Higher-order magnetic anisotropies and the nature of the spin-reorientation transition in face-centered-tetragonal Ni(001)/Cu(001)

Second- and fourth-order constants ${\mathrm{K}}_2$ , ${\mathrm{K}}_4$ of the magnetic anisotropy energy in tetragonally distorted Ni(001) ultrathin films on Cu(001) are determined as a function of temperature and film thickness. We measure a positive out-of-plane constant ${\mathrm{K}}_{4\mathrm{\perp }}$ ≈+0.24 μeV/atom and a negative in-plane constant ${\mathrm{K}}_{4\mathrm{\parallel }}$ near room temperature. This leads to a continuous (second or higher-order) spin-reorientation transition of the easy axis from an in-plane below ≈7 ML to a perpendicular orientation for thicker films. ${\mathrm{K}}_{4\mathrm{\parallel }}$ changes sign at ${\mathrm{d}}_{\mathrm{c}\mathrm{\parallel }}$ ≈6.7 ML which results in a change of the easy axis from the [100] direction below 6.7 ML to the [110] direction above. These results are quantitatively compared to Ni(111)/W(110) for which no out-of-plane reorientation is observed.