Anisotropic multiferroic properties of SrMnGe2O6 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 non-polar amplitude-modulated collinear sinusoidal magnetic structure emerges at TN1=4.36(2)K followed by a polar elliptical cycloidal spin structure below TN2=4.05(2)K. Pyroelectric current measurements on single crystal confirm the appearance of a spontaneous polarization within the (ac) plane below TN2 associated with the latter magnetic symmetry through extended Dzyaloshinsky-Moriya mechanism. The magnetic phase diagram was calculated considering the three isotropic exchange couplings relevant in this system. The magnetic excitations spectra of SrMnGe2O6 measured by inelastic neutron scattering were successfully modeled using a set of exchange interactions consistent with this phase diagram.
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