Magnetic characterization
SQUID magnetometry is routinely used for the characterization of SMMs. Of particular relevance are alternating current (AC) susceptibility and magnetization decay experiments, as a way to extract relaxation times across wide temperature ranges and characterize the so-called relaxation profile (\(\tau^{-1}\) vs T ) of the SMM (Figure 2a). The relaxation profile provides information on what the most effective pathway to relaxation of magnetization is in a given temperature range, and is generally described as:
\(\tau^{-1}=\tau_{0}^{-1}e^{\frac{-U_{\text{eff}}}{T}}+CT^{n}+\tau_{\text{QTM}}^{-1}\)(eq. 1)
where the first term accounts for a thermally-activated over-barrier pathway that involves one-phonon processes (Orbach relaxation), the second describes the effect of two-phonon processes (Raman relaxation) and the third considers quantum tunneling of magnetization (QTM). Normally, these three mechanisms are active in different temperature regimes (high, intermediate and low, respectively) and fitting the experimental data to eq. 1 yields the key parameters that define the SMM.
During AC susceptibility measurements the response of the sample’s magnetic moment under an oscillating field is recorded – if the characteristic relaxation rate coincides with the angular frequency of the AC field, a maximum is observed in the out-of-phase AC signal (Figure 2b bottom).[1] This is well-characterized by the generalized Debye model, which includes modelling of a distribution in \(\tau\) (\(\alpha\) in Figure 2b), which is usually disregarded in the subsequent data treatment. Similarly, magnetization decays can be used to extract relaxation times when \(\tau\) falls out the window of available frequencies in AC susceptometry; by applying a magnetic field, the magnetic moment of the sample can be saturated, after which the field is switched off and the time-evolution of the magnetization is recorded (Figure 2c), where the results are customarily fitted to a stretched exponential. As with AC susceptibility, the model function used to reproduce the experimental data assumes a distribution of relaxation times (\(\beta\) in Figure 2c), also usually ignored when modelling the relaxation profile. Indeed, the experimental error in\(\tau\) is quite small and errors for the parameters in eq. 1 are quite small.