Origin of perpendicular magnetic anisotropy in Co/Ni multilayers

We studied the variation in perpendicular magnetic anisotropy of (111) textured $\mathrm{Au}/N\ifmmode\times\else\texttimes\fi{}[\mathrm{Co}/\mathrm{Ni}]/\mathrm{Au}$ films as a function of the number of bilayer repeats $N$. The ferromagnetic resonance and superconducting quantum interference device magnetometer measurements show that the perpendicular magnetic anisotropy of Co/Ni multilayers first increases with $N$ for $N\ensuremath{\le}10$ and then moderately decreases for $N>10$. The model we propose reveals that the decrease of the anisotropy for $N<10$ is predominantly due to the reduction in the magnetoelastic and magnetocrystalline anisotropies. A moderate decrease in the perpendicular magnetic anisotropy for $N>10$ is due to the reduction in the magnetocrystalline and the surface anisotropies. To calculate the contribution of magnetoelastic anisotropy in the Co/Ni multilayers, in-plane and out-of-plane x-ray diffraction measurements are performed to determine the spacing between Co/Ni (111) and (220) planes. The magnetocrystalline bulk anisotropy is estimated from the difference in the perpendicular and parallel $g$ factors of Co/Ni multilayers that are measured using the in-plane and out-of-plane ferromagnetic resonance measurements. Transmission electron microscopy has been used to estimate the multilayer film roughness. These values are used to calculate the roughness-induced surface and magnetocrystalline anisotropy coefficients as a function of $N$.