Magnetocrystalline anisotropy of FePt: A detailed view

To get a reliable ab initio value for the magnetocrystalline anisotropy (MCA) energy of FePt, we employ the full-potential linearized augmented plane wave (FLAPW) method and the full-potential Korringa-Kohn-Rostoker (KKR) Green function method. The MCA energies calculated by both methods are in good agreement with each other. As the calculated MCA energy significantly differs from experiment, it is clear that many-body effects beyond the local density approximation are essential. It is not really important whether relativistic effects for FePt are accounted for by solving the full Dirac equation or whether the spin-orbit coupling (SOC) is treated as a correction to the scalar-relativistic Hamiltonian. From the analysis of the dependence of the MCA energy on the magnetization angle and on the SOC strength it follows that the main mechanism of MCA in FePt can be described within second order perturbation theory. However, a distinct contribution not accountable for by second order perturbation theory is present as well.

Figure 1

Crystal structure of bulk $\mathrm{L}{1}_0$ FePt.

Figure 2

Dependence of the total energy on the magnetization angle $\theta$ (circles) and its fit either as $K_1{sin}^2\theta$ (dashed line) or as $K_1{sin}^2\theta +K_2{sin}^4\theta$ (dash-dotted line). An overall view is in the left panel; a detailed view of the region close to $\theta ={90}^{\circ }$ is in the right panel.

Figure 3

Dependence of $E_{\mathrm{MCA}}$ on the SOC scaling factor $\lambda$. The markers denote calculated values of $E_{\mathrm{MCA}}$; the line represents a fit to these data within the $\lambda \in [0;0.4]$ interval.

Figure 4

Dependence of $E_{\mathrm{MCA}}$ on the SOC scaling factor at the Fe sites ${\lambda }_{\text{Fe}}$. The markers denote calculated values of $E_{\mathrm{MCA}}$; the line in the left panel represents a fit to these data within the ${\lambda }_{\text{Fe}}\in [0;0.4]$ interval.

Figure 5

Dependence of $E_{\mathrm{MCA}}$ on the SOC scaling factor at the Pt sites ${\lambda }_{\text{Pt}}$. The markers denote calculated values of $E_{\mathrm{MCA}}$; the line in the left panel represents a fit to these data within the ${\lambda }_{\text{Pt}}\in [0;0.4]$ interval.

Figure 6

Partial spin-resolved angular-momentum-projected density of states for Fe and Pt sites calculated within a nonrelativistic, a scalar-relativistic, and a fully-relativistic framework.