Calculation of exchange constants of the Heisenberg model in plane-wave-based methods using the Green's function approach

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, ${\mathrm{Li}}_2{\mathrm{MnO}}_3$, and ${\mathrm{KCuF}}_3$. The obtained exchange constants are in a good agreement with both the total energy calculations and experimental estimations for NiO and ${\mathrm{KCuF}}_3$. In the case of FeO our calculations explain the pressure dependence of the Néel temperature. ${\mathrm{Li}}_2{\mathrm{MnO}}_3$ 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.

Figure 1

Schematic view of the NiO crystal structure. The blue spheres denote oxygen ions, while the gray and magenta spheres denote two magnetic types of Ni. The figure was drawn using VESTA [21] software.

Figure 2

Imaginary part of the spin-up onsite (upper panel) Green's function of Ni ion and intersite (lower panel) Green's function for the pair of the Ni ions along $c$ axis (i.e., corresponding to $J_1$). The Green's function for the $e_g$ states is shown by solid black curve, and for the $t_{2g}$ states by the solid red curve. Zero energy corresponds to the Fermi level.

Figure 3

Schematic view of the $\mathrm{KCuF}3$ crystal structure. The blue and green spheres denote Cu ions of two different types, while the violet spheres denote F ions. The potassium ion in the center of the cell is not shown for clarity.

Figure 4

Imaginary part of the spin-down onsite (upper panel) Green's function of Cu ion and intersite (lower panel) Green's function for two Cu ions corresponding to $J_1$. The Green's function for $e_g$ states is shown by the solid black line, for $t_{2g}$ states by the solid red one. Zero energy corresponds to the Fermi level.

Figure 5

Crystal structure of ${\mathrm{Li}}_2{\mathrm{MnO}}_3$. Mn ions, shown by blue balls, are in octahedral surrounding of the O ions (red balls) and form honeycomb lattice, with Li (green balls) in the center of the honeycombs. These 2D hexagonal planes are stacked in the $c$ direction with Li ions in between.

Figure 6

Spin-polarized density of electronic states for ${\mathrm{Li}}_2{\mathrm{MnO}}_3$ obtained in the magnetic GGA calculation. Zero energy corresponds to the Fermi level.