Abstract
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 BiFeO below 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 along induces a cycloid with wave vector (), easy-axis anisotropy along the direction of the electric polarization induces higher harmonics of the cycloid, which split the modes at 2.49 and 2.67 meV and activate the 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 along 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 and modes, although their scattering intensities remain extremely weak. Even in the absence of easy-axis anisotropy, produces cycloidal harmonics that split and activate . However, the observed mode frequencies and selection rules require that both and are nonzero. This work also resolves an earlier disagreement between spectroscopic and inelastic neutron-scattering measurements.
- Received 19 February 2013
DOI:https://doi.org/10.1103/PhysRevB.87.134416
©2013 American Physical Society