Magnetic structure and multiferroic coupling in pyroxene NaFeSi2O6

By comprehensive neutron diffraction measurements we have studied the magnetic structure of aegirine (NaFeSi2O6) in and above its multiferroic phase. Natural aegirine exhibits two magnetic transitions into incommensurate magnetic order with a propagation vector of (k) over right arrow (inc) = (0, similar to 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 (P) over right arrow appearing along the b direction cannot be described by the most common multiferroic mechanism but follows (P) over right arrow proportional to ($) over right arrow (i) x (S) over right arrow (j). Synthetic NaFeSi2O6 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 NaFeSi2O6.