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Mechanisms and origin of multiferroicity

Motivated by the potential applications of their intrinsic cross-coupling properties, the interest in multiferroic materials has constantly increased recently, leading to significant experimental and theoretical advancements. From the theoretical point of view, recent progresses have allowed to identify different mechanisms responsible for the appearence of ferroelectric polarization coexisting with -- and coupled to -- magnetic properties. This chapter aims at reviewing the fundamental mechanisms devised so far, mainly in transition-metal oxides, which lie at the origin of multiferroicity.