Orbital magnetism and magnetic anisotropy energy of Co nanoparticles: Role of polytetrahedral packing, polycrystallinity, and internal defects

Abstract

We report extensive self-consistent electronic structure calculations in order to analyze the magnetic properties of Co nanoparticles with complex atomic configurations. Following recent experimental works, we consider polycrystalline structures in which a coexistence of bcc and compact (fcc) phases is present within the particles, polytetrahedral clusters, as well as fcc nanocrystals with ``stacking-fault-like'' defects. In all cases, the local spin moments ${S}_{\ensuremath{\delta}}(i)$ are found to be saturated $(\ensuremath{\sim}1.7{\ensuremath{\mu}}_{B})$, being almost independent of the direction of the magnetization $\ensuremath{\delta}$, the local atomic environment $i$, and the size of the particles, a behavior that is characteristic of magnetic materials in the large exchange regime. In contrast, the local-orbital moments ${L}_{\ensuremath{\delta}}(i)$ and the magnetic anisotropy energy (MAE) are found to be very sensitive to the size and structure of the systems. In our polycrystalline particles, we obtain considerably enhanced values for ${L}_{\ensuremath{\delta}}(i)$ at the internal bcc/fcc interfaces (even larger than at surfaces sites) and, interestingly, we obtain that by varying the fraction of bcc and fcc phases within the particles, several reorientations of the magnetization can be induced. Furthermore, our polytetrahedral structures are characterized by the existence of very isolated and low coordinated surface atoms, a fact that induces the formation of localized states with large local magnetic moments ${M}_{\ensuremath{\delta}}(i)$ $[{M}_{\ensuremath{\delta}}(i)=2{S}_{\ensuremath{\delta}}(i)+{L}_{\ensuremath{\delta}}(i)]$ of $3.7{\ensuremath{\mu}}_{B}$ and huge orbital contributions ${L}_{\ensuremath{\delta}}(i)$ as large as $2{\ensuremath{\mu}}_{B}$. Even if enhanced local MAE's are also found, negative and positive values are obtained in the different sites, resulting in nonadditive contributions that yield small energy barriers between our different considered $\ensuremath{\delta}$'s. Finally, we obtain that the existence of internal defects, created by locally interrupting the regular growth mode in fcc nanocrystals, considerably perturbs the electron spin-density distribution around the defect sites, leading to strong variations in ${L}_{\ensuremath{\delta}}(i)$ and to reorientations of the magnetization in the system.