PHYSICAL REVIEW B 86, 094436 (2012) Ab initio investigations of magnetic properties of FeCo monolayer alloy films on Rh(001) S. Blizak, 1,* G. Bihlmayer, 2,† and S. Bl ¨ ugel 2 1 University M’Hamed Bougara of Boumerd´ es (UMBB), Unit´ e de Recherche Mat´ eriaux Proc´ ed´ es et Environnement (ex: LMMC), 35000 Boumerd´ es, Algeria 2 Peter Gr¨ unberg Institut and Institute for Advanced Simulation, Forschungszentrum J¨ ulich and JARA, 52425 J¨ ulich, Germany (Received 6 July 2012; published 28 September 2012) The objective of this work is to employ spin-polarized density functional theory (sDFT) calculations for the exploration of ultrathin magnetic films with large magnetic moments and a strong perpendicular anisotropy. Monolayer films of Fe 1−x Co x (with x = 0, 0.25, 0.5, 0.75, and 1) on Rh(001) were addressed to study their magnetic properties using the all-electron full-potential linearized augmented plane wave (FLAPW) method in film geometry. We studied the magnetic order of these films including structural relaxations of the topmost layers. Fe 1−x Co x monolayer films were found to be ferromagnetic (FM) in a broad range of Co content x with a maximum magnetic moment of 2.8 μ B and of an out-of-plane magneto-crystalline anisotropy of 0.25 meV per magnetic atom at x = 0.5. The sDFT results were mapped onto a classical Heisenberg model, demonstrating FM Fe-Co and Co-Co couplings, while the Fe-Fe interaction is antiferromagnetic on Rh(001). The ordering temperature of the FeCo film was estimated to be well above room temperature (482 K). DOI: 10.1103/PhysRevB.86.094436 PACS number(s): 75.70.Ak, 73.20.−r, 71.15.Mb I. INTRODUCTION Materials with large magnetic moments and a strong perpendicular anisotropy are of great interest for information technology and recording media applications as well as magnetic field sensors. 1 In recent research, a great deal of attention has been devoted to transition-metal (TM) alloy films on various substrates. The (Fe 1−x Co x ) N /Rh(001) system is an important example, since films on Rh(001) 2,3 show a perpen- dicular anisotropy up to N = 15 ML in a broad composition range (with a maximum value around x = 0.5) even at room temperature. 4 3d transition metal monolayers on rhodium substrate have been systematically investigated within ab initio calculations in Ref. 5: The magnetic order was found to be ferromagnetic for Co whereas Fe favors an antiferromagnetic (AFM) ground state. In addition, calculations of the magnetic anisotropy energy (MAE) showed that the magnetization of both Fe and Co is oriented in-plane. Therefore, we address the following question: What happens when we take both iron and cobalt with a certain concentration? The answer to this question can be anticipated through the extensive experimental work realized by Yildiz and collaborators. In Ref. 2 they studied tetragonally distorted Fe 1−x Co x alloy films on Rh(001) which show a strong perpendicular anisotropy in a wide thick- ness (up to 15 ML) and composition range (i.e., Co content of 0.3 <x< 0.6). Theoretically, for FeCo alloys the stability of the cubic bulk phase as function of the concentration was investigated in Ref. 6 where a partially ordered B2 phase was predicted in a large concentration range. At the Rh(001) lattice constant tetragonalization has been predicted for Fe films 7 and for films on Rh(001) with a few layer thickness this was confirmed, also significantly affecting the magnetic ordering of the layers. 8 However, for tetragonalized (bulk) FeCo alloys large perpendicular anisotropies were found, 9 rendering this material useful for practical applications. These findings motivate a more systematic investigation of 3d transition-metal alloy films on the Rh(001) substrate. In this paper we investigate the magnetic properties of (ordered) Fe 1−x Co x alloy monolayers on Rh(001) for x = 0.0, 0.25, 0.5, 0.75, and 1.0. In Sec. II we outline the computational method, while in Sec. III we study the relaxations of the topmost layers, the magnetic order and moments, and the magnetic anisotropy and orbital moments, and we finally conclude with a summary in Sec. IV. II. COMPUTATIONAL DETAILS Thin films of Fe 1−x Co x on Rh(001) were addressed to study their magnetic properties using spin density functional theory (sDFT). 10–12 All calculations in this work were made using the FLEUR 13 implementation of the all-electron full-potential linearized augmented plane wave (FLAPW) method 14 in film geometry. 15 The generalized gradient approximation to the exchange-correlation functional of Perdew et al. is used. 16 Spin-orbit interactions were considered via a second variational step using the scalar-relativistic eigenfunctions as a basis. 17 The films are modeled by a symmetric seven-layer Rh(001) slab covered by 3d transition-metal monolayers (ML) on each side, using the calculated Rh in-plane lattice constant 3.819 ˚ A in Ref. 5. The plane wave (PW) cutoff parameter is chosen as k max = 7.56 ˚ A −1 with a muffin-tin sphere radius of R MT = 1.22 ˚ A for the 3d atoms and 1.28 ˚ A for the Rh atoms. III. Fe 1-x Co x MONOLAYER ON Rh(001) A. Relaxations Relaxations were considered for the topmost two layers, that is, the 3d ML and the interface layer Rh(I) (see Fig. 1). The number of k ‖ points used in the irreducible Brillouin zone (IBZ) were up to 78 for the c(2 × 2) surface unit cell and 15 for the p(2 × 2) configuration. The relative relaxations between the layers i and j are characterized by d ij = d ij − d 0 d 0 , (1) where d ij is the spacing between the layers i and j , and d 0 is the ideal bulk interlayer distance of the substrate (1.91 ˚ A). If there is some corrugation in the layer, we reference these numbers 094436-1 1098-0121/2012/86(9)/094436(8) ©2012 American Physical Society