation
- Exploring Graphene
- Build a graphene sheet
- Build a CNT
- Transmission spectrum of a GNR
- Twisted nanoribbon
- Möbius nanoribbon
- Buckling a graphene sheet
- Elastic scattering, mean free path, mobility: Impurity scattering in a silicon nanowire
- Introduction
- Defected silicon nanowires
- Elastic scattering mean free path
- Fermi levels in doped nanowires
- Doping dependent mobility
- Summary and discussion
- Appendix: Building the nanowires
- References
- Transport in graphene nanoribbons
- 2D Materials
- Meta-GGA and 2D confined InAs
- TB09 meta-GGA
- Bulk InAs band structure with TB09 meta-GGA
- Setting up and passivating an InAs slab
- Band structure with default hydrogen atoms
- Analyzing the results
- Passivation using pseudo-hydrogen
- Results
- Passivation using compensation charges
- Results
- Non-parabolicity in confined structures
- Nanowire band structure
- References
- Opening a band gap in silicene and bilayer graphene with an electric field
- Bilayer graphene
- Silicene
- References
- More reading
- Commensurate supercells for rotated graphene layers
- Additional rotated structures
- References
- Spin-dependent Bloch states in graphene nanoribbons
- Band structure of a zigzag nanoribbon
- Bloch states
- Introducing spin
- Electron density and Mulliken populations
- References
- Exploring Graphene
- Build a graphene sheet
- Build a CNT
- Transmission spectrum of a GNR
- Twisted nanoribbon
- Möbius nanoribbon
- Buckling a graphene sheet
- 2D Database and potentials
- Importing a Structure from the 2D Materials Database
- Creating and Setting a Calculator from a 2D Potential Set
- Phonon Bandstructure calculation
- References
- Meta-GGA and 2D confined InAs
- Phonons & Thermal Transport
- Calculating and using Dynamical Matrix
- Prerequisites
- Create the Workflow
- LCAOCalculator Settings
- Lattice optimization Settings
- Dynamical matrix Settings
- Running the calculation
- Analyzing the results
- Speeding up the calculation with ForceFields
- Vibrational modes and Vibration Visualizer
- MoS2 monolayer
- Nanophononic metamaterials
- Phonons, Bandstructure and Thermoelectrics
- Introduction
- Phonon Bandstructure of a Graphene Nanoribbon
- Analyzing the Results
- Algorithmic Details of the Phonon Calculator
- Calculating Electrical and Heat Transport for a Graphene Nanoribbon
- Phonon-limited mobility in graphene using the Boltzmann transport equation
- Geometry and electronic structure of graphene
- Phonons in Graphene
- Mobility of graphene
- Convergence of q- and k-point sampling
- Theory section
- References
- Thermoelectric effects in a CNT with isotope doping
- CNT device with tags for 14C doping
- Phonon transmission
- Electron transmission
- Thermoelectric transport properties
- References
- Inelastic Electron Spectroscopy of an H2 molecule placed between 1D Au chains
- Introduction
- Device setup
- Calculation of IETS
- Analysis
- References
- Using Thermochemistry Analyzer to Compare Chemical Reactions
- Background
- Getting started
- Understanding the Thermochemistry Analyzer GUI
- Example: Temperature Window for Thermal Atomic Layer Etching of HfO2 and ZrO2
- General Uses
- Interfacial thermal conductance
- Introduction
- Reverse non-equilibrium molecular dynamics (RNEMD)
- Non-equilibrium Green’s function method
- References
- Calculating and using Dynamical Matrix
- Molecular Dynamics
- How to Setup Basic Molecular Dynamics Simulations
- Pre-requisites
- NVE Simulations
- NVT Simulations
- NPT Simulations
- Conclusion
- Simulating Thin Film Growth via Vapor Deposition
- Introduction
- Simulation Strategies
- Preparing the System
- Setting up the Deposition Simulation
- Running the Simulation
- General Remarks
- Simulating Si Deposition using Silane
- Background
- Getting started
- Step 1: Reference Calculations
- Step 2: Adsorption and Dissociation of SiH4
- Step 3: Formation and Desorption of H2
- Conclusions
- References
- Simulating Ion Bombardment on Graphene Sheets
- Setting up the Graphene Sheet:
- Adding a Bombardment Atom
- Setting up the Simulation
- Modifying the Script
- References
- Uniaxial and Biaxial Stress in Silicon
- Introduction
- Uniaxial Stress
- Biaxial Stress
- Adding, Combining, and Modifying Classical Potentials
- Introduction
- Adding a New Classical Potential from Scratch
- A Potential for Amorphous Oxides
- Combining a Tersoff and a Lennard-Jones Potential
- Intra- and Inter-Layer Cohesion in MoS2
- Generating Amorphous Structures
- Introduction
- Amorphous Structure Generation with Classical MD Simulations
- Refining Amorphous Structures
- Creating Crystal/Amorphous Interfaces
- Further Examples
- Young’s modulus of a CNT with a defect
- CNT bulk configuration
- Configuring the MD simulation
- Adding Python hooks
- Computing Young’s modulus
- Visualize and analyse the results
- References
- Interfacial thermal conductance
- Introduction
- Reverse non-equilibrium molecular dynamics (RNEMD)
- Non-equilibrium Green’s function method
- References
- Diffusion in Liquids from Molecular Dynamics Simulations
- Theory
- Computational Procedure
- Analysis
- Simulating a creep experiment of polycrystalline copper
- Installing the polycrystal builder plugin
- Building the polycrystalline cell
- Analyzing the grain structure
- Setting up the creep simulation
- Running the simulation
- Analyzing the results
- Outlook
- References
- Metadynamics Simulation of Cu Vacancy Diffusion on Cu(111) - Using PLUMED
- Introduction
- Theoretical Background
- Metadynamics Simulation of Cu Vacancy on Cu(111)
- References
- Open-circuit voltage profile of a Li-S battery: ReaxFF molecular dynamics
- Amorphous Li0.4S compound
- Simulated annealing
- Open-circuit voltage
- Full open-circuit voltage profile
- Radial distribution functions
- References
- Viscosity in liquids from molecular dynamics simulations
- Theory
- Computational procedure
- Analyzing the results
- Extending the results
- Building an model of an epoxy thermoset material
- Theory
- Building the thermoset model
- Analyzing the Thermoset Reaction
- Conclusions
- Analyzing the thermo-mechanical properties of a polymer material
- Glass Transition Temperature
- Young’s Modulus and Poisson Ratio
- Conclusions
- Moment Tensor Potential (MTP) Training for Crystal and Amorphous Structures
- Prerequisites
- Overview of the MTP Training Workflow
- Crystal Training Data
- Amorphous Active Learning
- Final MTP Fitting
- Submitting the MTP Training Calculation
- Analyzing MTP Training Results
- MTP Validation for Crystals
- MTP Validation for Amorphous
- Summary and Outlook
- References
- Generating A Moment Tensor Potential for HfO2 Using Active Learning
- Background
- Getting Started
- Workflow
- Step 1: Prepare Initial Reference Configurations
- Step 2: Compute Reference Data and Setup Active Learning
- Step 3: Find an MTP with Lowest Error
- Validation MD Simulation
- References
- FAQ Section
- Training and Finetuning of MACE models
- Training a MACE model from scratch
- Naive Finetuning of foundation MACE models
- Multihead Finetuning of foundation MACE models
- Small study with additional models trained from scratch
- Validation of trained models
- Impact of important parameters
- General remarks
- Loading custom MACE models into QuantumATK
- Summary
- References
- How to Setup Basic Molecular Dynamics Simulations
- Molecular Electronics
- Building molecule–surface systems: Benzene on Au(111)
- Summary of workflow
- Detailed instructions
- References
- Building a molecular junction
- Benzene to DTB: Building the molecule
- Cleaving gold into two surfaces
- Combining the molecule and the surfaces
- Converting the central region to a device configuration
- References
- Molecular Device
- Zero-bias calculation
- Analysis of the zero-bias results
- I-V characteristics
- References
- Inelastic Electron Spectroscopy of an H2 molecule placed between 1D Au chains
- Introduction
- Device setup
- Calculation of IETS
- Analysis
- References
- Building molecule–surface systems: Benzene on Au(111)
- Spintronics
- Spin Transfer Torque
- Introduction
- Getting Started
- Calculate the STT
- Angle Dependence
- References
- Transmission spectrum of a spin-polarized atomic chain
- Building the 1D carbon chain
- Spin-parallel transmission spectrum
- Spin anti-parallel transmission spectrum
- Introduction to noncollinear spin
- From collinear to noncollinear spin
- Getting started
- Spin rotation of 120°
- Analysis
- Spin-orbit interactions
- Spin transport in magnetic tunnel junctions
- Introduction
- Getting started
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- Anti-parallel spin
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- References
- Relativistic effects in bulk gold
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- References
- Bi2Se3 topological insulator
- Build the Bi2Se3 crystal
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- Noncollinear calculations for metallic nanowires
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- References
- Electronic structure of NiO with DFT+U
- Prerequisites
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- References
- Bulk Magnetic Anisotropy Energy
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- Introduction
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- COSMICS project
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- COSMICS project
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- Generating A Magnetoresistive RAM (MRAM) Stack using the MRAM-Builder
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- Video
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- Reconstruction of the Si (100) surface - a geometry optimization study with QuantumATK
- Introduction
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- Background
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- Step 1: Reference Calculations
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- Calculation of Formation Energies
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- Uniaxial and Biaxial Stress in Silicon
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- References
- Relativistic effects in bulk gold
- GGA band structure
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- References
- Geometry optimization: CO/Pd(100)
- Bulk palladium
- Build the Pd(100) surface and relax it
- Relax the CO/Pd(100) system
- Relax the CO molecule
- Adsorption energy
- Modeling Vacancy Diffusion in Si0.5 Ge0.5 with AKMC
- Obtaining an Initial Structure
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- Conclusion
- Computing the piezoelectric tensor for AlN
- Introduction
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- Alternative way of calculating the piezoelectric coefficient \({e}_{33}\)
- Computing the Born effective charge
- References
- Formation energies of charged defects - manual workflow
- Procedure for calculating the formation energy
- Neutral As vacancy in GaAs
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- Appendix
- References
- Boron diffusion in bulk silicon
- Creating the B-doped Si crystal
- Running the AKMC simulation
- Adaptive Kinetic Monte Carlo Simulation of Pt Island Ripening
- Introduction
- Creating the initial configuration
- Setting up the AKMC Simulation
- Running the Simulation
- Analyzing the AKMC Simulation
- Conclusion
- References
- Adaptive Kinetic Monte Carlo Simulation of Pt on Pt(100)
- Introduction
- The AKMC method
- Creating the initial configuration
- Creating the AKMC script
- Analyzing the results
- Conclusion
- References
- Crystal Structure Prediction Scripter: Phases of TiO2
- Setting up the calculation
- Running the calculations and analyzing results
- References
- Electronic structure of NiO with DFT+U
- Prerequisites
- Introduction
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- DFT+U calculation for the NiO crystal
- DFT + Ab initio U calculation for the NiO crystal
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- DFT-D and basis-set superposition error
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- Discussion and summary
- Appendix
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- Using Thermochemistry Analyzer to Compare Chemical Reactions
- Background
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- Example: Temperature Window for Thermal Atomic Layer Etching of HfO2 and ZrO2
- General Uses
- Electronic Properties of Phase Change Material Ge2Sb2Te5
- Geometry
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- Polymer Builder
- Miscellaneous
- The DFTB model in ATK-SE
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- References
- Slater-Koster tight-binding models in ATK-SE
- Introduction
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- Silicon band structure
- Adding hydrogen
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- References
- Linear response current – how to compute it, and why it is often not a good idea
- Make Movies from QuantumATK Trajectory Files
- Creating Animated GIF
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- Crystal classifications
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- Reusing electrodes in device calculations
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- POV-Ray images from QuantumATK
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- Examining the .pov file
- Exporting pictures with POV-Ray
- Generating A High-k Metal Gate Stack Using the HKMG-Builder
- Introduction
- Workflow
- Generating A Magnetoresistive RAM (MRAM) Stack using the MRAM-Builder
- Introduction
- Workflow to generate the MgO-FeCo-MgO MRAM structure
- How to select the right calculator
- The Calculator types
- The DFT Calculators (LCAO and Plane Wave)
- The Semi Empirical Calculator
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- Transport calculations with QuantumATK
- Introduction
- Geometry for transport calculations
- Getting started
- Convergence of electrode parameters
- Zero-bias analysis
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- Summary
- Calculate the band structure of a crystal
- Start QuantumATK and create a new project
- Import the Silicon structure from the Database and send it to the Scripter
- Set up the calculation and analyse the band structure
- Phonons, Bandstructure and Thermoelectrics
- Introduction
- Phonon Bandstructure of a Graphene Nanoribbon
- Analyzing the Results
- Algorithmic Details of the Phonon Calculator
- Calculating Electrical and Heat Transport for a Graphene Nanoribbon
- Introducing the QuantumATK plane-wave DFT calculator
- Introduction
- How to calculate reaction barriers using the Nudged Elastic Band (NEB) method
- Create the initial and final states for the NEB
- Set up and run the NEB calculations
- Analyze the results
- Summary
- References
- Carbon Nanotube Junctions
- Setting up the geometry
- Capping a carbon nanotube
- Build an extended (5,5) carbon nanotube
- Cut the fullerene in half
- Capping the tube
- Finalizing the geometry
- Simple carbon nanotube device
- Build and geometry optimize a short CNT
- CNT device configuration
- Building a Si-Si3N4 Interface
- Preparations: Two crystals
- Building the interface
- Final adjustment
- Doubling down: Buried layer model
- Interface as a device model
- Build a graphene nanoribbon transistor
- Small nanoribbon transistor
- A longer nanoribbon transistor
- Commensurate supercells for rotated graphene layers
- Additional rotated structures
- References
- Nanosheet with a hole
- MoS2 Nanotubes
- Graphene–Nickel interface
- Creating the structure
- More configurations
- Stone–Wales Defects in Nanotubes
- Creating the defect and wrapping the tube
- Optimizing the structure
- Transmission spectrum
- References
- Building a molecular junction
- Benzene to DTB: Building the molecule
- Cleaving gold into two surfaces
- Combining the molecule and the surfaces
- Converting the central region to a device configuration
- References
- The DFTB model in ATK-SE
- New or Updated
- Manual
- General
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- Installing and running the software
- How to read this manual
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- Introduction
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- How to choose the right pretrained neural network based force field
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- NEGF: Device Calculators
- Introduction
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Version: 2016.3
In standard (collinear) spin-polarized calculations, the spin quantum number (up or down) is added to the electronic states. In contrast, noncollinear spin allows the electronic spin to point in any direction. This introduces a few more concepts – and possibilities! – which may be somewhat unfamiliar. This tutorial therefore provides a simple introduction to ATK-DFT calculations with noncollinear spin densities.
As briefly stated above, noncollinear magnetism refers to situations where the spin direction depends on position in such a way that there is no particular direction in which all the spins are (anti)parallel. Noncollinear spins are quite ubiquitous in nature, and include systems with spin spirals (e.g. chromium) and helicoids, canted spins (e.g. manganites), and most commonly domain walls in ferromagnetic materials. ATK allows you to study systems with noncollinear spins from first principles, but it is technically and conceptually quite different from the familiar case of collinear spin.
From collinear to noncollinear spin¶
It is important to realize that the familiar concept of spin as being either up or down – and all derived quantities also being labeled by this quantum number – does not work in a noncollinear DFT calculation. Instead, the eigenstate of an atom is a spinor with a certain mixing of both spin up and down channels, and many quantities – like the electron transmission spectrum – become a 2x2 matrix rather than two separate numbers (spin up and down transmission).
Another important aspect of noncollinear calculations in practice is that they require in general more CPU time and memory than the corresponding spin-polarized or unpolarized calculation. SCF convergence may also be harder to achieve, since the electronic states have more degrees of freedom.
Two key features have therefore been implemented in QuantumATK to improve the SCF convergence rate for noncollinear calculations:
use of a collinear spin-polarized calculation as starting point;
a special density mixing scheme which diagonalizes the density matrix before mixing it.
Using these techniques, the required number of iterations to reach the selfconsistent noncollinear ground state can be reduced substantially.
Getting started¶
As mentioned above, the recommended approach for noncollinear calculations is to use a collinear spin-polarized calculation as the initial state. This tutorial therefore takes as starting point the collinear spin-parallel ground state of a simple carbon-chain device obtained in the tutorial Transmission spectrum of a spin-polarized atomic chain.
Start by opening QuantumATK and create a new project. If you have not already completed the aforementioned tutorial, use a script to calculate the required spin-parallel ground state: carbon_para.py. The calculation takes less than 5 minutes and saves the result in the file carbon_para.nc.
You will now use the selfconsistent calculation stored in this file as the starting point for a noncollinear calculation of the same linear 1D chain of carbon atoms. However, instead of just considering the parallel and anti-parallel (left electrode up, right electrode down) spin configurations, you will consider any angle of spin rotation between the two electrodes.
Spin rotation of 120°¶
Open the QuantumATK 
Editor (or your own favorite editor) and copy/paste the following lines of ATK Python code into it:
The spin setup corresponds to the spin polarization of the atoms in the left electrode pointing along the transport axis C, while in the right electrode the polarization is rotated 120 degrees (polar angle in a coordinate system where the XY plane is the equator). In the central region, the angle is interpolated between these two values. Note that this is just the initial spin configuration – the actual spin polarization vectors will be computed selfconsistently and may therefore change (you can see the result below).
Note
The initial electrode spins are automatically identical to the initial spins on the atoms in the “electrode extensions” in the central region, in this case the 3 first and last atoms.
Save the script as carbon_nc120.py, and then run it – it should take a few minutes only. Remember that you can use the 
Job Manager for this.
Analysis¶
The NEGF calculation is done, and it’s time to do some analysis. Use the Script Generator to set up the post-SCF analysis calculations:
Open the
Script Generator.Double-click the
Analysis from File block to insert it into the Script panel. Then double-click the inserted block and select the file carbon_nc120.nc, which was generated in the previous section.Add a
MullikenPopulation analysis block.Add a
TransmissionSpectrum analysis block (use default parameters).Set the output file to carbon_nc120.nc.
Run the script using the
Job Manager.
The analysis script should look roughly like this:
1# -*- coding: utf-8 -*- 2# ------------------------------------------------------------- 3# Analysis from File 4# ------------------------------------------------------------- 5path = u'carbon_nc120.nc' 6configuration = nlread(path, object_id='gID000')[0] 7 8# ------------------------------------------------------------- 9# Mulliken Population 10# ------------------------------------------------------------- 11mulliken_population = MullikenPopulation(configuration) 12nlsave('carbon_nc120.nc', mulliken_population) 13nlprint(mulliken_population) 14 15# ------------------------------------------------------------- 16# Transmission Spectrum 17# ------------------------------------------------------------- 18kpoint_grid = MonkhorstPackGrid() 19 20transmission_spectrum = TransmissionSpectrum( 21 configuration=configuration, 22 energies=numpy.linspace(-2,2,101)*eV, 23 kpoints=kpoint_grid, 24 energy_zero_parameter=AverageFermiLevel, 25 infinitesimal=1e-06*eV, 26 self_energy_calculator=RecursionSelfEnergy(), 27 ) 28nlsave('carbon_nc120.nc', transmission_spectrum) 29nlprint(transmission_spectrum)Mulliken populations¶
The Mulliken populations is now available as an analysis object on the QuantumATK LabFloor, and can be inspected using the Text Representation tool in the right-hand panel bar.
You immediately notice the difference to the collinear case: Now the Mulliken population on each atom is described by 4 variables; Up, Down, Theta and Phi. Note that Phi=180 is equivalent to Phi=0. The sum of the up and down populations corresponds, as usual, to the total Mulliken charge (the number of electrons), and their difference – combined with the two angles – forms a spin polarization vector, which can be visualized in the QuantumATK 
Viewer:
It is clear that the spin polarization direction changes smoothly between the two values in the electrodes.
Tip
The Viewer view plane used in the image is ZX. Use the Camera settings menu to select a view plane different from the default ZY.
Transmission spectrum¶
The TransmissionSpectrum analysis object is also available on the LabFloor. Use the Text Representation tool to inspect it – you again see that it has 4 components; up, down, real-up-down and imag-up-down:
The last spin component (imag-up-down) is very small in this simple system, but will in general be important in cases where the spins have other directions.
Note
Any quantitty calculated using noncollinear spin is represented as a 2x2 matrix (a spinor) with different mixing of up and down components: \(\uparrow \uparrow\), \(\downarrow \downarrow\), \(\uparrow \downarrow\), and \(\downarrow \uparrow\).
As explained in the QuantumATK Manual section Spin, a range of different spin projections may be derived from these 4 basic components, including Sum, X, Y, and Z:
\[\begin{split}T(\text{Spin.Sum}) &= T(\uparrow \uparrow) + T(\downarrow \downarrow) \\ T(\text{Spin.X}) &= 2 \cdot \text{Re}(T(\uparrow \downarrow)) \\ T(\text{Spin.Y}) &= 2 \cdot \text{Im}(T(\uparrow \downarrow)) \\ T(\text{Spin.Z}) &= T(\uparrow \uparrow) - T(\downarrow \downarrow)\end{split}\]Use the Transmission Analyzer plugin to plot the transmission spectrum. The transmission components Sum, X, Y, and Z are by default included in the graph:
Tip
The drop-down menu Curves at the top-left of the window lets you choose which spin projection to include, while the lower “Active curve” option is for choosing which k-point resolved spectrum to show in the right-hand “Coefficients” plot (for this 1D system there is only one transmission coefficient, at (\(k_A\), \(k_B\))=(0,0), so the plot is rather uninteresting). This can also be chosen by clicking the corresponding transmission curve.
The Spin.Sum transmission spectrum is very similar to the parallel collinear case, and very different from the anti-parallel collinear case. This may surprise, since the spin configuration in the electrodes are more anti-parallel than parallel. However, due to the noncollinear degrees of freedom, the electron can propagate in a helical state when moving from left to right, and this allows for a high transmission. In fact, if you set the rotation angle to 180 degrees, corresponding to anti-parallel alignment of the electrodes, the result will be almost the same.
The figure below compares the transmission spectra for the collinear spin-parallel state and the noncollinear state, using the Compare Data plugin.
Spin-orbit interactions¶
Spin-orbit coupling (SOC) is most often neglected in electronic structure calculations, but it can actually be included in a noncollinear calculation, provided that suitable pseudopotentials are used. You can find more details in the tutorial Spin-orbit splitting of semiconductor band structures.
The carbon chain considered here has a very small SOC, so results with spin-orbit interactions included in the electronic structure method will hardly be different from those obtained above. Even so, if you wish to include SOC in calculations similar to the ones outlined in the section Spin rotation of 120°, simply change the exchange–correlation method and pseudopotentials used in the ATK-DFT calculator:
use spin-orbit GGA (SOGGA) exchange–correlation and SG15-SO pseudopotentials,
or use spin-orbit LDA (SOLDA) exchange–correlation and OMX pseudopotentials.
Spin-orbit GGA
When setting up the initial collinear calculation, saved as carbon_para.nc, choose SGGA exchange-corerlation instead of LSDA, and navigate to the Basis set/exchange correlation calculator settings and select the SG15-SO type pseudopotential. You will usually have the option to choose between three different basis set sizes:
Note
The density mesh cutoff should not be smaller than 100 Ha when using SG15 pseudopotentials.
Run the spin-polarized GGA calculation, which creates carbon_para.nc, and then use SOGGA.PBE exchange-correlation when setting up the calculator with spin-orbit coupling:
1# Read in the collinear calculation 2device_configuration = nlread('carbon_para.nc', DeviceConfiguration)[0] 3 4# Use the special noncollinear mixing scheme 5iteration_control_parameters = IterationControlParameters( 6 algorithm=PulayMixer(noncollinear_mixing=True) 7 ) 8 9# Get the calculator and modify it for spin-orbit GGA: 10calculator = device_configuration.calculator() 11calculator = calculator( 12 exchange_correlation=SOGGA.PBE, 13 iteration_control_parameters=iteration_control_parameters 14 )Spin-orbit LDA
When setting up the initial collinear calculation, saved as carbon_para.nc, navigate to the Basis set/exchange correlation calculator settings and select the OMX type pseudopotential. You will usually have the option to choose between different basis set sizes:
Note
The OMX potentials are in general fairly “hard”, so they often require a larger mesh cutoff than e.g. the FHI potentials, usually at least 150 Ha.
Run the spin-polarized LDA calculation, which creates carbon_para.nc, and then use SOLDA.PZ exchange-correlation when setting up the calculator with spin-orbit coupling:
1# Read in the collinear calculation 2device_configuration = nlread('carbon_para.nc', DeviceConfiguration)[0] 3 4# Use the special noncollinear mixing scheme 5iteration_control_parameters = IterationControlParameters( 6 algorithm=PulayMixer(noncollinear_mixing=True) 7 ) 8 9# Get the calculator and modify it for spin-orbit GGA: 10calculator = device_configuration.calculator() 11calculator = calculator( 12 exchange_correlation=SOLDA.PZ, 13 iteration_control_parameters=iteration_control_parameters 14 )Tip
What’s next? You should consider the tutorial Noncollinear calculations for metallic nanowires.
Noncollinear spin is essential when computing the spin transfer torque, see for example the tutorials Spin Transfer Torque and Spin transport in magnetic tunnel junctions.
The tutorials Spin-orbit splitting of semiconductor band structures and Relativistic effects in bulk gold give more details of spin-orbit calculations with ATK-DFT.
Tag » Collinear Or Noncollinear Calculator
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Collinear Or Non-Collinear Calculation - MYMATHTABLES.COM
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Collinearity - PLANETCALC Online Calculators
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Collinear Points Calculator
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Calculate Collinearity Of Three Points - EasyCalculation
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Collinear Points Free Online Calculator - Free Mathematics Tutorials
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Total Number Of Triangle Using Non Collinear Points Calculator
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Collinear Points Calculator - EndMemo
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Calculate Collinearity Of Three Points - Eguruchela
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Collinear Vectors Calculator
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Online Calculator. Collinear Vectors - OnlineMSchool
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Collinear Points - Definition, Formula, Examples - Cuemath
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Three-point Collinear Proof Calculator Online Calculation
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Collinear And Non-collinear Points In A Plane Examples - GeoGebra
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Collinear Points (Definition | Examples Of Collinear Points - Byju's