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.