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

Abstract

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 ${\mathrm{K}}_{4\mathrm{\ensuremath{\perp}}}$ \ensuremath{\approx}+0.24 \ensuremath{\mu}eV/atom and a negative in-plane constant ${\mathrm{K}}_{4\mathrm{\ensuremath{\parallel}}}$ near room temperature. This leads to a continuous (second or higher-order) spin-reorientation transition of the easy axis from an in-plane below \ensuremath{\approx}7 ML to a perpendicular orientation for thicker films. ${\mathrm{K}}_{4\mathrm{\ensuremath{\parallel}}}$ changes sign at ${\mathrm{d}}_{\mathrm{c}\mathrm{\ensuremath{\parallel}}}$ \ensuremath{\approx}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.