Magnetic moment and magnetic anisotropy of linear and zigzag4dand5dtransition metal nanowires: First-principles calculations

Abstract

An extensive ab initio study of the physical properties of both linear and zigzag atomic chains of all $4d$ and $5d$ transition metals (TMs) within the generalized gradient approximation by using the accurate projector-augmented wave method, has been carried out. The atomic structures of equilibrium and metastable states were theoretically determined. All the TM linear chains are found to be unstable against the corresponding zigzag structures. All the TM chains, except Nb, Ag, and La, have a stable (or metastable) magnetic state in either the linear or zigzag or both structures. Magnetic states appear also in the sufficiently stretched Nb and La linear chains and in the largely compressed Y and La chains. The spin magnetic moments in the Mo, Tc, Ru, Rh, W, Re chains could be large $(\ensuremath{\ge}1.0\text{ }{\ensuremath{\mu}}_{B}/\text{atom})$. Structural transformation from the linear to zigzag chains could suppress the magnetism already in the linear chain, induce the magnetism in the zigzag structure, and also cause a change in the magnetic state (ferromagnetic to antiferromagnetic or vice verse). The calculations including the spin-orbit coupling reveal that the orbital moments in the Zr, Tc, Ru, Rh, Pd, Hf, Ta, W, Re, Os, Ir, and Pt chains could be rather large $(\ensuremath{\ge}0.1\text{ }{\ensuremath{\mu}}_{B}/\text{atom})$. Importantly, large magnetic anisotropy energy $(\ensuremath{\ge}1.0\text{ }\text{meV}/\text{atom})$ is found in most of the magnetic TM chains, suggesting that these nanowires could have fascinating applications in ultrahigh-density magnetic memories and hard disks. In particular, giant magnetic anisotropy energy $(\ensuremath{\ge}10.0\text{ }\text{meV}/\text{atom})$ could appear in the Ru, Re, Rh, and Ir chains. Furthermore, the magnetic anisotropy energy in several elongated linear chains could be as large as 40.0 meV/atom. A spin-reorientation transition occurs in the Ru, Ir, Ta, Zr, La, Ta, and Ir linear chains when they are elongated. Remarkably, all the $5d$ as well as Tc and Pd chains show the colossal magnetic anisotropy (i.e., it is impossible to rotate magnetization into certain directions). Finally, the electronic band structure and density of states of the nanowires have also been calculated in order to understand the electronic origin of the large magnetic anisotropy and orbital magnetic moment as well as to estimate the conduction electron spin polarization.