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Register a new userCoulomb spin liquid in anion-disordered pyrochlore Tb$_2$Hf$_2$O$_7$
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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.
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We have studied the field induced magnetic structures in the spin liquid Tb$_2$Ti$_2$O$_7$, in a wide temperature (0.3$<$$T$$<$270 K) and field (0$<$$H$$<$7 T) range, by single crystal neutron diffraction with $bf{H}$ // [110] axis. We combined unpolarized neutron data with polarized ones, analyzed within the local susceptibility model. A ferromagnetic-like structure with $bf{k}$ = 0 propagation vector is induced, whose local order at low field and low temperature is akin to spin ice. The four Tb ions separate in $alpha$ and $beta$ chains having different values of the magnetic moments, which is quantitatively explained by taking the crystal field anisotropy into account. Above 2 T and below 2 K, an antiferromagnetic-like structure with $bf{k}$ = (0,0,1) is induced besides the $bf{k}$ = 0 structure. It shows a reentrant behavior and extends over a finite length scale. It occurs together with a broadening of the nuclear peaks, which suggests a field induced distortion and magnetostriction effect.
Inelastic neutron scattering reveals a broad continuum of excitations in Pr$_2$Zr$_2$O$_7$, the temperature and magnetic field dependence of which indicate a continuous distribution of quenched transverse fields ($Delta$) acting on the non-Kramers Pr$^{3+}$ crystal field ground state doublets. Spin-ice correlations are apparent within 0.2 meV of the Zeeman energy. A random phase approximation provides an excellent account of the data with a transverse field distribution $rho(Delta)propto (Delta^2+Gamma^2)^{-1}$ where $ Gamma=0.27(1)$ meV. Established during high temperature synthesis due to an underlying structural instability, it appears disorder in Pr$_2$Zr$_2$O$_7$ actually induces a quantum spin liquid.
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.
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.
MuSR experiments have been performed on powder sample of the ordered spin ice Tb$_2$Sn$_2$O$_7$ pyrochlore compound. At base temperature (T=35mK) the muon relaxation is found to be of dynamical nature which demonstrates that strong fluctuations persist below the ferromagnetic transition (T_C=0.87K). Hints of long range order appear as oscillations of the muon polarization when an external field is applied and also as a hysteretic behavior below T_C. We propose a dynamical and strongly correlated scenario where dynamics results from fluctuation of large spin clusters with the ordered spin ice structure.
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