Determining the zero-field cooling/field cooling blocking temperature from AC susceptibility data for single-molecule magnets

Abstract

We present a general relationship between the magnetisation blocking temperature (T_B) measured using the zero-field cooling/field cooling technique (ZFC/FC) and the temperature-dependent spin relaxation time obtained from AC susceptibility and magnetisation decay measurements. The presented mathematical approach supplies ZFC/FC blocking temperatures at any heating rate (R_H), providing comparable values to those obtained experimentally, as demonstrated by testing 107 examples for reported single-molecule magnets (SMMs) where the ZFC/FC curve has been measured. This procedure is examined in further detail for a new single-molecule magnet, [Dy(OPAd₂Bz)₂(H₂O)₄Br]Br₂·4THF (1) (OPAd₂Bz: di(1-adamantyl)benzylphosphine oxide). For this compound, ZFC/FC measurements were made over a broad range of heating rates (0.01–5 K min⁻¹), which agreed with the general behaviour predicted from AC susceptibility data. We discuss how the demagnetisation mechanism determines the sensitivity of T_B with respect to the heating rate: T_B is mostly insensitive to R_H for Orbach relaxation, while there is a larger sensitivity for Raman-limited systems. Our conclusions provide a clear physical interpretation of ZFC/FC blocking temperatures, aiding in the proper contextualization of this figure of merit.