Rich magnetoelectric phase diagrams of multiferroic single-crystal α-NaFeO2

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 Bab and along Bc, respectively. In zero magnetic field, two spin-density-wave orderings with different k vectors-(0, q, 1/2) in phase I and (q(a), q(b), q(c)) in phase II-appeared at T = 9.5 and 8.25 K, respectively. Below T = 5 K, a commensurate order with k = (0.5,0,0.5) was stabilized as the ground state in phase III. Both B-ab >= 3 T and B-c >= 5 T were found to induce ferroelectric phases at the lowest temperature (2 K), with an electric polarization that was not confined to any highly symmetric directions in phases IVab (3.3 <= B-ab <= 8.5 T), V-ab (8.5 <= B-ab <= 13.6 T), IVc (5.0 <= B-c <= 8.5 T), and V-c (8.5 <= B-c <= 13.5 T). In phase VIc, within a narrow temperature region in B-c, the polarization was confined to the ab plane. For each of the ferroelectric phases, the k vector was (q(a), q(b), q(c)), and noncollinear structures were identified, including a general spiral in IVab an ab cycloid in IVc and V-c, and a proper screw in VIc, along with a triclinic 11' magnetic point group allowing polarization in the general direction. Comparing the polarization direction to the magnetic structures in the ferroelectric phases, we conclude that the extended inverse Dzyaloshinskii-Moriya mechanism expressed by the orthogonal components p1 alpha r(ij) x (S-i x S-j) and p2 alpha S-i x S-j 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.