Temperature dependence of elastic moduli and period of magnetic spirals in cubic helimagnets with spins in non-equivalent positions

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Abstract

Critical phenomena in cubic helimagnets with nonequivalent magnetic atoms are investigated within the framework of the Weiss mean-field theory. The reason for the appearance of temperature dependences of elastic moduli and the pitch of the magnetic helicoid is found and the form of these dependences, determining the change in the conditions for the appearance of magnetic skyrmions in type II multiferroic Cu2OSeO3, is predicted.

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About the authors

V. A. Chizhikov

National Research Center “Kurchatov Institute”; MIREA — Russian Technological University

Author for correspondence.
Email: chizhikov@crys.ras.ru

Отделение “Институт кристаллографии им. А.В. Шубникова” Курчатовского комплекса кристаллографии и фотоники

Russian Federation, Moscow; Moscow

V. E. Dmitrienko

MIREA — Russian Technological University

Email: chizhikov@crys.ras.ru
Russian Federation, Moscow

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Supplementary files

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2. Fig. 1. Magnetic sublattice of the Cu2OSeO3 crystal. Sixteen copper atoms occupy Wyckoff positions 4a (Cu-I) and 12b (Cu-II) of space group P213. The spins of the atoms in nonequivalent positions (arrows) have opposite directions, making the crystal ferrimagnetic.

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3. Fig. 2. Temperature dependence of the average spins of copper atoms in two nonequivalent positions in the Cu2OSeO3 crystal, calculated in the mean field model: 1 – average spin σ1 of Cu-I atoms, 2 – average spin σ2 of Cu-II atoms, 3 – ratio σ2/σ1.

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4. Fig. 3. Temperature dependences of the elastic moduli of the magnetic structure of the Cu2OSeO3 helimagnet: orientational rigidity 𝒥 (1) and the Dzyaloshinskii–Moriya parameter 𝒟 (2), calculated within the mean field model. For ease of comparison at different temperatures, the dependences are normalized to the mean square of the spin: , , where <σ2> = (4σ12 + 12σ22)/16.

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5. Fig. 4. Temperature dependences of the wave number k (1) and the step p = 2π/k (2) of magnetic helicoids in the Cu2OSeO3 crystal, calculated within the mean field model. The helicoid step is given in the parameters a of the crystal lattice, the wave number is given in the inverse parameters.

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