The phenomenon of different time scales of ultrafast demagnetization has attracted much attention. This so-called diversity of ultrafast demagnetization has been explained by the microscopic three temperature model (M3TM) and by the Landau-Lifshitz-Bloch model (LLBM). Here, we revisit the basic three temperature model (3TM) and provide a general criterion for explaining the different time scales observed. We focus on the role of magnetic heat capacity, which we find mainly determines the slowing down of the demagnetization time with increasing ambient temperature and laser fluence. In this context, we clarify the role of magnetic heat capacity in the M3TM and compare the 3TM with the LLBM. To illustrate the role of magnetic heat capacity, we present a simulation of ultrafast demagnetization of Ni. Furthermore, we present time-resolved magneto-optic Kerr effect measurements of ultrafast demagnetization and specific heat of ${\mathrm{Fe}}_{46}{\mathrm{Cu}}_{6}{\mathrm{Pt}}_{48}$ from 300 K to close to its Curie temperature. While most of the prior experimental research used high-fluence laser pulses causing sizable temperature excursions of the sample, our experiments involve small temperature excursions, which are crucial for studying the role of magnetic heat capacity in ultrafast demagnetization. Our experimental results corroborate that the slowing down of ultrafast demagnetization is dominated by the increase of the magnetic heat capacity near the Curie temperature.
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