Magnetically driven band shift and metal-insulator transition in spin-orbit-coupled $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{I}{\mathrm{r}}_{1-x}\mathrm{R}{\mathrm{u}}_x\right)}_2{\mathrm{O}}_7$

We report a combined infrared and angle-resolved photoemission study of the electronic response of $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{I}{\mathrm{r}}_{1-x}\mathrm{R}{\mathrm{u}}_x\right)}_2{\mathrm{O}}_7$ ($x=0$, 0.22, 0.34). The low-temperature optical conductivities of the three compounds exhibit the characteristic feature of the effective total angular momentum $J_{\mathrm{eff}}=1/2$ antiferromagnetic Mott state. As the temperature increases across the antiferromagnetic ordering temperature $T_{\mathrm{N}}$, the indirect gap gradually closes whereas the direct gap remains open. In the optical conductivity of $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{I}{\mathrm{r}}_{0.66}\mathrm{R}{\mathrm{u}}_{0.34}\right)}_2{\mathrm{O}}_7$ which shows a thermally driven insulator-metal transition at $T_{\mathrm{N}}$, a Drude-like response from itinerant carriers is registered in the paramagnetic phase. We observe in angle-resolved photoemission data of $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{I}{\mathrm{r}}_{0.66}\mathrm{R}{\mathrm{u}}_{0.34}\right)}_2{\mathrm{O}}_7$ that the valence band shifts continuously toward the Fermi energy with the weakening of the antiferromagnetic order and crosses the Fermi level in the paramagnetic phase. Our findings demonstrate that the temperature-induced metal-insulator transition of the $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{I}{\mathrm{r}}_{1-x}\mathrm{R}{\mathrm{u}}_x\right)}_2{\mathrm{O}}_7$ system should be attributed to a magnetically driven band shift.

Figure 1

Optical conductivity spectra ${\sigma }_1\left(\omega \right)$ of $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{I}{\mathrm{r}}_{1-x}\mathrm{R}{\mathrm{u}}_x\right)}_2{\mathrm{O}}_7$ for (a) $x=0$, (b) $x=0.22$, and (c) $x=0.34$ in the energy region between 0 and 1 eV at selected temperatures. Insets show ${\sigma }_1\left(\omega \right)$ in the far-infrared energy region, i.e., $\omega <0.1\mathrm{eV}$. Optical SW(${\omega }_{\mathrm{c}}$) for (d) $x=0({\omega }_{\mathrm{c}}=0.35\mathrm{eV})$, (e) $x=0.22({\omega }_{\mathrm{c}}=0.32\mathrm{eV})$, and (f) $x=0.34({\omega }_{\mathrm{c}}=0.12\mathrm{eV})$. Dashed lines represent the antiferromagnetic ordering temperatures.

Figure 2

${\left[A\left(\omega \right)\hslash \omega \right]}^2$ and ${\left[A\left(\omega \right)\hslash \omega \right]}^{1/2}$ spectra at selected temperatures where $A$(ω) is absorption coefficient: (a), (d) $x=0$; (b), (e) $x=0.22$; (c), (f) $x=0.34$. The arrows represent the tangential line at inflection points of the spectra at 10 K. (g)–(i) Temperature variations in the magnitude of the direct and the indirect gaps ($2{\mathrm{\Delta }}_{\mathrm{D}}$ and $2{\mathrm{\Delta }}_{\mathrm{I}}$). Dashed lines represent the antiferromagnetic ordering temperatures.

Figure 3

(a)–(d) Constant energy contour of $\mathrm{S}{\mathrm{r}}_3{\left(\mathrm{I}{\mathrm{r}}_{0.66}\mathrm{R}{\mathrm{u}}_{0.34}\right)}_2{\mathrm{O}}_7$ at 70 K. (e)–(h) Constant energy contour at 220 K. The data are, respectively, taken at binding energy $E_{\mathrm{B}}=0$, 50, 100, and 150 meV. Black dashed lines in (a) and (e) represent Brillouin zone. Band dispersion along Γ-$X$ direction at 70 K (i) and 240 K (j). (k) Photoemission spectra taken at point A [blue dashed line in (i) and (j)]. (l) Temperature-dependent peak energies of the lower Hubbard band obtained at points A and B indicated in (i) and (j). The energies are extracted from fitting of the energy distribution curves (Fig. S2 of Supplemental Material). Thick lines are guides for the eye. (m) Photoemission spectra at point A over broad energy down to −1.2 eV.