Spin-orbit interaction, spin-phonon coupling, and anisotropy in the giant magnetoelastic effect in YMnO3

From the energies of various noncollinearly ordered spin configurations of YMnO3 obtained using first-principles density functional theory and spin-orbit coupling, we demonstrate a remarkable magnetocrystalline anisotropy in the ordering of spins of Mn3+ ions. We find that these spins are confined in the ab plane and ordered according to the Γ3 representation of the P63cm1′ space group in the insulating ground state, consistent with the observed magnetic order. In contrast, the state with the same magnetic symmetry (Γ3) and spins oriented along the c axis is metallic, with a distinct structure and significantly higher energy. We show how the spin-orbit coupling is crucial in giving the splitting and ordering of energies of d orbitals of Mn, which determine and explain the magnitude of observed local magnetic moment at the Mn site. We uncover a strong and anisotropic coupling of spins with the phonon modes of Γ1 symmetry and strain, which is shown within a Landau theory to constitute the microscopic mechanism of giant magnetoelastic effect observed at Néel temperature in hexagonal YMnO3. The anisotropy in higher order spin-phonon coupling is evident in significantly different frequencies of the zone-center Γ1, Γ5, and Γ6 phonons of the isosymmetric magnetic states with spins along the c axis and those in the ab plane, which are proposed as the spectroscopic signatures to be verified experimentally.