Fig. 5
From: Massive Dirac magnons in the three-dimensional honeycomb magnetic oxide \(\hbox {FeTiO}_3\)
Topological characteristics of \(\hbox {FeTiO}_3\) calculated for the DM model including \(J_1\), \(J_2\), \(J_3\), and \(|\textbf{A}|\) listed in Table 1. (a) The arrows show the in-plane directions of \(\hat{\textbf{h}}(\textbf{Q})\) or \((h_x, h_y)/|\textbf{h}|\) in Eq. (3). The colored contours superposed on them show the out-of-plane component \(h_z/|\textbf{h}|\). (b) Topological Berry curvature of the magnon mode above the Dirac gap calculated using \(\hat{\textbf{h}}(\textbf{Q})\) in (a). By integrating the Berry curvature in (b) over the 1st Brillouin zone, we obtain the Chern number \(C^+ = 1\).