Magnetic anisotropy energy and the anisotropy of the orbital moment of Ni in Ni/Pt multilayers

Angular-dependent x-ray magnetic circular dichroism experiments are performed on Ni/Pt multilayers at the Ni $L_{2,3}$ edges under magnetic fields up to 50 kG at a temperature of 10 K. By rotating the applied field away from the easy axis a decrease of the ratio of the orbital-to-spin magnetic moment ${\mu }_L/{\mu }_S$ of Ni is observed for perpendicularly magnetized Ni/Pt layers which show considerable magnetic anisotropy energy (≈20 μeV/atom). Saturation effects in the recorded spectra, depending on both the thicknesses of Ni and Pt, are shown to lead into erroneous conclusions in the determination of ${\mu }_L/{\mu }_S$ and they have to be considered in the analysis. An anisotropy of the Ni-orbital moment $\Delta {\mu }_L$ as large as 22% of ${\mu }_L$ is determined. $\Delta {\mu }_L$ is demonstrated to be the origin of the magnetic anisotropy energy of $3d$ ferromagnetic elements.