Skyrmion Crystal and Phase Transition in Magneto-Ferroelectric Superlattices: Dzyaloshinskii-Moriya Interaction in a Frustrated $J_1-J_2$ Model

Abstract

The formation of a skyrmion crystal and its phase transition are studied taking into account the Dzyaloshinskii-Moriya (DM) interaction at the interface between a ferroelectric layer and a magnetic layer in a superlattice. The frustration is introduced in both magnetic and ferroelectric films. The films have the simple cubic lattice structure. Spins inside magnetic layers are Heisenberg spins interacting with each other via nearest-neighbor (NN) exchange $J^m$ and next-nearest-neighbor (NNN) exchange $J^{2m}$. Polarizations in the ferroelectric layers are assumed to be of Ising type with NN and NNN interactions $J^f$ and $J^{2f}$. At the magnetoelectric interface, a DM interaction $J^{mf}$ between spins and polarizations is supposed. The spin configuration in the ground state is calculated by the steepest descent method. In an applied magnetic field $\mathbf{H}$ perpendicular to the layers, we show that the formation of skyrmions at the magnetoelectric interface is strongly enhanced by the frustration brought about by the NNN antiferromagnetic interactions $J^{2m}$ and $J^{2f}$. Various physical quantities at finite temperatures are obtained by Monte Carlo simulations. We show the critical temperature, the order parameters of magnetic and ferroelectric layers as functions of the interface DM coupling, the applied magnetic field and $J^{2m}$ and $J^{2f}$. The phase transition to the disordered phase is studied in details.\\ Keywords: kyrmions; phase transition; frustration; superlattice; magneto-ferroelectric coupling; Dzyaloshinskii-Moriya interaction; $J_1-J_2$ model; Monte Carlo simulation.

14 pages, 12 figures, published in Symmetry 2020, 12, 26; doi:10.3390/sym12010026

References in corpus (10)

• Role of the Dzyaloshinskii-Moriya interaction in multiferroic perovskites
• Additive interfacial chiral interaction in multilayers for stabilization of small individual skyrmion at room temperature
• Skyrmion Hall Effect Revealed by Direct Time-Resolved X-Ray Microscopy
• Theory of current-driven motion of Skyrmions and spirals in helical magnets
• Spin-orbit torque-driven skyrmion dynamics revealed by time-resolved X-ray microscopy
• Memory functions of magnetic skyrmions
• Antiferromagnetic skyrmion crystals: generation, topological Hall and topological spin Hall effect
• Skyrmion knots in frustrated magnets
• Vortices, skyrmions, and chirality waves in frustrated Mott insulators with a quenched periodic array of impurities
• Dzyaloshinskii-Moriya Interaction in Magneto-Ferroelectric Superlattices: Spin Waves and Skyrmions

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• Dynamic transformation between a skyrmion string and a bimeron string in a layered frustrated system
• Vortex Structure in Magnetic Nanodots: Dipolar Interaction, Mobile Spin Model, Phase Transition and Melting
• Quantum Spin-Wave Theory for non-collinear Spin Structures, a Review