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We have studied the Tb$_2$Sn$_2$O$_7$ frustrated magnet by neutrondiffraction under isotropic pressure of 4.6 GPa, combined with uniaxialpressure of 0.3 GPa, in the temperature range 0.06 K$<$T$<$100 K. Magneticorder persists under pressure but the ordered spin ice structure stabilized atambient 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 isinterpreted by a pressure induced enhancement of the spin liquid fluctuations.Above the ordering transition, short range spin correlations are affected bypressure, and ferromagnetic correlations are suppressed. The influence ofpressure on the ground state is discussed considering both isotropic and stresseffects.

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