  Using first principles calculations, we study the microscopic origin of
ferroelectricity (FE) induced by magnetic order in the orthorhombic HoMnO3. We
obtain the largest ferroelectric polarization observed in the whole class of
improper magnetic ferroelectrics to date. We find that the two proposed
mechanisms for FE in multiferroics, lattice- and electronic-based, are
simultaneously active in this compound: a large portion of the ferroelectric
polarization arises due to quantum-mechanical effects of electron orbital
polarization, in addition to the conventional polar atomic displacements. An
interesting mechanism for switching the magnetoelectric domains by an electric
field via a 180-degree coherent rotation of Mn spins is also proposed.
