Role of interfaces in higher order angular terms of magnetic anisotropies: ultrathin film structures

The role of interface inhomogeneities on macroscopic magnetic anisotropy terms was investigated using simple mathematical modeling. It is shown that the intrinsic anisotropies caused by the spin-orbit interaction in the presence of lateral inhomogeneities can create additional magnetic anisotropies with higher order angular terms, The lateral inhomogeneous distribution of the uniaxial anisotropy can result in the presence of a fourth order angular term. These anisotropies decrease the total energy, and their strength is affected by the exchange averaging effect. Large atomic terraces allow the local magnetic moment to deviate from the mean orientation resulting in negative higher order angular terms in magnetic anisotropies satisfying the sample symmetry. The negative sign results in the magnetic easy axes being oriented 45 degrees with respect to the intrinsic uniaxial axis. It is shown that the additional higher order terms do not always have to satisfy the time inversion symmetry. Odd powers in directional cosines can arise when the exchange restoring torque becomes comparable to or weaker than torques from the internal fields. The additional higher order angular terms in magnetic anisotropies decrease usually more rapidly with the sample thickness than the intrinsic interface anisotropies. Their rapid decrease in strength with an increasing sample thickness allows one to distinguish them from the intrinsic interface anisotropies. It will be shown that the magnetic anisotropies originating in interface inhomogeneities can play an important role in the magnetic phase transitions of ultrathin film structures. (C) 2001 Elsevier Science B.V. All rights reserved.