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Theory of Spin-Orbit Enhanced Electric-Field Control of Magnetism in Multiferroic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>BiFeO</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:math>
We present a microscopic theory that shows the importance of spin-orbit coupling in perovskite compounds with heavy ions. In ${\mathrm{BiFeO}}_{3}$ (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 …