Unbiased first-principles construction of complete tensorial spin Hamiltonians
Abstract
Magnetic ground states are commonly predicted using spin Hamiltonians whose interaction terms are selected a priori, potentially overlooking the microscopic interactions that govern complex magnetic order. Here, we introduce a general framework for the unbiased first-principles construction of symmetry-complete tensorial spin Hamiltonians and its automated implementation in AMATIS. The framework constructs the Hamiltonian directly from density-functional theory while rigorously enforcing quantum spin algebra and crystallographic symmetry. Applied to representative two-dimensional van der Waals magnets, the framework reproduces established magnetic interactions and uncovers hidden physics beyond conventional spin models, including chiral interactions that stabilize metastable skyrmions, higher-rank tensorial interactions that reconstruct the magnetic phase diagram and establish stabilizing competing multi-Q phases, and an emergent p-wave altermagnetic electronic structure. Our results demonstrate that unbiased tensorial Hamiltonian construction provides a predictive alternative to the conventional practice of manually selecting spin-model interactions, enabling first-principles discovery of unconventional magnetic phases.
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BibTeX
@misc{lu2026unbiased,
title = {{Unbiased first-principles construction of complete tensorial spin Hamiltonians}},
author = {Haichang Lu and Boyang Deng and Hiroshi Katsumoto and John Robertson and Weisheng Zhao and Stefan Blügel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13912},
eprint = {2609.13912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13912},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Unbiased first-principles construction of complete tensorial spin Hamiltonians
AU - Haichang Lu
AU - Boyang Deng
AU - Hiroshi Katsumoto
AU - John Robertson
AU - Weisheng Zhao
AU - Stefan Blügel
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13912
UR - https://arxiv.org/abs/2609.13912
AB - Magnetic ground states are commonly predicted using spin Hamiltonians whose interaction terms are selected a priori, potentially overlooking the microscopic interactions that govern complex magnetic order. Here, we introduce a general framework for the unbiased first-principles construction of symmetry-complete tensorial spin Hamiltonians and its automated implementation in AMATIS. The framework constructs the Hamiltonian directly from density-functional theory while rigorously enforcing quantum spin algebra and crystallographic symmetry. Applied to representative two-dimensional van der Waals magnets, the framework reproduces established magnetic interactions and uncovers hidden physics beyond conventional spin models, including chiral interactions that stabilize metastable skyrmions, higher-rank tensorial interactions that reconstruct the magnetic phase diagram and establish stabilizing competing multi-Q phases, and an emergent p-wave altermagnetic electronic structure. Our results demonstrate that unbiased tensorial Hamiltonian construction provides a predictive alternative to the conventional practice of manually selecting spin-model interactions, enabling first-principles discovery of unconventional magnetic phases.
ER -