We present a microscopic theory that shows the importance of spin-orbit coupling in perovskite compounds with heavy ions. In BiFeO3 (BFO) the spin-orbit coupling at the bismuth ion sites results in a special kind of magnetic anisotropy that is linear in the applied E field. This interaction can convert the cycloid ground state into a homogeneous antiferromagnet, with a weak ferromagnetic moment whose orientation can be controlled by the E-field direction. Remarkably, the E-field control of magnetism occurs without poling the ferroelectric moment, providing a pathway for reduced energy dissipation in spin-based devices made of insulators.

We have performed Raman scattering measurements on bismuth ferrite (BiFeO3) nanoparticles and studied both magnetic and lattice modes. We reveal strong anomalies between 140 K and 200 K at the frequency of magnon and E(LO1), E(TO1), and A1(LO1) phonon modes. These anomalies are related to a surface expansion and are enhanced for nanoparticle sizes approaching the spin cycloidal length. These observations point out the strong interplay between the surface, the lattice, and the magnetism for sizes of BiFeO3 nanoparticles close to cycloid periodicity.

Most multiferroic materials with coexisting ferroelectric and magnetic order exhibit cycloidal antiferromagnetism with wavelength of several nanometers. The prototypical example is bismuth ferrite (BiFeO3 or BFO), a room-temperature multiferroic considered for a number of technological applications. While most applications require small sizes such as nanoparticles, little is known about the state of these materials when their sizes are comparable to the cycloid wavelength. This work describes a microscopic theory of cycloidal magnetism in nanoparticles based on Hamiltonian calculations. It is demonstrated that magnetic anisotropy close to the surface has a huge impact on the multiferroic ground state. For certain nanoparticle sizes the modulus of the ferromagnetic and ferroelectric moments are bistable, an effect that may be used in the design of ideal memory bits that can be switched electrically and read out magnetically. arXiv:1812.08297v4 [cond-mat.mtrl-sci]