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Combined experimental and modeling studies of the magnetocaloric effect,ultrasound, and magnetostriction were performed on single-crystal samples ofthe spin-dimer system Sr$_3$Cr$_2$O$_8$ in large magnetic fields, to probe thespin-correlated regime in the proximity of the field-induced XY-typeantiferromagnetic order also referred to as a Bose-Einstein condensate ofmagnons. The magnetocaloric effect, measured under adiabatic conditions,reveals details of the field-temperature ($H,T$) phase diagram, a domecharacterized by critical magnetic fields $H_{c1}$ = 30.4 T, $H_{c2}$ = 62 T,and a single maximum ordering temperature $T_{{\rm max}}(45~$T$)\simeq$8 K. Thesample temperature was observed to drop significantly as the magnetic field isincreased, even for initial temperatures above $T_{{\rm max}}$, indicating asignificant magnetic entropy associated to the field-induced closure of thespin gap. The ultrasound and magnetostriction experiments probe the couplingbetween the lattice degrees of freedom and the magnetism in Sr$_3$Cr$_2$O$_8$.Our experimental results are qualitatively reproduced by a minimalisticphenomenological model of the exchange-striction by which sound wavesrenormalize the effective exchange couplings.

Enhanced spin correlations in the Bose-Einstein condensate compound Sr3Cr2O8