Figure 1

Crystal structure of YMn${}_2$O${}_5$. (a) Basic structural units of distorted Mn1O${}_6$ octahedra and Mn2O${}_5$ square pyramid. (b) Mn1-Mn2 connection projected onto $ab$ plane. The rectangular box represents the unit cell. (c) Blown-up view of the unit cell projected onto $ab$ plane. (d) Mn1-Mn2 connection projected onto $ac$ plane. Oxygen atoms have been represented with small balls, while the Mn atoms have been represented with large balls. Y atoms have been omitted for simplicity. In panel (a), different inequivalent oxygens are colored differently, while in the rest of the panels, to avoid complexity, they have been colored uniformly. Two inequivalent Mn atoms have been colored as magenta (dark grey) for Mn1 and golden (light grey) for Mn2. The dominant magnetic exchanges have been also marked.Reuse & Permissions

Figure 2

Density of states of YMn${}_2$O${}_5$ computed in plane-wave basis. (a) Non-spin-polarized DOS projected onto Mn1-$d$ (marked with dashed line), Mn2-$d$ (marked with solid line), and O-$p$ (marked as shaded area) characters. (b) Spin-polarized DOS computed with ferromagnetic alignment of Mn spins. (c) Spin-polarized DOS computed with antiferromagnetic alignment of Mn spins. Energy is plotted with respect to E${}_F$ (marked in the plots as a vertical dashed line).Reuse & Permissions

Figure 3

Superexchange processes connecting Mn1 and Mn2 [panel (a) and panel (b)] and that connecting two Mn2 atoms [panel (c) and panel (d)]. The exchanges denoted as $J_3$ and $J_4$ are of the first kind and the exchange denoted as $J_5$ is of the second kind.Reuse & Permissions

Figure 4

The magnetic unit cell considered for total energy calculations of different magnetic configurations. Different Mn atoms have been numbered.Reuse & Permissions

Figure 5

The cell used to carry out the magnon calculation. The atoms marked from 1–8 belong to the unit cell labeled as {$i,j$}. The magnetic exchanges with neighbors of Mn atoms belonging to neighboring unit cells (labeled as {$i\pm 1,j$} or {$i,j\pm 1$} are included in the Hamiltonian. The ground-state spin structure, considering the NMTO-derived magnetic exchanges are also shown with arrows.Reuse & Permissions

Figure 6

Calculated low-lying branches of magnon dispersion plotted along [100] (left panels) and [010] (right panels) directions compared to experimentally measured data considering different sets of magnetic interactions. Top-most panels: Magnon spectra calculated using parameter sets given by NMTO-downfolding calculations. Second panels from top: Magnon spectra calculated using parameter sets given by the calculation of Wang et al.[5] Third panels from top: Magnon spectra calculated using parameter sets given by the study of Kim et al.[6] Bottom panels: Experimentally measured data.Reuse & Permissions

Figure 7

Overlaps of the downfolded Mn-$d$ NMTOs at two Mn1 and Mn2 sites. Plotted are the orbital shapes (constant-amplitude surfaces) with the lobes of opposite signs labeled by black (magenta) and yellow (cyan) at site Mn2(Mn1). (a) Corner-sharing Mn1-Mn2 overlap corresponding to interaction “3”. (b) Corner-sharing Mn1-Mn2 overlap corresponding to interaction “4.’Reuse & Permissions