I. V. Solovyev, M. V. Valentyuk, V. V. Mazurenko
We discuss relative roles played by the magnetic inversion symmetry breaking and the ferroelectric (FE) atomic displacements in the multiferroic state of YMnO3. For these purposes we derive a realistic low-energy model, using results of first-principles calculations and experimental parameters of the crystal structure. Then, we solve this model in the Hartree-Fock approximation. We argue that the multiferroic state in YMnO3 has a magnetic origin, and the centrosymmetric Pbnm structure is formally sufficient for explaining details of the noncentrosymmetric magnetic ground state. The relativistic spin-orbit interaction lifts the degeneracy, caused by the frustration of isotropic interactions, and stabilizes a twofold periodic magnetic state, which is similar to the E-state apart from the spin canting. The noncentrosymmetric atomic displacements in the P2_1nm phase reduce the spin canting, but do not change the symmetry of the magnetic state. The effect of the P2_1nm distortion on the FE polarization P_a is twofold: (i) it gives rise to ionic contributions, associated with the Y and O sites; (ii) it affects the electronic polarization, through the change of the spin canting. The relatively small value of P_a, observed in the experiment, is caused by a partial cancelation of the electronic and ionic contributions in the experimental P2_1nm structure. Finally, we theoretically optimize the crystal structure, by using the LSDA+U approach and assuming the collinear E-type alignment. We have found that the agreement with the experimental data in this case is less satisfactory and P_a is largely overestimated. Although the magnetic structure can be formally tuned by varying the Coulomb repulsion U as a parameter, apparently LSDA+U fails to reproduce some fine details of the experimental structure, and the cancelation of different contributions in P_a does not occur.
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http://arxiv.org/abs/1208.3520
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