IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014 1100204 Magnetism and Magnetocrystalline Anisotropy in Low-Dimensional Rh and Ir Pankaj Kumar 1 , Ralph Skomski 2 , and Arti Kashyap 1 1 School of Basic Sciences, IIT Mandi, Mandi 175001, India 2 Nebraska Center for Materials and Nanoscience, Department of Physics and Astronomy, University of Nebraska, Lincoln, NE 68588 USA We report the ab initio calculations for angle resolved anisotropy in spin and orbital moment for zigzag chains of Rh and Ir. We present the site specific information about the spin and orbital moment in Rh and Ir zigzag chains. We observed a significant magnetocrystalline anisotropy energy (MAE) up to 17.5 meV/atom for Ir chains. We show that at the angles off the principal axes, orbital (L) and spin (S) angular momenta have different dynamics. We found a strong non-collinearity in the direction of spin and orbital moments in the plane perpendicular to the axis of the chains. The maximum orbital moments for the chains are along the axis of the chains. A ferromagnetic coupling has been observed in the zigzag chains of Rh as well as Ir. A key feature of the study is the alteration of the occupation states on changing the direction of magnetization vector, which results in switching the direction of MAE. Index Terms—Magnetic anisotropy, magnetization and density functional theory. I. I NTRODUCTION D ISENTANGLING spin and orbital angular momenta is of utmost importance in the spin dynamics. A change in the direction of magnetization vector alters the occupation of the states, which results in change in magnitude and direction of moments for the anisotropic systems, such as thin films and nanowires [1], [2]. Due to the directional nature of L and S, they can vary separately, which helps in tailoring the materials important for ultrafast magnetic recording media. Due to different dynamics of spin and orbital moment, L and S may combine parallel or antiparallel to each other according to Hund’s rules. This gives rise to anisotropic spin and orbital moments, which results in magnetocrystalline anisotropy ener- gies (MAEs) [3]–[10]. The directional properties are given by Bruno’s relation [11] but there are few cases where Bruno’s relation does not follow; for example, Au/Co/Au thin films, and Ni 2 MnGa shows a maximum orbital moment along the hard axis [11], [12]. Experimentally, spin and orbital moments along principal symmetry axes can be measured separately by X-ray magnetic circular dichroism [4]–[6], but there is no reason to expect that spin and orbital moments remain parallel for arbitrary magnetization directions [7]. Therefore, a measurement of spin and orbital moment anisotropies is essential for the thorough understanding of dynamics of L and S. In this paper, we considered zigzag chains of Rh and Ir to study the dependence of spin and orbital moment on each other and other magnetic properties against the spin quantization axis. To study the dynamics of L and S, spin and orbital moment vectors have to be appreciable. Rh and Ir are 4d and 5d elements and at nanoscale; they have appreciable spin moment, orbital Manuscript received February 20, 2014; accepted April 28, 2014. Date of current version November 18, 2014. Corresponding author: A. Kashyap (e- mail: arti@iitmandi.ac.in). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2014.2322315 moment, and large spin–orbit coupling (SOC). In addition, application of magnetic zigzag nanowires in regulating the Brownian fluctuations to transport the biological cells has drawn our interest to study the coupling of L and S in zigzag chains [13]. Coupling of L and S for 1-D chains has been studied exten- sively by many researchers. Most of the work has focus on the magnetics of linear chains of transition and late transition elements along the principle axes. Smogunov et al. [8] has studied the orientational aspects of the quantization axis for atomic chains of Pt. Coupling of L and S for linear and zigzag chains of 3d and 4d elements along the principle axes have been studied in [14] and [15]. However, in spite of much research in the field, surprisingly, very little is known about some aspects of MAE. This refers, in particular, to the relationship between the orbital moment and anisotropy at the angles off the principle axes in systems with low symmetry [16]–[19]. This includes, for example, ladder- and zigzag- shaped nanostructures, as contrasted to the usually considered systems with four-fold (linear chains) or higher symmetry around the symmetry axis. Therefore, for the thorough under- standing of L and S and effect of their non-collinear alignment on the other properties, the dynamics of magnetization at the angles off the planes are interesting to be studied. II. COMPUTATIONAL DETAILS The calculations have been performed within the frame- work of density functional theory, as implemented in the Vienna ab initio simulation package [20], [21]. The method uses an accurate frozen-core projector augmented plane wave method. Relativistic pseudopotentials were employed to do the anisotropy calculations, with exchange and corre- lation described in [22], using generalized gradient approx- imation. The chains are modeled by a standard supercell approach, ensuring that neighboring chains do not interact. MAE is calculated by adding SOC that is implemented in 0018-9464 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. 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