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The spectroscopic modes of multiferroic BiFeO$_3$ provide detailed information about the very small anisotropy and Dzyaloshinskii-Moriya (DM) interactions responsible for the long-wavelength, distorted cycloid below $TN = 640$ K. A microscopic model that includes two DM interactions and easy-axis anisotropy predicts both the zero-field spectroscopic modes as well as their splitting and evolution in a magnetic field applied along a cubic axis. While only six modes are optically active in zero field, all modes at the cycloidal wavevector are activated by a magnetic field. The three magnetic domains of the cycloid are degenerate in zero field but one domain has lower energy than the other two in nonzero field. Measurements imply that the higher-energy domains are depopulated above about 6 T and have a maximum critical field of 16 T, below the critical field of 19 T for the lowest-energy domain. Despite the excellent agreement with the measured spectroscopic frequencies, some discrepancies with the measured spectroscopic intensities suggest that other weak interactions may be missing from the model.
Multiferroic BiFeO3 undergoes a transition from a distorted spiral phase to a G-type antiferromagnet above a critical field H_c that depends on the orientation m of the field. We show that H_c(m) has a maximum when oriented along a cubic diagonal par
We report the direct observation of a resonance mode in the lowest-energy optic phonon very near the zone center around (111) in the multiferroic BiFeO$_3$ using neutron scattering methods. The phonon scattering intensity is enhanced when antiferroma
Multiferroics permit the magnetic control of the electric polarization and electric control of the magnetization. These static magnetoelectric (ME) effects are of enormous interest: The ability to read and write a magnetic state current-free by an el
Using THz spectroscopy, we show that the spin-wave spectrum of multiferroic BiFeO$_3$ in its high-field canted antiferromagnetic state is well described by a spin model that violates rhombohedral symmetry. We demonstrate that the monoclinic distortio
In this article the mechanism of the linear magnetoelectric (ME) effect in the rhombohedral multiferroic BiFeO$_3$ is considered. The study is based on the symmetry approach of the GinzburgLandau type, in which polarization, antiferrodistortion, and