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

We discuss the 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 electronic structure calculations and experimental parameters of the crystal structure below and above the FE transition. Then, we solve this model in the mean-field 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 the main details of the noncentrosymmetric magnetic ground state. The relativistic spin-orbit interaction lifts the degeneracy, caused by the frustration of isotropic exchange interactions in the ab plane, and stabilizes a twofold periodic noncollinear magnetic state, which is similar to the E state apart from the spin canting. The noncentrosymmetric atomic displacements in the P2(1)nm phase reduce the spin canting, but do not change the symmetry of the magnetic state. The effect of the P2(1)nm distortion on the FE polarization Delta P-a, parallel to the orthorhombic a axis, is twofold: (i) It gives rise to ionic contributions, associated with the oxygen and yttrium sites; (ii) it affects the electronic polarization, mainly through the change of the spin canting. The relatively small value of Delta P-a, observed in the experiment, is caused by a partial cancellation of the electronic and ionic contributions, as well as different contributions in the ionic part, which takes place for the experimental P2(1)nm structure. The twofold periodic magnetic state competes with the fourfold periodic one and, even in the displaced P2(1)nm phase, these two states continue to coexist in a narrow energy range. Finally, we theoretically optimize the crystal structure. For these purposes we employ the LSDA+U approach and assume the collinear E-type antiferromagnetic alignment. Then, we use the obtained structural information again as the input for the construction and solution of the low-energy model. We have found that the agreement with the experimental data in this case is less satisfactory and |Delta 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 cancellation of different contributions in Delta P-a does not occur.