Magnetic anisotropy of fcc transition-metal clusters: Role of surface relaxation - art. no. 177420

The magnetic-anisotropy energy (MAE) of fee transition-metal (TM) clusters (19 less than or equal toN less than or equal to 79) is determined using tw o different semiempirical schemes. First within a tight-binding calculation for the d band, the equilibrium geometries of the clusters, which are buil t by adding successive atomic shells around a central atom, are obtained by means of the fictitious Lagrangian method introduced by Car and Parrinello [Phys. Rev. Lett. 55, 2471 (1985); 60, 204 (1988)]. In this approach, both atomic and electronic structures are treated simultaneously in the minimiz ation algorithm, a procedure that reveals the existence of a highly nonunif orm relaxation profile of the intershell spacings in the clusters, which ma y contract as well as expand, in agreement with the results found at surfac es of TM's. In a second step, treating the spin-orbit coupling nonperturbat ively and also within the framework of a d-band Hamiltonian, we analyze the role of this complex interlayer-spacing distribution on the magnetoanisotr opic behavior of the clusters. In all cases, we perform single-point energy calculations, for two different directions of the magnetization delta, on the previously optimized geometries using the Car-Parrinello method. The MA E shows a complicated behavior as a function of cluster size, bond length, and d-band filling. Moreover, by investigating different relaxations, it is shown that the existence of this nonuniform pattern of interatomic distanc es causes appreciable changes in the magnitude of the MAE and can be also a t the origin of reorientations of the magnetization in the particles. We co nclude that this kind of structural transformations are essential for quant itative predictions of the MAE in cluster systems.