Optical Spectroscopic Studies of the Metal-Insulator Transition Driven by All-In–All-Out Magnetic Ordering in $5d$ Pyrochlore ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$

We investigated the metal-insulator transition (MIT) driven by all-in–all-out (AIAO) antiferromagnetic ordering in the $5d$ pyrochlore ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$ using optical spectroscopy and first-principles calculations. We showed that the temperature evolution in the band-gap edge and free carrier density were consistent with rigid upward (downward) shifts of electron (hole) bands, similar to the case of Lifshitz transitions. The delicate relationship between the band gap and free carrier density provides experimental evidence for the presence of an AIAO metallic phase, a natural consequence of such MITs. The associated spectral weight change at high energy and first-principles calculations further support the origin of the MIT from the band shift near the Fermi level. Our data consistently support that the MIT induced by AIAO ordering in ${\mathrm{Cd}}_2{\mathrm{Os}}_2{\mathrm{O}}_7$ is not close to a Slater type but instead to a Lifshitz type.

Figure 1

(a) $T$-dependent ${\sigma }_1(\omega )$ below 0.25 eV. The solid triangles highlight the phonons. The inset in (a) shows $T$-dependent ${\sigma }_1(\omega )$ at $\hslash \omega =20\mathrm{meV}$. (b) ${\alpha }^2(\omega )$ and ${\alpha }^{1/2}(\omega )$ at 150 K. The solid and dashed lines are extrapolation lines for two spectra. (c) $T$-dependent ${\alpha }^2(\omega )$.

Figure 2

(a) ${\sigma }_1(\omega )$ and (b) ${\epsilon }_1(\omega )$ at 200 K. The open circles are experimental data; the solid lines show the fitting results. The red and blue lines correspond to the Drude and ${\mathrm{CPM}}_0$ models, respectively. (c) ${\mathrm{\Delta }}_D(T)$ and ${\omega }_p^2(T)$. The error bars indicate the 95% confidence interval. Error bars smaller than the symbol size are omitted. (d) ${\omega }_p^2(T)$ as a function of ${\mathrm{\Delta }}_D(T)/k_{B}T$. The solid circles are experimental data, and the solid line is the best fitting result with the model. The dashed line shows the case of the thermal excitation limit. The ${\mathrm{\Delta }}_C$ values that correspond to the solid line are shown on the top axis. (e) A model band structure describing a Lifshitz-type MIT.

Figure 3

(a) ${\sigma }_1(\omega )$ with four different $T$. (b) $T$-dependent SW changes in three different energy regions. (c) ${\sigma }_1(\omega )$ from LDA calculations with four different $U$ values. Band structures with (d) $U=0.8$ and (e) 1.5 eV. The dashed and solid arrows in (d) and (e) indicate forbidden and allowed optical transitions corresponding to the ${\mathrm{SW}}_3$ region, respectively.