The crossover from one-dimensional (1D) to two-dimensional (2D) magnetic anisotropy of transition-metal nanostructures is investigated theoretically. The in-plane and off-plane magnetic anisotropy energies (MAEs) of stripes are determined systematically as a function of stripe width $m$ thereby bridging the gap between the 1D chain $(m=1)$ and the 2D monolayer $(m=\infty )$. The MAEs are in general enhanced upon reduction of dimensionality. They oscillate as a function of $m$, especially in the ultranarrow limit $(m⩽10)$ where the easy and hard axis depend strongly on $m$ and on the considered transition metal. The convergence to the 2D limit with increasing $m$ is found to be relatively slow, particularly concerning the in-plane anisotropy. Comparison between square and triangular lattices demonstrates the importance of the transversal structure of the stripe. The local contributions to the MAE and the correlation between MAE and average orbital moments are discussed. The magnetization-reorientation transitions observed as a function of $m$ reveal the remarkable richness and complexity of the crossover from 1D to 2D magneto-anisotropic behavior.

• Received 19 April 2005

DOI:https://doi.org/10.1103/PhysRevB.72.085427