Metal-Insulator Transition and Topological Properties of Pyrochlore Iridates

Combining density functional theory (DFT) and embedded dynamical mean-field theory (DMFT) methods, we study the metal-insulator transition in $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($R=\mathrm{Y}$, Eu, Sm, Nd, Pr, and Bi) and the topological nature of the insulating compounds. Accurate free energies evaluated using the charge self-consistent $\mathrm{DFT}+\mathrm{DMFT}$ method reveal that the metal-insulator transition occurs for an $A$-cation radius between that of Nd and Pr, in agreement with experiments. The all-in–all-out magnetic phase, which is stable in the Nd compound but not the Pr one, gives rise to a small ${\mathrm{Ir}}^{4+}$ magnetic moment of $\approx 0.4{\mu }_B$ and opens a sizable correlated gap. We demonstrate that within this state-of-the-art theoretical method, the insulating bulk pyrochlore iridates are topologically trivial.

Figure 1

Variation with respect to the $A$-cation radius of computed properties of $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ ($R=\mathrm{Y}$, Eu, Sm, Nd, Pr, and Bi). (a) Difference of free energies $F$ between PM and AIAO magnetic states for $R_2{\mathrm{Ir}}_2{\mathrm{O}}_7$. Solid circles (hollow squares) denote the values obtained using the $\mathrm{LDA}+\mathrm{DMFT}$ ($\mathrm{LDA}+\mathrm{U}$) method, plotted as zero when the AIAO state cannot be stabilized. Inset displays the LDA bandwidth of the $t_{2g}$ bands; shaded region highlights the insulating compounds. (b) Quasiparticle renormalization amplitude $Z_{\alpha }$ (see text for the definition) for the $J_{\mathrm{eff}}=1/2$ and $J_{\mathrm{eff}}=3/2$ states. Solid (dashed) lines denote the values in the PM (AIAO) states, with $Z$ for the $J_{\mathrm{eff}}=1/2$ orbital in the PM state of ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ (red triangle) shown for comparison. (c) Ordered moment of Ir atoms. All $\mathrm{LDA}+\mathrm{DMFT}$ calculations are done at 50 K.

Figure 2

(a) The LDA-like band structure of ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ with irreducible representations indicated at the time-reversal invariant momenta; numbers in parenthesis denote degeneracies. (b) Color map: spectral function of ${\mathrm{Nd}}_2{\mathrm{Ir}}_2{\mathrm{O}}_7$ in the AIAO magnetic state. Dotted lines: band structure of the effective topological Hamiltonian (see text for details). The parities of eight $J_{\mathrm{eff}}=1/2$-derived bands are indicated by “$+$” or “$-$” at the $L$ point. (c) Evolution of the eigenvalues of the effective topological Hamiltonian at $L$ with mixing fraction of the DMFT self-energy. Inset zooms in on the critical region indicated by the red square.