Magneto-optical Kerr effect in perpendicularly magnetized ${\left({\mathrm{Co}}_2{\mathrm{Pt}}_6\right)}_n∕\mathrm{Pt}\left(111\right)$ superstructures

Perpendicular magnetism facilitates an increase of the storage density by a factor 2–8 as compared to longitudinal recording. Besides the improved chemical and physical stability of $\mathrm{Co}∕\mathrm{Pt}$ superstructures compared to RE-TM alloys, a perpendicular easy axis can be obtained by selecting a suitable $\mathrm{Co}∕\mathrm{Pt}$ bilayer thickness ratio. For different repetition numbers $n⩽6$ ab initio calculated Kerr angles are presented for ${\left({\mathrm{Co}}_2{\mathrm{Pt}}_6\right)}_n$ superstructures on Pt(111) with a 6 Pt layers thick cap in a photon energy range of $1–8\mathrm{eV}$. The calculated maximum in the Kerr rotation angle occurs at an energy close to the experimentally observed value. Assuming an exponential decay of the gradient of ${\theta }_K$ with respect to $n$, an extrapolation of the calculated data to large $n$ was performed in order to compare the obtained results to available experimental data.

Figure 1

Diagonal elements of the layer-resolved complex dielectric tensor, ${\epsilon }_{xx}^p$ and ${\epsilon }_{zz}^p$, in the case of ${\left({\mathrm{Co}}_2{\mathrm{Pt}}_6\right)}_5∕\mathrm{Pt}\left(111\right)$. Note that only one unit ${\mathrm{Co}}_2{\mathrm{Pt}}_6$ is shown. The layers are labeled beginning with the last layer of the previous bilayer $(p=8)$. Vertical lines denote the interfaces between Pt and Co. Diamonds refer to $\mathrm{Re}\left({\epsilon }_{xx}^p\right)$ in the first, to $\mathrm{Im}\left({\epsilon }_{xx}^p\right)$ in the second, and to $\mathrm{Re}({\epsilon }_{xx}^p-{\epsilon }_{zz}^p)$ in the third row, triangles in turn refer to $\mathrm{Re}\left({\epsilon }_{zz}^p\right)$, $\mathrm{Im}\left({\epsilon }_{zz}^p\right)$, and $\mathrm{Im}({\epsilon }_{xx}^p-{\epsilon }_{zz}^p)$.

Figure 2

Off-diagonal elements of the layer-resolved complex dielectric tensor, ${\epsilon }_{xy}^p$ in the case of ${\left({\mathrm{Co}}_2{\mathrm{Pt}}_6\right)}_5∕\mathrm{Pt}\left(111\right)$. Diamonds denote $\mathrm{Re}\left({\epsilon }_{xy}^p\right)$, triangles $\mathrm{Im}\left({\epsilon }_{xy}^p\right)$, see also Fig. 1.

Figure 3

Layer-resolved magnetic moments in ${\left({\mathrm{Co}}_2{\mathrm{Pt}}_6\right)}_5∕\mathrm{Pt}\left(111\right)$. Full diamonds denote the spin-only, full triangles the orbital-only magnetic moments, the sum of both is represented by open diamonds.

Figure 4

MOKE for ${\left({\mathrm{Co}}_2{\mathrm{Pt}}_6\right)}_n∕\mathrm{Pt}\left(111\right)$ superstructures at an energy of $\hslash \omega =3\mathrm{eV}$. In the left part diamonds denote the Kerr rotation angle ${\theta }_K$, triangles the Kerr ellipticity angle ${\epsilon }_K$, and the dashed line an interpolation for ${\theta }_K$. In the right part the extrapolation to large $n$ is also shown.

Figure 5

Kerr rotation and ellipticity angles, ${\theta }_K$ and ${\epsilon }_K$, and the magnitude of the complex Kerr angle, $\mid {\Phi }_K\mid$, for different photon energies. In all three entries diamonds, triangles, and circles denote the calculated Kerr quantities of ${\left({\mathrm{Co}}_2{\mathrm{Pt}}_6\right)}_n∕\mathrm{Pt}\left(111\right)$ superstructures with repetition number $n=1$, 3, and 6, respectively. Open circles and squares refer to the calculated data for ${\theta }_K$ and ${\epsilon }_K$ of Ref. 24 in ${\mathrm{Co}}_2{\mathrm{Pt}}_7$ and ${\mathrm{Co}}_3{\mathrm{Pt}}_6$, respectively. Measured data for ${\theta }_K$, ${\epsilon }_K$, and ${\Phi }_K$ are denoted in the following way: In the case of ${\theta }_K$, dashed line: ${[\mathrm{Co}\left(3.75\mathrm{\AA }\right)∕\mathrm{Pt}\left(13.5\mathrm{\AA }\right)]}_{20}∕\mathrm{Pt}∕\mathrm{Si}$ (Ref. 6); dotted line: ${[\mathrm{Co}\left(3.75\mathrm{\AA }\right)∕\mathrm{Pt}\left(13.5\mathrm{\AA }\right)]}_{10}∕\mathrm{Pt}∕\mathrm{Si}$ (Ref. 6); dashed-dotted line: ${[\mathrm{Co}\left(4.5\mathrm{\AA }\right)∕\mathrm{Pt}\left(17.7\mathrm{\AA }\right)]}_{22}∕\mathrm{Si}$ (Ref. 5); dashed-dotted-dotted line: $[\mathrm{Co}\left(3.8\mathrm{\AA }\right)∕\mathrm{Pt}\left(13.4\mathrm{\AA }\right)]$ on a glass substrate (Ref. 24). For ${\epsilon }_K$, dashed line: ${[\mathrm{Co}\left(3.75\mathrm{\AA }\right)∕\mathrm{Pt}\left(13.5\mathrm{\AA }\right)]}_{20}∕\mathrm{Pt}∕\mathrm{Si}$ (Ref. 6); dotted line: ${[\mathrm{Co}\left(3.75\mathrm{\AA }\right)∕\mathrm{Pt}\left(13.5\mathrm{\AA }\right)]}_{10}∕\mathrm{Pt}∕\mathrm{Si}$ (Ref. 6); dashed-dotted-dotted line: $[\mathrm{Co}\left(3.8\mathrm{\AA }\right)∕\mathrm{Pt}\left(13.4\mathrm{\AA }\right)]$ on a glass substrate (Ref. 24). Finally, ${\Phi }_K$ of ${[\mathrm{Co}\left(4.1\mathrm{\AA }\right)∕\mathrm{Pt}\left(19\mathrm{\AA }\right)]}_{25}$ (Ref. 4) is given by a dashed line.

Figure 6

Extrapolation to higher values of $n$. Left entry: full symbols denote the ab initio calculated ${\theta }_K$ for $n=1$ (diamonds), 3 (triangles), and 6 (circles), respectively; open symbols denote data extrapolated to $n=10$ (diamonds), 20 (triangles), and $n\to \infty$ (circles), respectively. Right entry: ${\theta }_K\left(n\right)∕{\theta }_K(n=6)$ at $n=10$ (diamonds), $n=20$ (triangles), and $n\to \infty$ (circles).