Time depending magnetization of nanoparticles under radiofrequency fields: relaxation time in water for solid-liquid transition

In application as hyperthermia and nanowarming, power dissipation arises when the time-dependent magnetization \(M(t)\) of an out-of-equilibrium system of nanoparticles lags behind the applied field \(H(t)\). The key parameter governing this process is the relaxation time \(\tau\) of the system, which induces a phase shift \(\phi_n\) between \(H(t)\) and every nth harmonic component of \(M(t)\). In this work, we present an expression for \(M(t)\) in terms of \(\tau\) and the equilibrium magnetization, valid for any magnetic system exhibiting odd equilibrium response. From this calculation, we obtain a method for determining the effective \(\tau\) of a MNPs sample directly from the experimental measurement of \(M(t)\). Additionally, we demonstrate that the power dissipation (SAR: Specific Absorption Rate) of any magnetic sample under a sinusoidal field can be obtained from the first harmonic component of \(M(t)\). As an illustrative application, we explore the variation of \(\tau\) for magnetic MNPs in aqueous suspension during the melting process of the matrix. In this case, the change in \(\tau\) can be understood as a result of the reorientation of the MNPs in the direction of the applied field as the matrix becomes liquid.