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Register a new userIntertwined Magnetic Dipolar and Electric Quadrupolar Correlations in the Pyrochlore Tb$_2$Ge$_2$O$_7$
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We present a comprehensive experimental and theoretical study of the pyrochlore Tb$_2$Ge$_2$O$_7$, an exemplary realization of a material whose properties are dominated by competition between magnetic dipolar and electric quadrupolar correlations. The dipolar and quadrupolar correlations evolve over three distinct regimes that we characterize via heat capacity, elastic and inelastic neutron scattering. In the first regime, above $T^*=1.1$ K, significant quadrupolar correlations lead to an intense inelastic mode that cannot be accounted for within a scenario with solely magnetic dipole-dipole correlations. The onset of extended dipole correlations occurs in the intermediate regime, between $T^*=1.1$ K and $T_c = 0.25$ K, with the formation of a collective paramagnetic state characterized by extended ferromagnetic canted spin ice domains. Here, long-range order is impeded not only by the usual frustration operating in classical spin ice systems, but also by a competition between dipolar and quadrupolar correlations. Finally, in the lowest temperature regime, below $T_c=0.25$ K, there is an abrupt and significant increase in the dipole ordered moment. The majority of the ordered moment remains tied up in the ferromagnetic spin ice-like state, but an additional $mathbf{k}=(0,0,1)$ antiferromagnetic order parameter also develops. Simultaneously, the spectral weight of the inelastic mode, which is a proxy for the quadrupolar correlations, is observed to drop, indicating that dipole order ultimately wins out. Tb$_2$Ge$_2$O$_7$ is therefore a remarkable platform to study intertwined dipolar and quadrupolar correlations in a magnetically frustrated system and provides important insights into the physics of the whole family of terbium pyrochlores.
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The dynamical magnetic correlations in tbti, have been investigated using polarized inelastic neutron scattering. Dispersive excitations are observed, emerging from pinch points in reciprocal space and characterized by an anisotropic spectral weight. Anomalies in the crystal field and phonon excitation spectrum at Brillouin zone centers are also reported. These findings suggest that Coulomb phases, although they present a disordered ground state with dipolar correlations, allow the propagation of collective excitations. They also point out a strong spin-lattice coupling, which likely drives effective interactions between the $4f$ quadrupolar moments.
The charge ordered structure of ions and vacancies characterizing rare-earth pyrochlore oxides serves as a model for the study of geometrically frustrated magnetism. The organization of magnetic ions into networks of corner-sharing tetrahedra gives rise to highly correlated magnetic phases with strong fluctuations, including spin liquids and spin ices. It is an open question how these ground states governed by local rules are affected by disorder. In the pyrochlore Tb$_2$Hf$_2$O$_7$, we demonstrate that the vicinity of the disordering transition towards a defective fluorite structure translates into a tunable density of anion Frenkel disorder while cations remain ordered. Quenched random crystal fields and disordered exchange interactions can therefore be introduced into otherwise perfect pyrochlore lattices of magnetic ions. We show that disorder can play a crucial role in preventing long-range magnetic order at low temperatures, and instead induces a strongly-fluctuating Coulomb spin liquid with defect-induced frozen magnetic degrees of freedom.
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.
The XY-pyrochlore antiferromagnet ETO is studied by heat capacity measurements and electron spin resonance spectroscopy performed on single crystal samples. The magnetic phase diagrams are established for two directions of applied field, $Hparallel [100]$ and $Hparallel [111]$. In the magnetically ordered phase observed below $T_N=1.2$ K, the magnetic excitation spectrum consists of a Goldstone mode acquiring an isotropic gap in an applied field, and another mode with a gap softening in the vicinity of a field-induced phase transition. This second-order transition takes place at a critical field $H_c$ above which the magnetization process is accompanied by a canting of the magnetic moments off their local easy-planes. The specific heat curves for $Hparallel [100]$ ($Hgg H_c$) are well described by a model presuming a single dispersionless excitation mode with the energy gap obtained from the spectroscopic measurements.
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$^{4+}$.
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