Structural and magnetic short-range order in fluorite ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$

We studied structural and magnetic ordering in ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$ using synchrotron x-ray diffraction, neutron diffraction and total scattering, ac and dc susceptibility, and inelastic neutron scattering. Diffraction measurements reveal an average disordered fluorite structure with additional diffuse scattering features, which are caused by structural short-range orthorhombic order, as evidenced by the neutron pair distribution function measurements. The ac susceptibility measurements show a broad peak at $T_f\approx 0.35$ K that displays Arrhenius behavior with an activation energy of 2.51(5) meV. Zero-field neutron scattering measurements show broad magnetic diffuse scattering in the elastic channel with an antiferromagnetic-type gapless excitation extending to 1.5 meV. A polarized state with partial spin order is induced with an applied magnetic field which opens a gapped excitation that increases monotonically with field strength.

Figure 1

(a) Summary of the effect of stuffing additional rare-earth cations (which replace Ti cations) into the pyrochlore structure. Blue spheres denote rare-earth (RE) cations, cyan spheres denote Ti cations, and red spheres denote oxygen anions. The red polyhedra represent tetrahedra composed of magnetic RE cations. (b) For a “fully stuffed” pyrochlore ($A_2{\mathrm{TiO}}_5$ stoichiometry), when the RE cations are smaller than Dy, the “defect-fluorite” structure forms in which the RE and Ti atoms share occupancy of a single site. (c) An orthorhombic structure forms at equilibrium with no site mixing when the RE cation is dysprosium or larger.

Figure 2

X-ray and neutron diffraction patterns of ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$ measured at room temperature (red and black lines, respectively). Diffuse scattering is evident in both measurements but is much more pronounced in the neutron measurements. The average structure is consistent with the defect-fluorite structure as evidenced by Rietveld refinement of the x-ray diffraction pattern ($R_{wp}=12.7$, inset).

Figure 3

(a) Neutron pair distribution function (PDF) of ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$ measured at room temperature (open blue circles) refined with various structural models (solid lines). The defect-fluorite ($Fm\overline{3}m$, solid red line) and defect-pyrochlore ($Fd\overline{3}m$, solid magenta line) models fit the data very poorly ($R_{wp}=0.477$ and 0.306, respectively). The orthorhombic symmetry, characteristic of $A_2{\mathrm{TiO}}_5$ stoichiometry with smaller A-site cations, reproduces the data well (solid orange line, $R_{wp}=0.111$). (b) Goodness-of-fit parameter $R_{wp}$ obtained from “boxcar” refinement using the defect-fluorite structure in which the fit range is incrementally shifted to higher $r$ values. The fit range was always 9 Å. The minimum $r$ value used for the fit range is shown on the $x$ axis. The fit is poor at low $r$ values but improves at higher $r$ values, eventually saturating above $r_{\min }\approx 15\AA$.

Figure 4

Inverse dc susceptibility ${\chi }_{dc}$ (open black circles) as a function of temperature for ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$. The Curie-Weiss law fits the data well (dashed red line), resulting in a Curie-Weiss temperature ${\theta }_{CW}$ of $-3.18\left(3\right)$ K. The effective magnetic moment was evaluated to be 3.145(2)${\mu }_B$ using the Curie constant from the fit. Magnetization measurements saturate below the moment of free ${\mathrm{Yb}}^{3+}$ (inset).

Figure 5

(a) Frequency dependence of the real (${\chi }^{\prime }$, solid lines) and imaginary (${\chi }^{″}$, dashed lines) parts of ac susceptibility (left and right axes, respectively) as a function of temperature for ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$. The peak in ${\chi }^{\prime }$ shifts to higher $T$ with Arrhenius dependence as frequency is increased (inset). The activation energy extracted from the fit to the Arrhenius equation is 2.51(5) meV (dashed black line). (b) Field dependence of the real (${\chi }^{\prime }$, solid lines) and imaginary (${\chi }^{″}$, dashed lines) parts of ac susceptibility (left and right axes, respectively) as a function of temperature for ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$. The peak in ${\chi }^{\prime }$ shifts to lower $T$ as the applied field is increased (inset).

Figure 6

Contour maps of the powder-averaged inelastic neutron scattering spectrum of ${\mathrm{Yb}}_2{\mathrm{TiO}}_5$ ($\lambda =5\AA$). (a) The zero-field spectrum at 5 K. (b)–(d) Spectra at 60 mK under various field strengths. A gapless excitation centered at $\left|Q\right|\approx 1{\AA }^{-1}$ is evident at 60 mK under zero field in (b). An energy gap forms under applied magnetic field in (c) and (d).

Figure 7

The elastic neutron scattering data by integrating within $-0.05\le E\le 0.05$ meV ($\lambda =5\AA$). There is little difference in the data from 5 K to 60 mK under zero applied field (black squares), indicating the lack of long-range magnetic order. The intensity of the (111) and (200) Bragg peaks (inset) increases under applied magnetic field, indicating a transformation to a spin-polarized, long-range magnetic ordered state (red circles). There is an additional diffuse peak that emerges around $\left|Q\right|\approx$ 2 Å, indicating that short-range order is still present in the presence of a 4-T field. Error bars represent one standard deviation determined assuming Poisson statistics.

Figure 8

(a) $Q$ dependence of inelastic neutron scattering spectra (Fig. 6) from integrating within $E=0.2–1.5\mathrm{meV}$. The high-intensity position of the excitation does not change as a function temperature or applied field. (b) Energy dependence of inelastic neutron scattering data in Fig. 6 from integrating $0.5–1.5\AA {}^{-1}$.