Regensburg 2022 – scientific programme
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MA: Fachverband Magnetismus
MA 14: Cooperative Phenomena: Spin Structures and Magnetic Phase Transitions
MA 14.3: Talk
Tuesday, September 6, 2022, 10:15–10:30, H47
Derivation of Spin Hamiltonian by Algebraic Methods — •Hiroshi Katsumoto1, Fabian Lux1,2, Yuriy Mokrousov1,2, and Stefan Blügel1 — 1Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, 52425 Jülich, Germany — 2Institute of Physics, Johannes Gutenberg University Mainz, 55099 Mainz, Germany
Complex magnetism is known to emerge from competing Heisenberg interactions and higher-order spin interactions [1]. In addition, previously unknown interactions such as the Chiral-Chiral interaction due to topological orbital magnetism turn also out to be essential to explain the magnetic properties [2]. However, a method for uniquely deriving spin Hamiltonians that captures the spin interactions of a given system has not yet been established. In this presentation, we give rigorous spin Hamiltonians for isotropic spin interactions for a given total localized spin S and the number of magnetic sites. The derivation of the spin Hamiltonian is based on the algebraic structure that the spin operators follow for arbitrary spin magnitude. By organizing the algebraic structure obeyed by the general spin operators, we discuss the construction of the exact spin Hamiltonian and the higher-order terms of interactions, especially for the cases S = 1/2 and 1.
We acknowledge funding from the European Research Council grant 856538 (project "3D MAGIC"); and Deutsche Forschungsgemeinschaft (DFG) through SPP-2137 and SFB-1238 (project C1).
[1] M. Hoffmann et al., Phy. Rev. B 101, 024418 (2020).
[2] S. Grytsiuk et al., Nat. Commun. 11, 511 (2020).