Therefore, frequency and temperature dependent AC susceptibility measurements on 2-Tb and 3-Tb were performed. At the lowest available temperature of 2 K and without the application of an external field, a maximum in the out-of-phase component of the susceptibility of 2-Tb is observed around 1 Hz (Fig. ). The maximum decreases in intensity upon increasing the temperature, which is commonly observed for SMMs, unless strong antiferromagnetic interactions are present between paramagnetic centers. Additionally, with increasing temperature the maximum shifts first slowly later quickly to higher frequencies. Such behavior is typical for dominant Raman relaxation at lower temperatures and Orbach relaxation, which is becoming dominant at elevated temperatures. The highest temperature at which reliable data were acquired was 58 K. It should be stated here, that at low T a rather high out-of-phase signal is obtained at high frequencies, which might be related to a fast-relaxing species, possibly introduced by partial decomposition of the sample. While the position of the maximum doesn't remain identical at low T, which would be a sign of relaxation via QTM, tunnelling is still likely to be present and relevant at low T. Thus, we have performed similar AC susceptibility measurements under the application of an external DC magnetic field of 2000 Oe which, by lifting the degeneracy of the ground state, should improve the energy barrier to relaxation. The field was chosen as the field resulting in the slowest relaxation (maximum observed at lowest frequency). Under the applied field, the lowest temperature at which a maximum is observed shifted to 16 K, where the maximum is centered around 0.1 Hz and the signal remains observable up to 60 K (Fig. ). The trend at which the maximum is shifting its frequency position resembles that of Raman and Orbach relaxation. Analogously, AC susceptibility measurements at zero field and 2000 Oe were performed on a sample of 3-Tb. At zero field and 2 K a maximum is observed around 30 Hz, therefore, significantly faster compared to 2-Tb (Fig. ). A reliable maximum was detected up to 38 K. The T-dependence of the maximum suggests much stronger contribution of quantum tunnelling compared to 2-Tb, as the maximum doesn't shift in frequency at low T. Similarly, the available temperature range was improved by the application of the external 2000 Oe field, resulting in an observed maximum between 9 K and 60 K (Fig. ). In order to validate out assumptions, the recorded frequency dependent inphase and out-of-phase components were simultaneously fit to a generalized Debye model allowing the determination of the relaxation time τ (Table , S3, S5, S6). Based on the description above, we have attempted fits of τ vs. T using a combination of Orbach, Raman and QTM processes for the data collected at zero external field using equation (1):