  The coupling between ferroelectric and magnetic orders in multiferroic
materials and the nature of magnetoelectric (ME) effects are enduring
experimental challenges. In this work, we have studied the response of
magnetization to ferroelectric switching in thin-film hexagonal YbFeO3, a
prototypical improper multiferroic. The bulk ME decoupling and potential
domain-wall ME coupling were revealed using x-ray magnetic circular dichroism
(XMCD) measurements with in-situ ferroelectric polarization switching. Our
Landau theory analysis suggests that the bulk ME-coupled ferroelectric
switching path has a higher energy barrier than that of the ME-decoupled path;
this extra barrier energy is also too high to be reduced by the magneto-static
energy in the process of breaking single magnetic domains into multi-domains.
In addition, the reduction of magnetization around the ferroelectric domain
walls predicted by the Landau theory may induce the domain-wall ME coupling in
which the magnetization is correlated with the density of ferroelectric domain
walls. These results provide important experimental evidence and theoretical
insights into the rich possibilities of ME couplings in hexagonal ferrites,
such as manipulating the magnetic states by an electric field.
