MagneticTB

**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 topol…

4. TIGHT-BINDING 4.2 Model Hamiltonians VERIFIED
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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.

Reference Papers

Reference papers are not yet linked for this code.

Full Documentation

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

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