Ordered Spin Ice State and Magnetic Fluctuations in ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$

We have studied the spin liquid ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ by neutron diffraction and specific heat measurements. Below about 2 K, the antiferromagnetic liquidlike correlations mostly change to ferromagnetic. Magnetic order settles in two steps, with a smeared transition at 1.3(1) K, then an abrupt transition at 0.87(2) K. A new magnetic structure is observed, akin to an ordered spin ice, with both ferromagnetic and antiferromagnetic character. It suggests that the ordered ground state results from the influence of dipolar interactions combined with a finite anisotropy along $⟨111⟩$ axes. The moment value of $3.3(3){\mu }_{\mathrm{B}}$ deduced from the specific heat is well below that derived from the neutron diffraction of $5.9(1){\mu }_{\mathrm{B}}$, which is interpreted by the persistence of slow collective magnetic fluctuations down to the lowest temperatures.

Figure 1

Magnetic intensity of ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ versus the scattering vector $q=4\pi \sin \theta /\lambda$. A spectrum in the paramagnetic phase (100 K) was subtracted. Intensities at 1.0 K have an offset of 10 for clarity. Arrows show the position of the Bragg peaks and near neighbor liquid peak ($L$) calculated in Ref. 18.

Figure 2

Magnetic diffraction pattern of ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ at 0.10 K versus the scattering angle $2\theta$. A spectrum at 1.2 K was subtracted. The neutron wavelength is 2.52 Å. Solid lines show the best refinement and the difference spectrum (bottom). In the inset, the magnetic structure is shown.

Figure 3

Ordered magnetic moment $M$ versus temperature (filled circles) and squared intensity of the (200) magnetic peak, scaled to the moment at 0.10 K (open circles). $T_c$ is determined from the peak in the specific heat. The correlation length $L_c$, deduced from the width of the magnetic Bragg peaks, and the angle $\alpha$ with the local anisotropy axis are plotted in the insets.

Figure 4

Specific heat $C_p$ in ${\mathrm{Tb}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$. The curves below 0.8 K are the sum of a ${\mathrm{T}}^3$ magnon contribution and of a nuclear Schottky anomaly, the latter being computed for 3 moment values (see text). The electronic entropy variation is shown in the inset. The arrows label the transition at $T_c=0.87\mathrm{K}$.