Magnetoelastics of a Spin Liquid: X-Ray Diffraction Studies of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathbf{O}}_7$ in Pulsed Magnetic Fields

We report high resolution single crystal x-ray diffraction measurements of the frustrated pyrochlore magnet ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, collected using a novel low temperature pulsed magnet system. This instrument allows characterization of structural degrees of freedom to temperatures as low as 4.4 K, and in applied magnetic fields as large as 30 T. We show that ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ manifests intriguing structural effects under the application of magnetic fields, including strongly anisotropic giant magnetostriction, a restoration of perfect pyrochlore symmetry in low magnetic fields, and ultimately a structural phase transition in high magnetic fields. It is suggested that the magnetoelastic coupling thus revealed plays a significant role in the spin liquid physics of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at low temperatures.

Figure 1

Typical time-resolved diffraction data showing magnetostriction. Left panel: Magnetic field generated at the sample as a function of time, for a charging voltage of 1.1 kV. Right panel: False-color intensity map of a $\theta -2\theta$ scan of pulses through the (008) Bragg peak.

Figure 2

(a) TMS measured on the (008) Bragg peak with $H\parallel [110]$. (b) With the magnetic field rescaled by temperature, data with $T>20\mathrm{K}$ collapse onto a single curve, well described by the square of a Brillouin function (solid line). At lower temperatures, TMS is empirically described by a power law (dashed line). (c) Anisotropy of TMS ($T\sim 20\mathrm{K}$). (d) A subsection of the pyrochlore lattice. Dark (blue) spins have easy axes transverse to [110], while light (red) spins do not. All spins have a component of their easy axis along [100].

Figure 3

Magnetic-field-induced suppression of (0, 0, 6), with $H\parallel [100]$. Left panel: Results of a $\theta -2\theta$ scan through the peak position at 6.5 K, with a peak field of 7 T [compare with Fig. 1]. Right panel: Temperature dependence of integrated intensity order parameters. (Because of high incident flux on the sample, the temperature of the scattering volume while measuring this weak feature may have been higher than the nominal values by $\sim 5\mathrm{K}$).

Figure 4

$\theta$ vs $2\theta$ mesh scans of the (008) Bragg peak, at $T=24\mathrm{K}$ and in falling magnetic field ($H\parallel [110]$). Above 25 T, the peak is extended along the $\theta$ direction and split in $2\theta$. Below 25 T, a single peak is observed which is resolution limited in both $\theta$ and $2\theta$.