Interplay of localized and itinerant character of Ru ions: Tl${}_2$Ru${}_2$O${}_7$ versus Hg${}_2$Ru${}_2$O${}_7$

We carry out a comparative study of the electronic structure of two pyrochlore ruthenate compounds, Tl${}_2$Ru${}_2$O${}_7$ and Hg${}_2$Ru${}_2$O${}_7$, in terms of first principles calculations. Our study reveals the Ru $d$ electrons in Hg${}_2$Ru${}_2$O${}_7$ to be much more delocalized compared to that in Tl${}_2$Ru${}_2$O${}_7$. The subtle change in the Ru-$d$ bandwidths in the two compounds, triggered by the differences in Hg 5$d$–Ru 4$d$ hybridization compared to that of Tl 5$d$–Ru 4$d$, bring in the observed differences in behavior. Our study further shows that the development of long range noncollinear antiferromagnetic structure at low temperature is sufficient to produce the insulating solution in Hg${}_2$Ru${}_2$O${}_7$, in line with the prediction from recent nuclear magnetic resonance study.

Figure 1

Spin-polarized GGA DOS for HRO (left) and TRO (right). The dominant contributions of various degrees of freedoms have been marked. The zero of the energy is set at $E_F$.

Figure 2

Top panels: GGA+U DOS for HRO (left) and TRO (right). Bottom panels: Ru-$t_{2g}$ DOS for HRO (left) and TRO (right) projected onto $a_{1g}$ (shaded area) and $e_g^{\pi }$ (dashed lines). The zero of the energy is set at $E_F$.

Figure 3

Schematic DOS corresponding to $a_{1g}$ (shaded region) and $e_g^{\pi }$ (unshaded region) states for HRO (top panel) and TRO (bottom panel).

Figure 4

Non-spin-polarized DOS projected onto Hg/Tl-$d$ (solid line), Hg/Tl-$s$ (shaded region), and O${}^{\prime }$-$p$ (dashed line) for HRO (upper panel) and TRO (lower panel). Insets: projection of Hg/Tl-$d$ character (marked by fatness) in Ru-$t_{2g}$ bands.

Figure 5

Effective Ru-$e_g^{\pi ,2}$ Wannier functions for HRO (top panel), TRO (middle panel), and their difference (bottom panel) obtained from the NMTO-downfolding calculation. The lobes of opposite signs are colored as blue (dark gray) and yellow (light gray). The weights sitting at $A$ sites have been encircled.

Figure 6

GGA+U density of states, corresponding to Conf.$c$ (see text for details). The inset shows the arrangements of Ru spins corresponding to Conf.$c$, shown in the kagome layer of the Ru pyrochlore lattice.