We investigated, by using soft x rays, one of the most fundamental properties in multiferroics, that is, coupled or decoupled feature among coexisting multiple (anti)ferroic order parameters for two types of multiferroic hexaferrites. Circular dichroic signals observed at x-ray resonance for diffraction and absorption enable us to resolve several kinds of magnetic domains, which are spatial distributions of the respective order parameters. We examined magnetic field effects on the domains and unveiled the features of the order parameters. It is found that the coupled or decoupled features of the order parameters are explained by the symmetry analysis based on the Landau theory. These findings contribute to an understanding of magnetoelectric couplings in multiferroics and to exploiting a wide variety of their functionalities. In addition, we suggest a circular dichroic specular off-peak scattering at resonance as a powerful technique for studying a surface state of a magnetic order in an expansive range of quantum materials.
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