Abstract
Due to the complicated magnetic and crystallographic structures of BiFeO3, its magnetoelectric (ME)
couplings and microscopic model Hamiltonian remain poorly understood. By employing a firstprinciples
approach, we uncover all possibleMEcouplings associated with the spin-current (SC) and
exchange-striction (ES) polarizations, and construct an appropriate Hamiltonian for the long-range
spin-cycloid in BiFeO3. First-principles calculations are used to understand the microscopic origins of
theMEcouplings.Wefind that inversion symmetries broken by ferroelectric and antiferroelectric
distortions induce the SC and the ES polarizations, which cooperatively produce the dynamicME
effects in BiFeO3. A model motivated by first principles reproduces the absorption difference of
counter-propagating light beams called non-reciprocal directional dichroism. The current paper
focuses on the spin-driven (SD) polarizations produced by a dynamic electric field, i.e. the dynamic
MEcouplings. Due to the inertial properties of Fe, the dynamic SD polarizations differ significantly
from the static SD polarizations. Our systematic approach can be generally applied to any multiferroic
material, laying the foundation for revealing hiddenMEcouplings on the atomic scale and for
exploiting opticalMEeffects in the next generation of technological devices such as optical diodes.
