Editing Superparamagnetism (section)

=== Blocking temperature ===

Let us imagine that the magnetization of a single superparamagnetic nanoparticle is measured and let us define <math>\tau_\text{m}</math> as the measurement time. If <math>\tau_\text{m} \gg \tau_\text{N}</math>, the nanoparticle magnetization will flip several times during the measurement, then the measured magnetization will average to zero. If <math>\tau_\text{m} \ll \tau_\text{N}</math>, the magnetization will not flip during the measurement, so the measured magnetization will be what the instantaneous magnetization was at the beginning of the measurement. In the former case, the nanoparticle will appear to be in the superparamagnetic state whereas in the latter case it will appear to be “blocked” in its initial state.

The state of the nanoparticle (superparamagnetic or blocked) depends on the measurement time. A transition between superparamagnetism and blocked state occurs when <math>\tau_\text{m} = \tau_\text{N}</math>. In several experiments, the measurement time is kept constant but the temperature is varied, so the transition between superparamagnetism and blocked state is seen as a function of the temperature. The temperature for which <math>\tau_\text{m} = \tau_\text{N}</math> is called the ''blocking temperature'':

:<math>T_\text{B} = \frac{K V}{k_\text{B} \ln \left(\frac{\tau_\text{m}}{\tau_0}\right)}</math>

For typical laboratory measurements, the value of the logarithm in the previous equation is in the order of 20–25.

Equivalently, blocking temperature is the temperature below which a material shows slow relaxation of magnetization.<ref>{{Cite journal|last1=Cornia|first1=Andrea|last2=Barra|first2=Anne-Laure|last3=Bulicanu|first3=Vladimir|last4=Clérac|first4=Rodolphe|last5=Cortijo|first5=Miguel|last6=Hillard|first6=Elizabeth A.|last7=Galavotti|first7=Rita|last8=Lunghi|first8=Alessandro|last9=Nicolini|first9=Alessio|last10=Rouzières|first10=Mathieu|last11=Sorace|first11=Lorenzo|date=2020-02-03|title=The Origin of Magnetic Anisotropy and Single-Molecule Magnet Behavior in Chromium(II)-Based Extended Metal Atom Chains|url=https://doi.org/10.1021/acs.inorgchem.9b02994|journal=Inorganic Chemistry|volume=59|issue=3|pages=1763–1777|doi=10.1021/acs.inorgchem.9b02994|issn=0020-1669|pmc=7901656|pmid=31967457|hdl=11380/1197352 }}</ref>