Symmetry Analysis of Magnetoelectric Effects in Honeycomb Antiferromagnet Co₄Nb₂O₉

Abstract

Magnetoelectric effects in honeycomb antiferromagnet Co4Nb2O9 are investigated on the basis of symmetry analyses of Co 2+ ions in trigonal P3c1 space group. For each Co 2+ ion, the possible spin dependence is classified by C3 point-group symmetry. This accounts for the observed main effect that an electric polarization rotates in the opposite direction at the twice speed relative to the rotation of the external magnetic field applied in the ab-plane. Inversion centers and twofold axes in the unit cell restrict the active spin-dependence of the electric polarization, which well explains the observed experimental results. Expected optical properties of quadrupolar excitation and various types of dichroism are also discussed. arXiv:1908.03004v1 [cond-mat.str-el]

Theoretical Study of Magnetoelectric Effects in Honeycomb Antiferromagnet Co4Nb2O9

“…For Co 4 Nb 2 O 9 , we clarified that only the type-II theory accounts for both the 2θ-rotation and the field-sweeping process. We conclude that they originate from the local quadrupoles of the O x 2 −y 2 = (S x ) 2 − (S y ) 2 and O xy = S x S y + S y S x types [8]. This is because that O x 2 −y 2 (A) − O x 2 −y 2 (B) and O xy (A) − O xy (B) combinations can be realized [12].…”

“…When the magnetic ion occupies a site lacking the inversion symmetry as in honeycomb lattices, the electric dipole can be described by the product of spin operators at the same site (type-II theory), and we also present Table III for the type-II theory [8]. Notice that Tables I, II, and III are general and applicable to other honeycomb antiferromagnets such as BaNi 2 (PO 4 ) 2 [16], BaNi 2 V 2 O 8 [17], and MnPS 3 [18].…”

“…Table III. Electric polarization induced by product of spin operators at the same site (type-II theory) [8]. K 1 , K 1 , K 2 , and K 2 are independent coefficients.…”

“…In Ref. 8, we reported that the observed magnetoelectric effect of the 2θ-rotation and the field-sweeping process can be well explained by the type-II theory. In this paper, we also explore another possibility on the basis of the type-I theory.…”

“…As shown in Fig. 2(b), the expectation values of the spin operators on the two sublattices are expressed as [8]…”