3 Temperature-dependent magnetization

In order to calculate the temperature dependent magnetization of $Co(111)\setminus Ag_{1}$ system, we have modeled a thin film system with 5 atomic layers and a total of $N=845$ spins. We apply the constrained Monte Carlo method described in chapter 4 to evaluate the temperature dependence of macroscopic parameters.

Figure 6.15: Magnetization versus temperature for a thin film with 5 magnetic layers, such the parameters correspond to the values extracted for the $Co(111)\setminus Ag_{1}$ system. Two approximations of the exchange interactions (TET and IEC) are used.

In Fig. 6.15, we present the average magnetization as a function of the temperature for the two approximations described above.

We can see that the two models of the exchange interaction reproduce the same dependence of the magnetization with temperature, giving the same Curie temperature and adjust perfectly. This is a natural fact since it is known that the Curie temperature is defined by the total exchange strength only. The calculated Curie temperature has been interpolated as $Tc \approx 1200 K$, compared to the known experimental value $Tc=1388-1403K$ [184], our calculated value is smaller. As we showed in Chapter 4 this is due to the loss of neighbors for the surface spins.