Spin Dynamics and Magnetic Order in Magnetically Frustrated ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$

We report a study of the geometrically frustrated magnetic material ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ by the positive muon-spin relaxation technique. No signature of a static magnetically ordered state is detected while neutron magnetic reflections are observed in agreement with a published report. This is explained by the dynamical nature of the ground state of ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$: the ${\mathrm{Tb}}^{3+}$ magnetic moment characteristic fluctuation time is $\simeq {10}^{-10}\mathrm{s}$. The strong effect of the magnetic field on the muon-spin-lattice relaxation rate at low fields indicates a large field-induced increase of the magnetic density of states of the collective excitations at low energy.

Figure 1

(a) Low temperature dependence of the specific heat per mole of Tb measured for our ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ sample. The sharp maximum is the signature of a magnetic transition occurring at $T_{\mathrm{lr}}=0.88\mathrm{K}$. The solid line is a fit to a model explained in the main text. (b) Magnetic powder diffraction pattern of ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ versus the scattering angle $2\theta$ obtained from the subtraction of data recorded at 0.11 and 1.23 K. Neutrons of wavelength 2.453 Å were used. The solid lines show the best refinement and the difference spectrum (bottom). From the pattern analysis we extract a ${\mathrm{Tb}}^{3+}$ magnetic moment ${\mu }_{\mathrm{Tb}}=5.4(1){\mu }_{\mathrm{B}}$, which makes an angle of 14.2° with the local $⟨111⟩$ axis. A measurement (not shown) at 0.98 K gives ${\mu }_{\mathrm{Tb}}=1.6(2){\mu }_{\mathrm{B}}$ and a Rietveld refinement of the diffraction pattern recorded at 100 K is consistent with space group $Fd\overline{3}m$ (lattice and oxygen position parameters equal to $a=10.427\AA$ and $x=0.337$).

Figure 2

(a) Two sets of $\mu \mathrm{SR}$ spectra recorded, respectively, at 0.17 and 2.4 K. For clarity the latter ones have been vertically shifted by 0.05. The numbers written next to each spectrum correspond to the longitudinal magnetic field, expressed in Tesla, for which the data have been recorded. The solid lines are fits to the stretched exponential relaxation function, $P_Z^{\exp }(t)=\exp [(-{\lambda }_{Z}t{)}^{\alpha }]$, where $\alpha =1$ in zero field. (b) Spin-lattice relaxation rate ${\lambda }_Z$ versus temperature, deduced from spectra recorded using a cooling down sequence. The data were taken in zero field, with the exception of some spectra above 4 K which were recorded in a longitudinal field $B_{\mathrm{ext}}=2\mathrm{mT}$. All the corresponding spectra were fitted with $\alpha =1$. The solid line is deduced from the density of states introduced in the main text.

Figure 3

Field dependence of ${\lambda }_Z$ measured at low fields for ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ using an experimental protocol explained in the main text. An amazing initial increase of ${\lambda }_Z$ is observed at 3.2 K, i.e., far above $T_{\mathrm{sr}}$, and down to 0.17 K. The shooting up of ${\lambda }_Z$ at high field displayed for $T=2.4\mathrm{K}$ is also quite unexpected. The full line specifies the initial slope at 0.17 K, which is $0.11\mu {\mathrm{s}}^{-1}{\mathrm{mT}}^{-1}$.