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
allel to the electric polarization P and a minimum in the equatorial plane normal to P when two magnetic domains with the highest critical fields are degenerate. The measured critical field along a cubic axis is about 19 T but H_c is predicted to vary by as much as 2.5 T above and below this value. The orientational dependence of H_c(m) is more complex than indicated by earlier work, which did not consider the competition between magnetic domains.
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.
The molecule-based magnet [Ru$_2$(O$_2$CMe)$_4$]$_3$[Cr(CN)$_6$] contains two weakly-coupled, interpenetrating sublattices in a body-centered cubic structure. Although the field-dependent magnetization indicates a metamagnetic transition from an anti
ferromagnet to a paramagnet, the hysteresis loop also exhibits a substantial magnetic remanance and coercive field uncharacteristic of a typical metamagnet. We demonstrate that this material behaves like two giant moments with a weak antiferromagnetic coupling and a large energy barrier between the orientations of each moment. Because the sublattice moments only weakly depend on field in the transition region, the magnetic correlation length can be directly estimated from the magnetization.
