Project C10: Phys. Rev. B 2017

Temperature scaling of the Dzyaloshinsky-Moriya interaction in the spin wave spectrum

The temperature scaling of the micromagnetic Dzyaloshinsky-Moriya exchange interaction is calculated from saturated to vanishing magnetization. We use Green's function theory to derive the finite-temperature spin wave spectrum of ferromagnetic systems described by a classical atomistic spin model Hamiltonian with temperature-independent parameters. Within this model, we find universal expressions for the temperature scaling not only of the Dzyaloshinsky-Moriya interaction but also of the Heisenberg exchange stiffness and the single-ion anisotropy. In the spirit of multiscale models, we establish a clear connection between the atomistic interactions and the temperature-dependent coefficients in the spin wave spectrum and in the micromagnetic free-energy functional. We demonstrate that the corrections to mean-field theory or the random phase approximation for the temperature scaling of Dzyaloshinsky-Moriya and Heisenberg exchange interactions have very similar forms. In the presence of thermal fluctuations and Dzyaloshinsky-Moriya interaction an anisotropylike term emerges in the spin wave spectrum which, at low temperature, increases with temperature, in contrast to the decreasing single-ion anisotropy. We evaluate the accuracy of the theoretical method by comparing it to the spin wave spectrum calculated from Monte Carlo simulations.

Levente Rózsa, Unai Atxitia and Ulrich Nowak
Phys. Rev. B 96, 094436 (2017)
DOI: 10.1103/PhysRevB.96.094436