Field-Induced Order and Spin Waves in the Pyrochlore Antiferromagnet ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$

High resolution time-of-flight neutron scattering measurements on ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ reveal a rich low temperature phase diagram in the presence of a magnetic field applied along $[110]$. In zero field at $T=0.4\mathrm{K}$, ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ is a highly correlated cooperative paramagnet with disordered spins residing on a pyrochlore lattice of corner-sharing tetrahedra. Application of a small field condenses much of the magnetic diffuse scattering, characteristic of the disordered spins, into a new Bragg peak characteristic of a polarized paramagnet. At higher fields, a magnetically ordered phase is induced, which supports spin wave excitations indicative of continuous, rather than Ising-like, spin degrees of freedom.

Figure 1

Neutron scattering for $-0.5\mathrm{meV}<\hslash \omega <0.5\mathrm{meV}$ and within the $(H,H,L)$ plane of ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$ at $T=1\mathrm{K}$ is shown for (a) $H=0\mathrm{T}$, (b) $H=2\mathrm{T}$, and (c) $H=8.5\mathrm{T}$. Panel (d) shows high energy resolution scattering at $T=0.1\mathrm{K}$, integrated in $\mathbf{Q}$ and including the $(0,0,2)$ position. The quasielastic and low-lying inelastic scattering extends to $\sim 0.25\mathrm{meV}$ and it is dramatically diminished in fields as low as 1 T.

Figure 2

The integrated intensity of the $(1,1,2)$ and $(0,0,2)$ Bragg peaks as a function of $H$ at $T=0.4\mathrm{K}$ are shown, along with the integrated quasielastic scattering making up the diffuse scattering. Note the complementarity of the $(0,0,2)$ Bragg scattering and the diffuse scattering and that both exhibit hysteresis with field.

Figure 3

The temperature dependence of the $(1,1,2)$ Bragg peak in $H=7\mathrm{T}$, as well as the $(0,0,2)$ Bragg peak in both $H=1$ and 7 T is shown. The inset shows the phase diagram for the magnetically long range ordered state in ${\mathrm{Tb}}_2{\mathrm{Ti}}_2{\mathrm{O}}_7$, as determined by time-of-flight and triple axis neutron scattering and by ac-susceptibility measurements. All lines shown are guides to the eye.

Figure 4

Neutron scattering data within the $(0,0,L)$-energy plane at $T=0.4\mathrm{K}$ and (a) $H=0$, (b) $H=1\mathrm{T}$, (c) $H=2\mathrm{T}$, and (d) $H=3\mathrm{T}$ are shown.