Reorientation transition in ${\mathrm{Fe}}_n∕\mathrm{Au}\left(100\right)$

Experimental investigations and theoretical magnetic anisotropy energy calculations show a reorientation transition of the magnetization in ${\mathrm{Fe}}_n∕\mathrm{Au}\left(100\right)$ from a normal-to-plane to an in-plane direction at about three monolayers of Fe. In the present paper the magneto-optical properties of this system are investigated theoretically by using the spin-polarized relativistic screened Korringa-Kohn-Rostoker method, the Kubo-Greenwood equation for finite photon frequencies, and a classical optical approach that takes into account all reflections and interferences. By varying the thickness of the Fe film, the reorientation of the ground-state magnetization is clearly traced as a strong decrease in the calculated Kerr rotation angles for oblique incidence of light. For all film thicknesses under consideration, it is found that by continuously varying the angle of the incident light the Kerr rotation angle reaches a maximum at an incidence of about 70°. In the case of normal incidence a direct proportionality of the Kerr angles to the normal component of the magnetization is demonstrated by changing the orientation of the magnetization. When relating Kerr angles as calculated for a set of angles between the surface normal and the orientation of the magnetization to the corresponding magnetic anisotropy energy a very compact description of the occurring reorientation transition can be given. Moreover, based on these data and using a simple phenomenological picture a qualitative description of the Kerr angles with respect to applied external fields is provided.

Figure 1

The Kerr setup used in the calculations in the case of $p$-polarized incident light. Here $\alpha$ and $\beta$ specify the orientation of the magnetization $\mathbf{M}$ and the direction of the incident light, respectively. Both are specified with respect to the surface normal. Note that the magnetization always lies in the plane of incidence.

Figure 2

Top: SMOKE experiments by Liu and Bader (Ref. 1). Circles denote the measured data for the polar, whereas triangles for the longitudinal Kerr setup. Bottom: calculated values of the Kerr rotation angle ${\theta }_K$ in the case of $p$-polarized incident light and for the magnetic ground state of ${\mathrm{Fe}}_n∕\mathrm{Au}\left(100\right)$. Circles mark the theoretical results for a normal incidence $(\beta =0°)$ and triangles for an incidence of $\beta =70°$ (see also Fig. 1).

Figure 3

The calculated Kerr rotation angle (upper part) and ellipticity angle (lower part) for different angles of incidence (see Fig. 1) for the corresponding magnetic ground state of ${\mathrm{Fe}}_n∕\mathrm{Au}\left(100\right)$.

Figure 4

The calculated Kerr rotation angle as a function of the angle of incidence $\beta$ and for different thicknesses of Fe films on Au(100). Open circles, squares, and triangles refer to 1, 2, and 3 ML of Fe on the top of Au(100), respectively; full circles, squares, and triangles to 4, 5, and 6 ML, respectively.

Figure 5

The calculated Kerr angles in the case of normal incidence for ${\mathrm{Fe}}_4∕\mathrm{Au}\left(100\right)$ as a function of the angle $\alpha$ (see Fig. 1).

Figure 6

The calculated Kerr angles displayed as a function of the magnetic anisotropy energy for different thicknesses of the Fe film on Au(100). Full symbols refer to Kerr rotation, open symbols to Kerr ellipticity angles. The data for this figure were obtained by varying the angle of magnetization $\alpha$ while the angle of incidence is fixed to $\beta =0°$ (see Fig. 1).

Figure 7

The calculated Kerr angles displayed as a function of a longitudinal ($H_{\mathrm{ext}}^{\Vert }$, right part) and a polar ($H_{\mathrm{ext}}^{\perp }$, left part) external magnetic field applied to ${\mathrm{Fe}}_n∕\mathrm{Au}\left(100\right)$ for $n⩽3$ and $n>4$, respectively. As in Fig. 6 the data for this figure were obtained by varying $\alpha$ and keeping the angle of incidence fixed to $\beta =0°$ (see also Fig. 1).