Magnon spectrum of transition-metal oxides: Calculations including long-range magnetic interactions using the $\mathrm{LSDA}+U$ method

We present $\mathrm{LSDA}+U$ calculations of the magnon frequencies of transition-metal monoxides (TMOs) using the frozen magnon approach. We systematically vary $U$ to investigate the effect of the on-site Coulomb repulsion on various properties such as the gap, the magnetic moment, and the magnon energies. For all TMOs, a similar behavior of the gap and moment with respect to $U$ is found: the gaps start to increase linear and saturate for large $U$. The moment is enhanced by $\approx$$0.4{\mu }_B$ towards the pure spin limit. Magnon energies are strongly suppressed on increasing the on-site Coulomb repulsion. The reason for this behavior is related to charge localization.

Figure 1

AFM ground state (top row) and symmetry of the spin excitation (2nd and 3rd rows). The volume $V_i$ in Eq. (2) for which the on-site moment is calculated is indicated by the white sphere.

Figure 2

Example of the double index notation, where we have two magnetic atoms (located at ${\vec{\tau }}_1$ and ${\vec{\tau }}_2$) per unit cell (dashed hexagon).

Figure 3

AFM structure of the TMOs; the red balls are oxygen and the large blue ones are the TM atoms. The yellow arrows indicate the localized magnetic moments.

Figure 4

The energy surface $E_{\mathbf{q}}-E_0^{\text{AFM}}$ as a function of the angles ${\theta }_1$ and ${\theta }_2$ for NiO. The energies have been calculated with LSDA using $\mathbf{q}={\mathbf{b}}_{\mathbf{3}}/2$.

Figure 5

Gap (in eV) as a function of $U$ (in eV). The closed symbols are $\mathrm{LSDA}+U$, the open ones are $\mathrm{GGA}+U$ and the dashed lines indicate the range of reported experimental values for the gap.

Figure 6

Moment (in ${\mu }_B$) as a function of $U$ (in eV). The closed symbols are $\mathrm{LSDA}+U$, the open ones are $\mathrm{GGA}+U$, the dashed lines are the experimental values[40, 56, 57] for the moment and the solid gray lines are the pure spin limits.

Figure 7

Magnon spectrum for NiO, CoO, and MnO. LSDA results are shown with red circles, the two different values of $U$ with green squares and blue diamonds, experiment[61, 62, 63] with black triangles, and the $J_1{J}_2$ results[5] with orange line.

Figure 8

Amount of charge located in the atom muffin tin as a function of the parameter $\lambda$ [see Eq. (41)]. Plotted are always the differences to $\lambda =0$ values. The open symbols are $\mathrm{GGA}+U$, the filled are $\mathrm{LSDA}+U$ calculations. For all materials, the TM charge is plotted with red triangles, oxygen with black circles, and the interstitial region with green squares. The numbers at the right upper and lower corners denote the number of electrons in the muffin tin for the maximum value of $\lambda$.

Figure 9

Néel temperatures as a function of $U$ for NiO, CoO, and MnO. The dashed lines denote the experimental values[56] and the gray solid lines are Monte Carlo simulations.[29]