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Register a new userLow temperature and high pressure Raman and x-ray studies of pyrochlore Tb$_2$Ti$_2$O$_7$ : phonon anomalies and possible phase transition
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We have carried out temperature and pressure-dependent Raman and x-ray measurements on single crystals of Tb$_2$Ti$_2$O$_7$. We attribute the observed anomalous temperature dependence of phonons to phonon-phonon anharmonic interactions. The quasiharmonic and anharmonic contributions to the temperature-dependent changes in phonon frequencies are estimated quantitatively using mode Gr{u}neisen parameters derived from pressure-dependent Raman experiments and bulk modulus from high pressure x-ray measurements. Further, our Raman and x-ray data suggest a subtle structural deformation of the pyrochlore lattice at $sim$ 9 GPa. We discuss possible implications of our results on the spin-liquid behaviour of Tb$_2$Ti$_2$O$_7$.
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Terbium titanate (Tb$_2$Ti$_2$O$_7$) is a spin-ice material with remarkable magneto-optical properties. It has a high Verdet constant and is a promising substrate crystal for the epitaxy of quantum materials with the pyrochlore structure. Large single crystals with adequate quality of Tb$_2$Ti$_2$O$_7$ or any pyrochlore are not available so far. Here we report the growth of high-quality bulk crystals using the Czochralski method to pull crystals from the melt. Prior work using the automated Czochralski method has suffered from growth instabilities like diameter fluctuation, foot formation and subsequent spiraling shortly after the seeding stage. In this study, the volumes of the crystals were strongly increased to several cubic centimeters by means of manual growth control, leading to crystal diameters up to 40 mm and crystal lengths up to 10 mm. Rocking curve measurements revealed full width at half maximum values between 28 and 40 for 222 reflections. The specific heat capacity c$_p$ was measured between room temperature and 1573 K by dynamic differential scanning calorimetry and shows the typical slow parabolic rise. In contrast, the thermal conductivity kappa(T) shows a minimum near 700 K and increases at higher temperature T. Optical spectroscopy was performed at room temperature from the ultraviolet to the near infrared region, and additionally in the near infrared region up to 1623 K. The optical transmission properties and the crystal color are interpreted to be influenced by partial oxidation of Tb$^{3+}$ to Tb$^{4+}$.
By means of ac magnetic-susceptibility measurements, we find evidence for a new magnetic phase of Tb$_2$Ti$_2$O$_7$ below about 140 mK in zero magnetic field. In magnetic fields parallel to [111], this phase---exhibiting frequency- and amplitude-dependent susceptibility and an extremely slow spin dynamics---extends to about 70 mT, at which it gives way to another phase. The field dependence of the susceptibility of this second phase, which extends to about 0.6 T, indicates the presence of a weak magnetization plateau below 50 mK, as has been predicted by a single-tetrahedron four-spin model, giving support to the underlying proposal that the disordered low-field ground state of Tb$_2$Ti$_2$O$_7$ is a quantum spin ice.
Both amorphous and crystalline materials frequently exhibit low temperature specific heats in excess of what is predicted using the Debye model. The signature of this excess specific heat is a peak observed in $C/T^3$ textit{versus} $T$. To understand the curious absence of long-range ordering of local distortions in the crystal structure of pyrochlore Bi$_2$Ti$_2$O$_7$, we have measured the specific heat of crystalline Bi$_2$Ti$_2$O$_7$ and related compounds. We find that the peak in $C/T^3$ versus $T$ in Bi$_2$Ti$_2$O$_7$ falls at a substantially lower temperature than other similar compounds, consistent with the presence of disorder. This thermodynamic evidence for disorder in crystalline Bi$_2$Ti$_2$O$_7$ is consistent with quenched configurational disorder among Bi lone pairs produced by geometrical frustration, which could represent a possible realization of charge ice.
The oxide pyrochlore Bi$_2$Ti$_2$O$_7$ is in some ways analogous to perovskite PbTiO$_3$, in that Bi$_2$Ti$_2$O$_7$ has two cations, Bi$^{3+}$ and Ti$^{4+}$ in oxidation states that are normally associated with a propensity to off-center. However, unlike PbTiO$_3$, Bi$_2$Ti$_2$O$_7$ is experimentally observed to remain cubic down to 2 K, while the only observed ionic displacements are local and incoherent. Here we report first-principles calculations of the zone-center phonons of the ordered cubic pyrochlore which reveal several lattice instabilities. An analysis of the structural energetics suggest that the ordered cubic pyrochlore is unstable with respect to distortion towards a ferroelectric ground state with a large polarization. Our results suggest a key role of a frustrated soft polar mode in the dielectric properties of bismuth pyrochlores.
We report temperature-dependent Raman scattering and X-ray diffraction studies of pyrochlore iridates, (Eu$_{1-x}$Bi$_x$)$_2$Ir$_2$O$_7$, for x=0, 0.02, 0.035, 0.05 and 0.1. The temperature variation in Raman experiments spans from 4 K to 300 K, covering the metal-insulator phase transition accompanied by paramagnetic to all-in/all-out (AIAO) spin ordering (T$_N$). These systems also show a Weyl semi-metal (WSM) phase at low temperatures (below ~50 K). We show that the Ir-O-Ir bond bending mode, A$_{1g}$ (510 cm$^{-1}$), shows anomalous softening in the magnetically ordered AIAO state, arising primarily from the spin-phonon interaction due to the phonon-modulation of the Dzyaloshinskii-Moriya (DM) spin-exchange interaction. The two stretching modes, T$_{2g}^1$ (307 cm$^{-1}$) and T$_{2g}^2$ (382 cm$^{-1}$) harden significantly in the magnetic insulating phase. The T$_{2g}$ phonons also show anomalous temperature dependence of their mode frequencies, hitherto unreported, due to strong electron-phonon coupling. The signatures of the WSM state are observed in phonon renormalization below 50 K due to strong electron-phonon interaction. Our experimental results establish strong magneto-elastic coupling below T$_N$ and significant electron-phonon interactions in the metallic phase above T$_N$ as well as in the low-temperature WSM state.
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