Magnetic order in ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$ under high pressure: From ordered spin ice to spin liquid and antiferromagnetic order

We have studied the ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$ ordered spin ice by neutron diffraction under an isotropic pressure of 4.6 GPa, combined with a stress of 0.3(1) GPa. Measurements down to a temperature of 0.06 K and up to 100 K probe the effect of pressure both on ground state and spin fluctuation in the paramagnetic region. In the pressure-induced ground state, the ordered spin ice structure with a ${\mathbf{k}}_0=0$ propagation vector persists, but it coexists with a structure with ${\mathbf{k}}_1=\left(0,0,1\right)$. The ordered moment at 0.06 K is reduced, suggesting that pressure also enhances the spin liquid fluctuations at $T\sim 0$. In the paramagnetic region, applying pressure changes the short-range spin correlations and suppresses the ferromagnetic correlations. The influence of pressure is discussed considering both isotropic pressure and stress effects.

Figure 1

(Color online) Magnetic diffraction pattern in ${\text{Tb}}_2{\text{Sn}}_2{\text{O}}_7$ at 0.06 K under a pressure of 4.6 GPa $\left(P_u\sim 0.4\text{GPa}\right)$. A spectrum at 4.5 K was subtracted. The solid line is a refinement involving ${\mathbf{k}}_0$ and ${\mathbf{k}}_1$ structures. Top: spin structures in one tetrahedron, having propagation vectors ${\mathbf{k}}_0$ (left) and ${\mathbf{k}}_1$ (right). The local anisotropy axes are in dashed lines.

Figure 2

(Color online) (a) integrated intensity of the F (◻, ○) and AF (◼, ●) peaks versus temperature under pressure $\left(P_i=4.6\text{GPa},P_u=0.4\text{GPa}\right)$. Lines are guides for the eye. Inset: (200) peak intensities with and without pressure, scaled at 0.06 K. (b) Temperature dependence of the lattice constant at ambient pressure.

Figure 3

(Color online) Magnetic SRO patterns at 1.5 K; a pattern at 100 K was subtracted. (a) Ambient pressure. The solid line is a fit as described in text. Dashed-dotted (dashed) line shows the liquidlike (Lorenzian) component. (b) SRO pattern measured at ambient pressure and under pressure $\left(P_i=4.6\text{GPa},P_u=0.2\text{GPa}\right)$ in the same $q$ range. Solid lines are fits as described in text.

Figure 4

Temperature dependence of the first-neighbor correlations in the paramagnetic region. Solid line is a guide to the eye.