Spin and orbital orderings behind multiferroicity in delafossite and related compounds

Abstract

Coupling between noncollinear magnetic ordering and ferroelectricicty in magnetoelectric multiferroics has been extensively studied in the last decade. Delafossite family compounds with triangular lattice structure provide a great opportunity to study the coupling between spin and electric dipole in multiferroics due to the variety of magnetic phases with different symmetry. This review introduces the magnetic and ferroelectric phase transitions in delafossite ferrites, CuFe(1-x)X(x)O(2) (X = Al, Ga), AgFeO(2) and the related compound α-NaFeO(2). In CuFeO(2), the ferroelectric phase appears under a magnetic field or chemical substitution. The proper screw magnetic ordering with the magnetic point group 21', which has been determined by detailed analysis in neutron diffraction experiments, induces the ferroelectric polarization along the monoclinic b axis in CuFeO2. The cycloidal magnetic orderings are realized in AgFeO(2) and α-NaFeO(2), which are of the point group m1' allowing polarization in the ac plane. The emergence of ferroelectric polarization can be explained by both the extended inverse Dzyaloshinsky-Moriya effect and the d − p hybridization mechanism. These mechanisms are supported by experimental evidence in CuFe(1-x)Ga(x)O2. The polarized neutron diffraction experiment demonstrated one-to-one correspondence between ferroelectric polarization and spin helicity, S(i) × S(j). The incommensurate orbital ordering with 2 Q wave vector, observed by the soft x-ray resonant diffraction experiment, proved that the spin-orbit interaction ties spin and orbital orders to each other, playing a crucial role for the emergence of ferroelectricity in CuFe(1-x)Ga(x)O2.

Magnetic ordering and ferroelectricity in multiferroic2H−AgFeO2: Comparison between hexagonal and rhombohedral polytypes

“…This is consistent with the lack of the electric polarization in the temperature range of 11 K T 14 K. In the refinement procedure, we constrained the values of the magnetic moments to be identical in the ICM2 and ICM3 phases. The magnetic structure of the ICM2 phase determined in the present work for the 2H -AgFeO 2 polytype is similar to the magnetic polar phase found in CuFe 1−x Ga x O 2 [15,20,22]. The magnetic point symmetries, however, are different, nonpolar 2221 ′ in the former and polar 21 ′ in the later cases.…”

57Fe Mössbauer study of unusual magnetic structure of multiferroic 3R-AgFeO2

“…The Neel temperature is given in the form T N = aJ(q), where J(q) is the Fourier transform of the exchange integral J(r i ), and q is the propagation vector representing the magnetic structure. Taking into account the almost complete coincidence of the T N1 values of CuFeO 2 (T N1 = 16 K, [9]) and AgFeO 2 (T N1 = 14(1) K, Fig. 2), the observed increase of frustration (Q CW /T N ) in the case of AgFeO 2 may be ascribed to the strengthening of its own magnetic interactions.…”

“…The copper ferrite has a collinear foursublattice (4SL) ground state ¯¯ with a commensurate propagation vector Q = (0, ½, ½) m [10] in the monoclinic cell. At the same time, according to recent neutron diffraction experiments [9,12], the magnetic ordering in 3R-AgFeO 2 …”

Magnetoelectric properties of multiferroic CuCrO2 studied by means of ab initio calculations and Monte Carlo simulations

“…The electric polarization emerges upon the spiral-spin ordering [20,30,31], which reflects the strong coupling between non-collinear magnetic ordering and ferroelectricity in CuCrO 2 . Within the spin-current model or the inverse Dzyaloshinskii-Moriya (DM) mechanism [32][33][34], the electric polarization P ij produced between the canted spins S i and S j , located at sites i and j, respectively, is given by…”