Exchange constants of the Heisenberg model in the plane-wave based methods using the Green’s function approach

Abstract:

An approach to compute exchange parameters of the Heisenberg model in plane-wave based methods is presented. This calculation scheme is based on the Green’s function method and Wannier function projection technique. It was implemented in the framework of the pseudopotential method and tested on such materials as NiO, FeO, Li2MnO3, and KCuF3. The obtained exchange constants are in a good agreement with both the total energy calculations and experimental estimations for NiO and KCuF3. In the case of FeO our calculations explain the pressure dependence of the N´eel temperature. Li2MnO3 turns out to be a Slater insulator with antiferromagnetic nearest neighbor exchange defined by the spin splitting. The proposed approach provides a unique way to analyze magnetic interactions, since it allows one to calculate orbital contributions to the total exchange coupling and study the mechanism of the exchange coupling.

RESULTS AND DISCUSSION

A. NiO 

NiO is one of the typical systems on which different calculation schemes are tested. It is a charge-transfer insulator with a band gap ∼ 4 eV [22] and local magnetic moment of 1.77µB[23]. NiO crystallizes in the rocksalt (NaCl) structure and exhibits an antiferromagnetic ordering of type-II fcc (AFM II-type) [24], with planes of opposite spins being repeated in alternating order along [111], see Fig. 1. This type of magnetic ordering is due to the strong next-nearest-neighbor (nnn) coupling between nickel ions via oxygens 2p shell. The N´eel temperature is TN = 523 K[25]. Since accounting for strong electronic correlations is crucial in the case of NiO [26], we used the LSDA+U method [27] for the calculation of electronic and magnetic properties. The on-site Coulomb repulsion and intra-atomic Hund’s rule exchange parameters were chosen to be U = 8.0 eV and JH = 0.9 eV, respectively [26]. We used the Perdew-Zunger exchange-correlation potential [28], 45 Ry and 360 Ry for the charge density and kinetic energy cutoffs, and 512 k-points in the Brillouinzone (BZ). The unit cell consists of two formula units to simulate AFM II-type. 

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https://arxiv.org/pdf/1411.4169.pdf