Neutron scattering studies of the ferroelectric distortion and spin dynamics in the type-1 multiferroic perovskiteSr0.56Ba0.44MnO3

The magnetic order, spin dynamics, and crystal structure of the multiferroic ${\mathrm{Sr}}_{0.56}{\mathrm{Ba}}_{0.44}{\mathrm{MnO}}_3$ have been investigated using neutron and x-ray scattering. Ferroelectricity develops at $T_C=305$ K with a polarization of 4.2 $\mu {\mathrm{C}/\mathrm{cm}}^2$ associated with the displacements of the Mn ions, while the ${\mathrm{Mn}}^{4+}$ spins order below $T_N\approx 200$ K into a simple $G$-type commensurate magnetic structure. Below $T_N$ the ferroelectric order decreases dramatically, demonstrating that the two order parameters are strongly coupled. The ground state spin dynamics is characterized by a spin gap of 4.6(5) meV and the magnon density of states peaking at 43 meV. Detailed spin wave simulations with a gap and isotropic exchange of $J=4.8\left(2\right)$ meV describe the excitation spectrum well. Above $T_N$ strong spin correlations coexist with robust ferroelectric order.