  Multiferroics are materials where two or more ferroic orders coexist owing to
the interplay between spin, charge, lattice and orbital degrees of freedom. The
explosive expansion of multiferroics literature in recent years demon-strates
the fast growing interest in this field. In these studies, the first-principles
calculation has played a pioneer role in the experiment explanation, mechanism
discovery and prediction of novel multiferroics or magnetoelectric materials.
In this review, we discuss, by no means comprehensively, the extensive
applications and successful achievements of first-principles approach in the
study of multiferroicity, magnetoelectric effect and tunnel junc-tions. In
particular, we introduce some our recently developed methods, e.g., the orbital
selective external potential (OSEP) method, which prove to be powerful tools in
the finding of mechanisms responsible for the intriguing phe-nomena occurred in
multiferroics or magnetoelectric materials. We also summarize first-principles
studies on three types of electric control of magnetism, which is the common
goal of both spintronics and multiferroics. Our review offers in depth
understanding on the origin of ferroelectricity in transition metal oxides, and
the coexistence of fer-roelectricity and ordered magnetism, and might be
helpful to explore novel multiferroic or magnetoelectric materi-als in the
future.
