We present a time-resolved study of the magnetization dynamics in a microstructured Cr|Heusler|Pt waveguide driven by the Spin-Hall-Effect and the Spin-Transfer-Torque effect via short current pulses. In particular, we focus on the determination of the threshold current at which the spin-wave damping is compensated. We have developed a novel method based on the temporal evolution of the magnon density at the beginning of an applied current pulse at which the magnon density deviates from the thermal level. Since this method does not depend on the signal-to-noise ratio, it allows for a robust and reliable determination of the threshold current which is important for the characterization of any future application based on the Spin-Transfer-Torque effect.In the last years, the field of magnon spintronics 1 has attracted prominent interest since it offers great potential to realize future logic devices. In this field, currents of magnons, the quanta of spin-waves, are used to transport and process information. Recently, a set of prototype devices has been realized such as, e.g., the magnonic majority gate 2,3 , in which the logic state of the output signal is determined by the majority of the input states. Other works on magnon based devices such as the magnon transistor 4 , the spin-wave multiplexer 5 , domain walls as spinwave nanochannels 6 , graded-index magnonics 7 or a signal splitter based on caustic-like spin-wave beams 8 pave the way towards a controlled spin-wave transfer in magnonic networks.However, the application of these devices is limited by the finite magnon lifetime and, hence, the limited magnon propagation length determined by the Gilbert damping 9 . Thus, an efficient amplification of spin-waves or a control of the effective damping is inevitable. The latter can be achieved by employing the Spin-TransferTorque effect (STT) 10 . This effect yields an additional torque on the magnetization which can be co-aligned with the Gilbert damping torque resulting in an effective spin-wave damping given by the interplay of the Gilbert damping and the STT effect. This led, e.g., to the development of spin-torque nano-oscillators based on point-contacts which allow to generate oscillations in the GHz-range by DC currents 11,12 . Furthermore, in combination with the Spin-Hall-Effect (SHE) 13 to convert a charge current into a spin current in a normal metal, the SHE-STT effect allows for the control of the effective spin-wave damping also in spatially extended magnonic devices [14][15][16][17][18][19] . To achieve large SHE-STT induced effects with minimal current densities, the use of new materials with a low spin-wave damping, such as cobalt-based Heusler compounds 20 , is very promising. Using the SHE, e.g. in a Pt layer adjacent to a cobalt-based Heusler compound, the SHE-STT effect offers a powerful link to combine magnonics with CMOS technologies.Up to now, most of the reported studies on the manipulation of spin-waves in a magnonic waveguide via the SHE-STT effect only use static DC currents or quasi-DC p...