4 Temperature-dependent anisotropy

In chapter 4 we presented the constrained Monte Carlo method and we showed that this method is a powerful tool to determine the temperature dependence of the effective anisotropy of the system. Below we present the results for the temperature-dependent anisotropy for a $Co(111)\setminus Ag_{1}$ thin films.

Figure 6.16: Effective anisotropy constant versus temperature (left) and critical exponent at low temperatures (right) for a $Co(111)\setminus Ag_{1}$ thin films with 5 magnetic layer for the two approximations of the exchange interactions (TET and IEC).

In the left side of Fig. 6.16 the temperature-dependent effective anisotropy is plotted. In contrast to what happens in the temperature-dependent magnetization case, the use of the isotropic exchange constant modifies the results.

The effective value at $T=0K$ is also different being larger in the case of full but truncated exchange tensor than for the isotropic exchange constant approximation. Such an increment of the initial effective anisotropy is due to the fact that in the first case the "two-site" anisotropy and the DM interaction are included explicitly. The DM interaction favors the orientation of the magnetization in plane, leading to a reduction of the anisotropy out-of-plane, but the contribution of the "two-site" anisotropy favors the anisotropy perpendicular to the surface of the sample and this contribution is more important leading to a net increment of the anisotropy out-of-plane. The IEC approximation includes these contributions in a modified "uniaxial anisotropy" which is obviously wrong.

We have also calculated the low-temperature scaling exponents $\gamma$ of the anisotropy with magnetization and we have observed that in the case of TET $\gamma\approx2.69$ and in the case of IEC $\gamma\approx3$. That discrepancy of the results is due to that in TET case and differently to IEC approximation we have taken into account the total exchange matrix, which has an important contribution of the "two-site" anisotropy. As it has been shown by Mryrasov et al. [185] this term is responsible of the deviation from $\gamma=3$ exponent (typical for uniaxial anisotropy) in the case of $FePt$.