Coexisting magnetic order and cooperative paramagnetism in the stuffed pyrochlore ${\text{Tb}}_{2+x}{\text{Ti}}_{2-2x}{\text{Nb}}_x{\text{O}}_7$

Neutron-scattering and magnetization measurements have been performed on the stuffed pyrochlore system ${\text{Tb}}_{2+x}{\text{Ti}}_{2-2x}{\text{Nb}}_x{\text{O}}_7$. We find that despite the introduction of chemical disorder and increasingly antiferromagnetic interactions, a spin-glass transition does not occur for $T\ge 1.5\text{K}$ and cooperative paramagnetic behavior exists for all $x$. For $x=1$, ${\text{Tb}}_3{\text{NbO}}_7$, an antiferromagnetically ordered state coexisting with cooperative paramagnetic behavior is seen without applying any external fields or pressure, a situation advantageous for studying this cooperative behavior.

Figure 1

(Color online) (a) ${\theta }_W\left(x\right)$ determined from Curie-Weiss fits to ${\chi }^{-1}\left(T\right)$. The line is a guide to the eye. (b) ${\chi }^{-1}\left(T\right)$ for $x=0.2$ and 1 and the corresponding Curie-Weiss fits. (c) $M\left({\mu }_{0}H\right)$ for each $x$ at $T=2\text{K}$. (d) ZFC and FC $\chi \left(T\right)$ data for $x=1$ at ${\mu }_{0}H=0.01\text{T}$. (e) A blowup of the low-temperature portion of the $x=1\chi \left(T\right)$ data.

Figure 2

(Color online) (a) $I\left(E\right)$ for $x=0.2$ at $T=50$, 10, and 1.5 K after summing between $1<Q<1.2{\text{Å}}^{-1}$. (b) $I\left(E\right)$ as in (a) at $T=1.5\text{K}$ for each $x$. Arrows indicate the approximate positions of crystal-field excitations. (c) $I\left(Q\right)$ for $x=0.2$ after summing between $-0.1<E<0.1\text{meV}$ at $T=50$, 10, and 1.5 K. (d) $I\left(Q\right)$ as in (c) at $T=1.5\text{K}$ for each $x$.

Figure 3

(Color online) The scattered neutron intensity due to spin-spin correlations as a function of $Q$ for (a) $x=0.2$, (b) 0.4, (c) 0.6, and (d) 1, as described in the text. Lines are fits as described in the text. The rise at low $Q$ for all $x$ may be due to air scattering.

Figure 4

(Color online) $T=50\text{K}$ (a) and $T=1.5\text{K}$ (b) powder-diffraction data for ${\text{Tb}}_3{\text{NbO}}_7$ and their refinements. The diagram in (a) shows the Tb/Nb sublattice of side sharing tetrahedra, while the diagram in (b) shows the AFM order. Top and bottom sets of tic marks indicate positions of the fluorite and pyrochlore Bragg peaks, respectively. The middle set of tic marks in (b) indicates the positions of the magnetic Bragg peaks. Uncertainties are statistical in nature and within the size of the symbols.