Electronic correlation and spin-orbit coupling in J1-J2 square lattice antiferromagnetism MoOPO4

We investigated the electronic and magnetic properties of the tetragonal molybdenum phosphate MoOPO4 by means of first-principles calculations based on the density functional theory within the semilocal generalized gradient approximation that includes the Hubbard repulsion term to take into account the electronic correlations. Furthermore, the spin-orbit coupling is explored through noncollinear magnetic calculations. Our results demonstrated that the Néel ordering on the square lattice plane, experimentally observed, is indeed the magnetic ground state on condition that the effective electronic correlation correction is smaller than 2.0 eV. Otherwise, the ferromagnetic alignment is established. In addition, the out-of-plane ferromagnetic interaction is well reproduced. The computed exchange constants, extracted from the classical Heisenberg model, show that the modest antiferromagnetic in-plane nearest-neighbor coupling plays a decisive role in the stabilization of the Néel spin alignment, in conjunction with the remarkable ferromagnetic in-plane next nearest-neighbor interaction. Moreover, the sign and relative amplitude of the exchange coupling parameters is sensitive to the correlation strength we applied. The density of states and spin density analysis demonstrated that the exclusively occupied dxy orbital results in the pure S = 1/2 spin moment and negligible spin-orbit coupling, which is originated from the large displacement of Mo ions inside the MoO6 octahedra along the apical direction.