Giant spin-induced polarization and optical-diode effect by electromagnons in BiFeO$_{\mathrm{3}}$

Type-$I$ multiferroics where spin and electric polarization order at distinct temperatures were believed to have smaller couplings between them compared to type-\textit{II} multiferroics such as TbMnO$_{\mathrm{3}}$. However, we recently discovered unexpectedly huge couplings between spin and electric polarization in representative type-$I$ multiferroic BiFeO$_{\mathrm{3}}$. This hidden coupling leads to record-high spin-induced ferroelectric polarizations (\textasciitilde 3.0 $\mu $C/cm$^{\mathrm{2}})$ [1] which is one or two order larger than in any other multiferroics. Also, the spin-polarization couplings in \textit{dynamic} region [2] generates strong electromagnons resulting in sizable one-way optical transparency at the spin-wave excitations [3]. Overall, we show how our theoretical results revive studies in revealing hidden but huge spin-polarization couplings and their dynamic interactions with light in type-$I$ multiferroics. [1] J. H. Lee and R. Fishman, Physical Review Letters, 115, 207203 (2015). [2] \quad J. H. Lee, I. Kezsmarki, and R. Fishman$, $New Journal of Physics 18, 043205 (2016). [3] R. Fishman, J. H. Lee \textit{et al}., Physical Review B, 92, 094422 (2015). *This work has been done by collaborations with R. Fishman (ORNL) and I. Kezsmarki (U of Budapest).