Magnetic structure and multiferroic coupling in pyroxeneNaFeSi2O6

Abstract

By comprehensive neutron diffraction measurements we have studied the magnetic structure of aegirine $({\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6})$ in and above its multiferroic phase. Natural aegirine exhibits two magnetic transitions into incommensurate magnetic order with a propagation vector of ${\stackrel{P\vec}{k}}_{\mathrm{inc}}=(0,\ensuremath{\sim}0.78,0)$. Between 9 and 6 K, we find a transverse spin-density wave with moments pointing near the $c$ direction. Below 6 K, magnetic order becomes helical and spins rotate in the $ac$ plane. The same irreducible representation is involved in the two successive transitions. In addition, the ferroelectric polarization $\stackrel{P\vec}{P}$ appearing along the $b$ direction cannot be described by the most common multiferroic mechanism but follows $\stackrel{P\vec}{P}\ensuremath{\propto}{\stackrel{P\vec}{S}}_{i}\ifmmode\times\else\texttimes\fi{}{\stackrel{P\vec}{S}}_{j}$. Synthetic ${\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6}$ does not exhibit the pure incommensurate helical order but shows coexistence of this order with a commensurate magnetic structure. By applying moderate pressure to natural aegirine, we find that the incommensurate magnetic ordering partially transforms to the commensurate one, underlining the nearly degenerate character of the two types of order in ${\mathrm{NaFeSi}}_{2}{\mathrm{O}}_{6}$.