Abstract
In this article, we focus on (1) type-II multiferroics driven by spiral spin orderings and (2) magnetoelectric couplings in multiferroic skyrmion-hosting materials. We present both phenomenological understanding and microscopic mechanisms for spiral spin state, which is one of the essential starting points for type-II multiferroics and magnetic skyrmions. Two distinct mechanisms of spiral spin states (frustration and Dzyaloshinskii–Moriya [DM] interaction) are discussed in the context of the lattice symmetry. We also discuss the spin-induced ferroelectricity on the basis of the symmetry and microscopic atomic configurations. We compare two well-known microscopic models: the generalized inverse DM mechanism and the metal-ligand d-p hybridization mechanism. As a test for these models, we summarize the multiferroic properties of a family of triangular-lattice antiferromagnets. We also give a brief review of the magnetic skyrmions. Three types of known skyrmion-hosting materials with multiferroicity are discussed from the view point of crystal structure, magnetism, and origins of the magnetoelectric couplings. For exploration of new skyrmion-hosting materials, we also discuss the theoretical models for stabilizing skyrmions by magnetic frustration in centrosymmetric system. Several basic ideas for material design are given, which are successfully demonstrated by the recent experimental evidences for the skyrmion formation in centrosymmetric frustrated magnets.
Estimation for the Double Rayleigh Distribution Based on Multiply Type-II Censored Samples