Regensburg 2025 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe
TUT: Tutorien
TUT 4: Tutorial: Do it Yourself Guide for Simulating Complex Magnetism: From Theoretical Foundations to Hands-on Spin-dynamics (joint session O/TUT)
TUT 4.1: Tutorium
Sonntag, 16. März 2025, 16:00–16:45, H10
Derivation of the spin-lattice Hamiltonian: Heisenberg, beyond Heisenberg, DMI, nematic exchange — •Hiroshi Katsumoto — Peter Grünberg Institut, Forschungszentrum Jülich and JARA, 52428 Jülich, Germany
Magnetization textures, such as domain walls, skyrmions, or hopfions, are very active areas of condensed matter physics. These magnetic textures are usually explained based on the Heisenberg and the relativistic Dzyaloshinskii-Moriya interaction (DMI). Comparisons with experiments have shown that, in many cases, these interactions are insufficient, and a whole range (sometimes called a zoo) of higher-order symmetric and antisymmetric interactions have been proposed. In this tutorial, based on four elemental ingredients: Coulomb interaction, indistinguishability of electrons, spin, and spin-orbit interaction (SOI), I present a framework for systematically constructing exact spin-lattice models containing all spin Hamiltonians, including higher-order terms dependent on spin quantum numbers and lattice size. Examples of spin Hamiltonians for spin-1/2 and spin-1 systems up to four lattice sites are discussed. The tutorial also explores higher-order relativistic exchange interactions derived from SOI. I consider perturbations up to the 2nd order of SOI and organize (anti)symmetric interactions. Finally, the classicalization of quantum spin relevant to magnetism in solids is discussed, culminating in a spin-lattice model that provides a theoretical framework for extracting material-dependent exchange interactions via numerical calculations and enables the modeling of magnetic textures. – DFG supports the work through SPP-2137 Skyrmionics.
Keywords: Spin Hamiltonian; Higher-order interaction; DMI; Magnetism