We report measurements of the specific heat of the quantum spin liquid system SrCu2(BO3)2 in continuous magnetic fields H of up to 33 T. The specific heat vs temperature at zero field shows an anomaly at 8 K, marking the opening of a gap in the spin singlet excitations. At fields H~12 T, we clearly see a second anomaly that shifts to lower temperatures as H is increased. We attribute its origin to single triplet excitations of the singlet dimer ground state. This conclusion is supported by calculations of the specific heat, which reproduce the experimental data, made using the finite temperature Lanczos method to solve a Shastry-Sutherland Hamiltonian including nearest and next-nearest neighbor Dzyaloshinsky-Moriya interactions. The parameters used to fit the data are the exchange constants J = 74 K and J/J = 0.62, and the Dzyaloshinsky-Moriya coupling constants |D|=6.1K, and $|D|=2.2K.
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