We've been looking at HamGNN recently and its ability to predict the Hamiltonian of any crystal quickly via GNN. Orders of magnitude faster than traditional DFT.
Currently, only a spin-independent universal model has been publish, but soon a universal model with SOC effects will be published.
Below is a practical “menu” of what you can do once you have a Hamiltonian, grouped by how much spin information it carries. The lists are far from exhaustive, but they cover the quantities most people actually compute in materials workflows.
(e.g. non-magnetic DFT, tight binding without spin)
Category | Typical outputs you can trust | Remarks |
|---|---|---|
Electronic structure | Band energies E(k), density of states (DOS), Fermi surface, effective masses |
Good for semiconductors, simple metals where spin splitting is negligible |
Charge-based transport | Electrical conductivity, Seebeck coefficient, mobility (Boltzmann or Landauer) | Assumes spin-degenerate channels (factor-of-2 symmetry) |
Optics (spin-averaged) | Dielectric function ε(ω), joint DOS, absorption spectra | Ignores circular-dichroism & spin-selection rules |
Total energies & forces | Equation of state, phonons (via force constants), electron-phonon coupling (spin-averaged) | Magnetic contributions missing, so MAE, DMI, etc. are zero by construction |
Simple topology | Chern numbers of spin-less models, Hofstadter bands, spinless quantum Hall phases | Works only if the real-world system truly behaves spin-less (rare) |
(separate ↑ and ↓ blocks, but no spin-orbit coupling)
Adds a degree of freedom for magnetism but still treats spin as a good quantum number aligned along one axis.
Extra things you unlock | Why the scalar version can’t give them |
|---|---|
Magnetic moments (local & total), exchange splitting | Need separate ↑ / ↓ occupations |
Stoner criterion, itinerant-magnet stability | Depends on spin-resolved DOS at E_F |
Heisenberg J-couplings, Curie temperature estimates | Map energy differences between spin configurations |
Spin-dependent transport: TMR, GMR in collinear stacks | Requires spin-channel-resolved transmission |
Spin filtering in molecules & junctions | Transmission matrix must keep track of spin label |
Limitations: no spin mixing ⇒ no anisotropy, no Rashba, no DMI, no topological insulator gaps; magnetisation direction fixed by hand.
(2 × 2 spin blocks with off-diagonal SOC terms; what Uni-HamGNN predicts)
This is the “relativistic” Hamiltonian; it couples orbital motion to spin and allows arbitrary magnetisation directions.
New physics you can now model | Typical derived quantities |
|---|---|
Magnetocrystalline anisotropy (MAE) | constants, easy-axis direction |
Dzyaloshinskii–Moriya interaction (DMI) | Spiral pitch, Skyrmion stability maps |
Spin textures in k-space | Rashba & Dresselhaus splitting, spin-momentum locking |
Topological band indices | invariants, Chern numbers with spin, Weyl node chirality & positions |
Berry curvature–driven responses | Intrinsic spin Hall & anomalous Hall conductivity, valley Hall effect |
Orbital magnetic moments | Needed for g-factor predictions, XMCD analysis |
Optical & magneto-optical effects | Circular dichroism (MCD), Kerr & Faraday rotation |
Spin-torque & damping parameters | From Kubo or scattering-matrix formalisms |
Spin-dependent scattering | Elliot–Yafet spin relaxation, spin-orbit torque efficiencies |
Quantised edge & surface states | TI/TCI surface Dirac cones, Fermi-arc spectra in Weyl semimetals |
Side bonus: once spin-orbit is there, you can always “collapse” back to the collinear or scalar cases by zeroing SOC or enforcing a single spin channel, but the reverse is not possible without new calculations.
Is the material magnetic or are you interested in spin transport?
Yes → at least a collinear spin-polarised Hamiltonian.
Do you care about anisotropy, topological protection, valley physics, heavy elements, or Berry-curvature-driven phenomena?
Yes → you must include spin-orbit coupling (full 2 × 2 blocks).
Otherwise (e.g. silicon electronics, basic phonon spectra, many organic semiconductors), a spin-independent Hamiltonian is often sufficient and cheaper.
Rule of thumb:
Anything that changes when you rotate a magnetisation vector, break inversion symmetry, or look at individual spin channels will be wrong unless SOC is in the Hamiltonian.