Characterisation of magnetic relaxation on extremely long timescales

The use of magnetisation decay measurements to characterise very slow relaxation of the magnetisation in single-molecule magnets are becoming increasingly prevalent as relaxation times move to longer timescales outside of the AC susceptibility range. However, experimental limitations and a poor understanding of the distribution underlying the stretched exponential function, commonly used to model the data, may be leading to misinterpretation of the results. Herein we develop guidelines on the experimental design, data fitting, and analysis required to accurately interpret magnetisation decay measurements. Different measures of the magnetic relaxation rate extracted from magnetisation decay measurements of [Dy(Dtp)2][Al{OC(CF3)3}4], fitted using different combinations of fixing or freely fitting different parameters, are compared to those obtained using the innovative square-wave “waveform” technique of Hilgar et al, which is comparable to AC susceptometry for measurement of relaxation rates on long timescales. The most reliable measure of the relaxation time for magnetisation decays is found to be the the average logarithmic relaxation time, $e^{⟨ln [τ]⟩}$, obtained via a fit of the decay trace using a stretched exponential function, where the initial and equilibrium magnetisation are fixed to first measured point and target values respectively. This new definition has causes the largest differences to traditional approaches in the presence of large distributions or relaxation rates, with differences up to 50% with β = 0.45, and hence could have a significant impact on the chemical interpretation of magnetic relaxation rates. A necessary step in progressing towards chemical control of magnetic relaxation is the accurate determination of relaxation times, and such large variations in experimental measures stress the need for consistency in fitting and interpretation of magnetisation decays.