  The magnetic and dielectric properties of the multiferroic triangular lattice
magnet compound alpha-NaFeO2 were studied by magnetization, specific heat,
dielectric permittivity, and pyroelectric current measurements and by neutron
diffraction experiments using single crystals grown by a hydrothermal synthesis
method. This work produced magnetic field (in the monoclinic ab-plane, B_ab,
and along the c*-axis, B_c) versus temperature magnetic phase diagrams,
including five and six magnetically ordered phases in B_ab and along B_c,
respectively. Comparing the polarization direction to the magnetic structures
in the different ferroelectric phases, we conclude that the extended inverse
Dzyaloshinskii-Moriya mechanism expressed by the orthogonal components p1 ~ rij
x (Si x Sj ) and p2 ~ Si x Sj can explain the polarization directions. Based on
calculations incorporating exchange interactions up to fourth-nearest-neighbor
(NN) couplings, we infer that competition among antiferromagnetic second NN
interactions in the triangular lattice plane, as well as weak interplane
antiferromagnetic interactions, are responsible for the rich phase diagrams of
alpha-NaFeO2.
