Neutron spectroscopic study of crystal field excitations inTb2Ti2O7andTb2Sn2O7

Abstract

We present time-of-flight inelastic neutron scattering measurements at low temperature on powder samples of the magnetic pyrochlore oxides ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Tb}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$. These two materials possess related, but different ground states, with ${\mathrm{Tb}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$ displaying ``soft'' spin ice order below ${T}_{\mathrm{N}}\ensuremath{\sim}0.87$ K, while ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ enters a hybrid, glassy spin ice state below ${T}_{\mathrm{g}}\ensuremath{\sim}0.2$ K. Our neutron measurements, performed at $T=1.5$ and 30 K, probe the crystal field states associated with the $J$ = 6 states of Tb${}^{3+}$ within the appropriate $Fd\overline{3}m$ pyrochlore environment. These crystal field states determine the size and anisotropy of the Tb${}^{3+}$ magnetic moment in each material's ground state, information that is an essential starting point for any description of the low-temperature phase behavior and spin dynamics in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ and ${\mathrm{Tb}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$. While these two materials have much in common, the cubic stanate lattice is expanded compared to the cubic titanate lattice. As our measurements show, this translates into a factor of $\ensuremath{\sim}$2 increase in the crystal field bandwidth of the $2J+1=13$ states in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ compared with ${\mathrm{Tb}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$. Our results are consistent with previous measurements on crystal field states in ${\mathrm{Tb}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$, wherein the ground-state doublet corresponds primarily to ${m}_{J}=|\ifmmode\pm\else\textpm\fi{}5\ensuremath{\rangle}$ and the first excited state doublet to ${m}_{J}=|\ifmmode\pm\else\textpm\fi{}4\ensuremath{\rangle}$. In contrast, our results on ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ differ markedly from earlier studies, showing that the ground-state doublet corresponds to a significant mixture of ${m}_{J}=|\ifmmode\pm\else\textpm\fi{}5\ensuremath{\rangle}$, $|\ensuremath{\mp}4\ensuremath{\rangle}$, and $|\ifmmode\pm\else\textpm\fi{}2\ensuremath{\rangle}$, while the first excited state doublet corresponds to a mixture of ${m}_{J}=|\ifmmode\pm\else\textpm\fi{}4\ensuremath{\rangle}$, $|\ensuremath{\mp}5\ensuremath{\rangle}$, and $|\ifmmode\pm\else\textpm\fi{}1\ensuremath{\rangle}$. We discuss these results in the context of proposed mechanisms for the failure of ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ to develop conventional long-range order down to 50 mK.