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

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.