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Mankovsky, Sergiy; Polesya, Svitlana und Ebert, Hubert (2021): Topologically driven three-spin chiral exchange interactions treated from first principles. In: Physical Review B, Bd. 104, Nr. 5, 54418

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Abstract

The mechanism behind the three-spin chiral interaction (TCI) included in the extended Heisenberg Hamiltonian and represented by an expression worked out recently [Phys. Rev. B 101, 174401 (2020)] is discussed. It is stressed that this approach provides a unique set of the multispin exchange parameters that are independent of each other either due to their different order of perturbation or due to different symmetry. This ensures in particular the specific properties of the TCI that were demonstrated previously via fully relativistic first-principles calculations, and that result from the common influence of several issues not explicitly seen from the expression for the TCI parameters. Therefore, an interpretation of the TCI is suggested, showing explicitly its dependence on the relativistic spin-orbit coupling and on the topological orbital susceptibility (TOS). This is based on an expression for the TOS that is worked out on the same footing as the expression for the TCI. Using first-principles calculations, we demonstrate in addition numerically the common topological properties of the TCI and TOS. To demonstrate the role of the relativistic spin-orbit coupling (SOC) for the TCI, a so-called topological spin susceptibility is introduced. This quantity characterizes the SOC-induced spin magnetic moment on the atom in the presence of noncollinear magnetic structure, giving a connection between the TOS and TCI. Numerical results again support our conclusions.

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