Official Resources
- Homepage: https://github.com/zhangzeyingvv/MagneticTB
- Repository: https://github.com/zhangzeyingvv/MagneticTB
- License: GPL-3.0
Overview
MagneticTB is a Mathematica package designed for the automated construction of tight-binding models for materials with any of the 1651 Magnetic Space Groups (MSGs). It greatly simplifies the theoretical modeling of magnetic topological materials by automatically generating symmetry-allowed Hamiltonian matrices based on user-supplied Wyckoff positions and orbital characters.
Scientific domain: Topological Magnetism, Symmetry Analysis
Target user community: Theorists building effective models for magnetic systems
Theoretical Methods
- Magnetic Space Group Theory: Full implementation of the representation theory for all 1651 magnetic space groups (Type I, II, III, IV).
- Symmetry-Adapted Models: Construction of invariant Hamiltonian terms.
- Corepresentations: Handling of anti-unitary symmetries (Time-Reversal * Geometric operation).
- Wyckoff Positions: Input atoms based on standard crystallographic sites.
Capabilities
- Model Generation:
- Spinless and Spinful models.
- Inclusion of Spin-Orbit Coupling (SOC).
- Input:
- MSG number (BNS or OG setting).
- Orbitals (s, p, d, f) on specific sites.
- Output:
- Parameterized Hamiltonian matrix $H(\mathbf{k})$.
- Relationships between hopping parameters enforced by symmetry.
- Interoperability: Can export models for use in other codes or numerical analysis.
Key Strengths
- Automation: Removes the tedious and error-prone process of manually deriving symmetry constraints for complex magnetic Unit cells.
- Completeness: Supports the full table of magnetic space groups, not just the non-magnetic ones.
- Integration: Works within Mathematica, allowing immediate symbolic manipulation of the result.
Inputs & Outputs
- Inputs: Mathematica function calls specifying the group and orbitals.
- Outputs: Symbolic matrices and rules for parameters.
Interfaces & Ecosystem
- MagneticKP: Companion package for k·p models.
- WannierTools: Models can be exported for topological surface state calculation.
Performance Characteristics
- Speed: Symbolic generation is generally fast (seconds to minutes) for standard unit cells.
- Scaling: Capability depends on the number of orbitals; very large bases might slow down symbolic algebra.
Comparison with Other Codes
- vs. Pybinding: Pybinding builds numerical models for known Hamiltonians. MagneticTB derives the Hamiltonian from symmetry.
- vs. TB2J: TB2J extracts magnetic parameters from DFT. MagneticTB constructs the model form from symmetry principles.
Application Areas
- Antiferromagnetic Spintronics: Modeling collinear and non-collinear antiferromagnets.
- Chiral Magnets: Studying topological band crossings in magnetic systems.
Community and Support
- Development: Institute of Physics, CAS (Zeying Zhang).
- Source: GitHub.
Verification & Sources