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Magnetic order in Tb$_2$Sn$_2$O$_7$ under high pressure: from ordered spin ice to spin liquid and antiferromagnetic order

We have studied the Tb$_2$Sn$_2$O$_7$ frustrated magnet by neutron diffraction under isotropic pressure of 4.6 GPa, combined with uniaxial pressure of 0.3 GPa, in the temperature range 0.06 K$<$T$<$100 K. Magnetic order persists under pressure but the ordered spin ice structure stabilized at ambient pressure below 1.3 K partly transforms into an antiferromagnetic one. The long range ordered moment at 0.06 K is reduced under pressure, which is interpreted by a pressure induced enhancement of the spin liquid fluctuations. Above the ordering transition, short range spin correlations are affected by pressure, and ferromagnetic correlations are suppressed. The influence of pressure on the ground state is discussed considering both isotropic and stress effects.