Spin state and spectroscopic modes of multiferroic BiFeO3

Spectroscopic modes provide the most sensitive probe of the very weak interactions responsible for the properties of the long-wavelength cycloid in the multiferroic phase of BiFeO3 below T-N approximate to 640 K. Three of the four modes measured by terahertz (THz) and Raman spectroscopies were recently identified using a simple microscopic model. While a Dzyaloshinskii-Moriya (DM) interaction D along [-1,2,-1] induces a cycloid with wave vector (2 pi/a)(0.5 + delta, 0.5,0.5 - delta) (delta approximate to 0.0045), easy-axis anisotropy K along the [1,1,1] direction of the electric polarization P induces higher harmonics of the cycloid, which split the Psi(1) modes at 2.49 and 2.67 meV and activate the Phi(2) mode at 3.38 meV. However, that model could not explain the observed low-frequency mode at about 2.17 meV. We now demonstrate that an additional DM interaction D' along [1,1,1] not only produces the observed weak ferromagnetic moment of the high-field phase above 18 T but also activates the spectroscopic matrix elements of the nearly degenerate, low-frequency Psi(0) and Phi(1) modes, although their scattering intensities remain extremely weak. Even in the absence of easy-axis anisotropy, D' produces cycloidal harmonics that split Psi(1) and activate Phi(2). However, the observed mode frequencies and selection rules require that both D' and K are nonzero. This work also resolves an earlier disagreement between spectroscopic and inelastic neutron-scattering measurements. DOI: 10.1103/PhysRevB.87.134416