Magnetic and ferroelectric orderings in multiferroic α-NaFeO2

The triangular based antiferromagnet alpha-NaFeO2 has been studied by magnetization, dielectric, and neutron diffraction measurements as a function of temperature and magnetic field. The appropriate (H - T) phase diagram was constructed revealing a complex behavior due to a competition between several magnetic phases. In zero field, the system undergoes a sequence of magnetostructural transitions; initially from paramagnetic R (3) over bar m1' phase to the incommensurate spin density wave (ICM1) at T-N1 = 11 K with the nonpolar (3 + 1) magnetic superspace group C2/m1' (0, beta, 1/2)s0s, then, below T-N2 = 7.5 K, the ICM1 phase coexists with the polar cycloidal ordering (ICM2) possessing the Cm1'(0, beta, 1/2)0s superspace symmetry and finally the commensurate collinear ordering (CM) with the nonpolar magnetic space group P(a)2(1)/m develops below T-N3 = 5.5 K as the ground state of the system. A small amount of ICM2 coexists with the ICM1 and CM phases resulting in a nonzero measured polarization below T-N2. Magnetic field destabilizes the collinear ground state and promotes the polar ICM2 phase resulting in a drastic increase of the polarization. The symmetry of the zero field cycloidal structure allows the two orthogonal components p(1) proportional to r(ij) x (S-i x S-j) and p(2) proportional to S-i x S-j to contribute to the macroscopic polarization through the inverse DM effect. The applied magnetic field reduces the symmetry of the ICM2 phase down to the triclinic P-1(alpha, beta, gamma)0, resulting in admixture of another cycloidal and helical components both generating magnetic field switchable polarization p(3) perpendicular to p(1) and p(2).