Magnetic excitations inTb2Sn2O7andTb2Ti2O7as measured by inelastic neutron scattering

Abstract

We have measured the magnetic excitations by inelastic neutron scattering in the paramagnetic phase down to $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, in ${\mathrm{Tb}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$, which remains spin liquid down to $0.05\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, and in ${\mathrm{Tb}}_{2}{\mathrm{Sn}}_{2}{\mathrm{O}}_{7}$, which shows an ordered spin ice state below $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The temperature dependence of the crystal field excitations, measured in the energy range $0--10\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$, shows striking differences between the two compounds. The neutron data were reasonably reproduced by a set of crystal field parameters, showing that while the two compounds have similar values of the gap between the first two crystal field doublets, the associated wave functions are exchanged. This difference comes from a change in sign of the crystal field parameter ${B}_{6}^{0}$. The neutron data also suggest that an excitation at very low energy (about $0.03\phantom{\rule{0.3em}{0ex}}\mathrm{THz}$) is present in both compounds. Using these sets of crystal field parameters, the high field magnetization and low field susceptibility data can be correctly reproduced by taking the exchange interaction into account in the molecular field approximation. The values obtained for the exchange integral are discussed.