Incommensurate spin ordering and excitations in multiferroic SrMnGe2O6

Anisotropic multiferroic properties of $\mathrm{SrMnG}{\mathrm{e}}₂{\mathrm{O}}₆$ pyroxene single crystals were systematically investigated by means of magnetization, heat capacity, pyroelectric current measurement, and elastic and inelastic neutron-scattering experiments. Single-crystal neutron diffraction allows us to unambiguously reveal the presence of two incommensurate magnetic orderings: a nonpolar amplitude-modulated collinear sinusoidal magnetic structure emerges at ${T}_{\mathrm{N}1}=4.36(2)\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ followed by a polar elliptical cycloidal spin structure below ${T}_{\mathrm{N}2}=4.05(2)\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Pyroelectric current measurements on single crystal confirm the appearance of a spontaneous polarization within the ($ac$) plane below ${T}_{\mathrm{N}2}$ associated with the latter magnetic symmetry through the extended Dzyaloshinskii-Moriya mechanism. The magnetic phase diagram was calculated considering the three isotropic exchange couplings relevant in this system. The magnetic excitations spectra of $\mathrm{SrMnG}{\mathrm{e}}₂{\mathrm{O}}₆$ measured by inelastic neutron scattering were successfully modeled using a set of exchange interactions consistent with this phase diagram.