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We discuss relative roles played by the magnetic inversion symmetry breakingand the ferroelectric (FE) atomic displacements in the multiferroic state ofYMnO3. For these purposes we derive a realistic low-energy model, using resultsof first-principles calculations and experimental parameters of the crystalstructure. Then, we solve this model in the Hartree-Fock approximation. Weargue that the multiferroic state in YMnO3 has a magnetic origin, and thecentrosymmetric Pbnm structure is formally sufficient for explaining details ofthe noncentrosymmetric magnetic ground state. The relativistic spin-orbitinteraction lifts the degeneracy, caused by the frustration of isotropicinteractions, and stabilizes a twofold periodic magnetic state, which issimilar to the E-state apart from the spin canting. The noncentrosymmetricatomic displacements in the P2_1nm phase reduce the spin canting, but do notchange the symmetry of the magnetic state. The effect of the P2_1nm distortionon the FE polarization P_a is twofold: (i) it gives rise to ioniccontributions, associated with the Y and O sites; (ii) it affects theelectronic polarization, through the change of the spin canting. The relativelysmall value of P_a, observed in the experiment, is caused by a partialcancelation of the electronic and ionic contributions in the experimentalP2_1nm structure. Finally, we theoretically optimize the crystal structure, byusing the LSDA+U approach and assuming the collinear E-type alignment. We havefound that the agreement with the experimental data in this case is lesssatisfactory and P_a is largely overestimated. Although the magnetic structurecan be formally tuned by varying the Coulomb repulsion U as a parameter,apparently LSDA+U fails to reproduce some fine details of the experimentalstructure, and the cancelation of different contributions in P_a does notoccur.

Magnetic structure and ferroelectric activity in orthorhombic YMnO3: relative roles of magnetic symmetry breaking and atomic displacements