Measurements of the thermal conductivity as a function of temperature and magnetic field in the 2D dimer spin system SrCu2(BO3)2 are presented. In zero magnetic field the thermal conductivity along and perpendicular to the magnetic planes shows a pronounced double-peak structure as a function of temperature. The low-temperature maximum is drastically suppressed with increasing magnetic field. Our quantitative analysis reveals that the heat current is due to phonons and that the double-peak structure arises from pronounced resonant scattering of phonons by magnetic excitations.During the last few years the thermal conductivity (κ) of low dimensional spin systems has attracted considerable interest [1][2][3][4][5][6]. One reason is that in these materials a large magnetic contribution κ mag to the heat current may be present as observed e.g. for the spin ladder material Sr 14−x Ca x Cu 24 O 41 [6]. Another reason is that the phononic heat current κ ph probes the spectrum of magnetic excitations as well as the spin-phonon coupling [3][4][5]. The latter is very important in some of the low dimensional spin systems, e.g. in the spin-Peierls compound CuGeO 3 [4,5]. Both issues, the magnetic contribution to the heat current as well as the interaction of the phonons with magnetic excitations, are to a large extent unexplored and not well understood.A material of particular interest in this context is SrCu 2 (BO 3 ) 2 (SCBO) [7]. The Cu 2+ ions form a quasi-2D spin system which is by virtue of the crystal geometry an experimental realization of the Shastry-Sutherland model [8]. In SCBO the intra-dimer and inter-dimer couplings are of magnitude J 1 ≃ 72 K and J 2 ≃ 43 K, i.e. J 2 /J 1 ≃ 0.6 [9]. As expected for this ratio SCBO has a dimerized singlet ground-state separated from the excited triplet states by a finite gap ∆ ≃ 35 K as seen in the magnetic susceptibility [10] or in inelastic neutron scattering [11]. From the latter it is also known that the triplet excitations are almost dispersionless, i.e the group velocity is very small, in agreement with theoretical calculations [12][13][14][15]. Thus, a sizeable κ mag is not expected for SCBO making this material a natural candidate to study the influence of magnetic excitations on κ ph . In this letter we present measurements of the thermal conductivity of SCBO along (κ a ) and perpendicular (κ c ) to the 2D spin planes in a large temperature (2.5-275 K) and magnetic field range (0-17 T). In zero field, both κ a and κ c show pronounced double-peak structures as a function of T . For both directions the low-T maximum is drastically suppressed by a magnetic field. We present a model based on a purely phononic thermal conductivity and explain the double-peak structure and its field dependence by strong damping of the phononic heat current due to resonant scattering of phonons by magnetic excitations. With the same parameters our model considerably improves the description of the magnetic field dependence of the specific heat of SCBO [16].For our study two samples of rectan...