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The temperature scaling of the micromagnetic Dzyaloshinsky-Moriya exchangeinteraction is calculated for the whole range of temperature. We use Green'sfunction theory to derive the finite-temperature spin wave spectrum offerromagnetic systems described by a classical atomistic spin modelHamiltonian. Within this model, we find universal expressions for thetemperature scaling not only of the Dzyaloshinsky-Moriya interaction but alsoof the Heisenberg exchange stiffness and the single-ion anisotropy. In thespirit of multiscale models, we establish a clear connection between theatomistic interactions and the temperature-dependent coefficients in the spinwave spectrum and in the micromagnetic free energy functional. We demonstratethat the corrections to mean-field theory or the random phase approximation forthe temperature scaling of Dzyaloshinsky-Moriya and Heisenberg exchangeinteractions assume very similar forms. In the presence of thermal fluctuationsand Dzyaloshinsky-Moriya interaction an anisotropy-like term emerges in thespin wave spectrum which, at low temperature, increases with temperature, incontrast to the decreasing single-ion anisotropy. We evaluate the accuracy ofthe theoretical method by comparing it to the spin wave spectrum calculatedfrom Monte Carlo simulations.

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