Uncertainty estimates for magnetic relaxation times and magnetic relaxation parameters

The use of alternating current (AC) magnetometry to measure magnetic relaxation times is one of the most fundamental measurements for characterising single-molecule magnets (SMMs). These measurements, performed as a function of frequency, temperature and magnetic field, give vital information on the underlying magnetic relaxation process(es) occurring in the material. The magnetic relaxation times are usually fitted to model functions derived from spin-phonon coupling theories that allow characterisation of the mechanisms of magnetic relaxation. The parameters of these relaxation models are then often compared between different molecules in order to find trends with molecular structure that may guide the field to the next breakthrough. However, such meta-analyses of the model parameters are doomed to over-interpretation unless uncertainties in the model parameters can be quantified. Here we determine a method for obtaining uncertainty estimates in magnetic relaxation times from AC experiments, and provide a program called CC-FIT2 for fitting experimental AC data as well as the resulting relaxation times, to obtain relaxation parameters with accurate uncertainties. Applying our approach to three archetypal families of high-performance dysprosium(iii) SMMs shows that accounting for uncertainties has a significant impact on the uncertainties of relaxation parameters, and that larger uncertainties appear to correlate with crystallographic disorder in the compounds studied. We suggest that this type of analysis should become routine in the community.