PHYSICAL REVIEW B 83, 184424 (2011) Ab initio study of energetics and magnetism of Fe, Co, and Ni along the trigonal deformation path M. Zelen´ y, 1,2 M. Fri´ ak, 1,3,4,5 and M. ˇ Sob 1,5,6 1 Institute of Physics of Materials, Academy of Sciences of the Czech Republic, ˇ Zi ˇ zkova 22, CZ-616 62 Brno, Czech Republic 2 COMP/Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, FI-00076 Aalto, Finland 3 Max-Planck-Institut f¨ ur Eisenforschung GmbH, Max-Planck-Strasse 1, D-40237 D¨ usseldorf, Germany 4 Institute of Condensed Matter Physics, Faculty of Science, Masaryk University, Kotl´ a ˇ r sk´ a 2, CZ-611 37 Brno, Czech Republic 5 Central European Institute of Technology, CEITEC MU, Masaryk University, Kamenice 5, CZ-625 00 Brno, Czech Republic 6 Department of Chemistry, Faculty of Science, Masaryk University, Kotl´ a ˇ r sk´ a 2, CZ-611 37 Brno, Czech Republic (Received 7 February 2011; revised manuscript received 21 March 2011; published 24 May 2011) A detailed theoretical study of structural and magnetic behavior of iron, cobalt, and nickel along the trigonal transformation paths at various volumes per atom is presented. The total energies are calculated by a spin-polarized full-potential linearized augmented plane wave method within the generalized gradient approximation and are displayed in contour plots as functions of trigonal c/a ratio and volume per atom. The borderlines between various magnetic modification are shown for Fe and Ni. In the case of Ni, these phase boundaries between nonmagnetic and ferromagnetic phases occur even at the experimental value of volume per atom. On the other hand, Co keeps its ferromagnetic order in the whole region of the volume and shape deformation studied. Fe does not exhibit any transition between the ferromagnetic and nonmagnetic arrangement, but at low volumes per atom around the fcc structure, phase boundaries between the ferromagnetic high-spin, ferromagnetic low-spin, and antiferromagnetic states have been found. Fe and Co exhibit minima on the curve of the energy difference between ferromagnetic (FM) and nonmagnetic states in the same areas where Ni loses its FM ordering. Both structures do not exhibit any higher symmetry, but there is a coalescence of the second and third and fifth and sixth coordination spheres (c/a = 1.27) or of the third and fourth coordination spheres (c/a = 2.83). DOI: 10.1103/PhysRevB.83.184424 PACS number(s): 63.70.+h, 71.15.Nc, 75.50.−y I. INTRODUCTION Iron, cobalt, and nickel have been for a long time at the center of attention because of their unique magnetic properties. In particular, ferromagnetism in these metals is very important not only for their magnetic properties per se, but because it stabilizes the body-centered cubic (bcc) ground-state structure of Fe and the hexagonal closed-packed (hcp) ground-state structure of Co. Had the magnetism been absent, the nonmagnetic state of both elements would exhibit the same structure as the corresponding 4d and 5d metals in the same columns of the Periodic Table, i.e., Fe would have the hcp structure in analogy with Ru and Os and Co would crystallize in the face-centered cubic (fcc) structure in analogy with Rh and Ir. The origin of ferromagnetism in Fe, Co, and Ni consists in the high density of states at the Fermi level of nonmagnetic configurations in these metals, which leads to the spin polarization of the valence band. 1–4 Recently, a great deal of attention was also paid to thin films of these metals, because they have a wide use in practical applications, especially in data storage devices. In fact, thin films show how to stabilize 3d metals in deformed structures, which can exhibit partially or completely different magnetic behavior than their ground states. A nice illustrative example showing the changes in magnetic behavior is elemental iron. If it is deposited on the Cu(001) substrate, its fcc structure with antiferromagnetic (AFM) ordering is stabilized 5,6 similarly as in iron precipitates embedded into a Cu matrix. 7,8 This stabilization happens primarily due to a high deformation of the film or of the precipitate, which keeps it coherent with the substrate or with the matrix. It turns out that the substrate or the matrix just mechanically constrain the material of the film or of the precipitate in those deformed structures. For thin iron films, this was reliably demonstrated with the help of ab initio calculations, 9 which provide a very good tool for the study of these highly deformed states. Another example of stabilized nonequilibrium configurations is Ni and Co overlayers with the bcc structure, which were prepared on a GaAs (001) substrate. 10,11 In addition, a Co film with a tetragonally dis- torted bcc structure was reported on Pd and Pt substrates. 12,13 Many theoretical studies are focused on the behavior of 3d and other metals along the tetragonal deformation path (also called the Bain’s path), which is accomplished by an uniaxial deformation along the [001] direction. This path connects the bcc and fcc structures 9,14,15 and is suitable for a description of the geometry of the structures that occur in thin films on the (001) substrates (mainly with the fcc structure). However, there is no significant change of magnetic properties of Ni and Co along this path, as shown in previous studies. 16,17 Consequently, most Ni and Co thin films on fcc (001) substrates studied up to now prefer ferromagnetic ordering (Ref. 18 and references therein). Only Fe changes magnetic ordering from ferromagnetic to antiferromagnetic along this path 9 or to a spin-spiral structure, when noncollinear arrangement is admitted. 19 An interesting alternative is provided by films on (111) fcc substrates, where they exhibit a trigonally distorted fcc structure or hcp structure. 20 Here, for example, Ni with hcp structure subjected to a large biaxial deformation loses its ferromagnetism, but these deformed states are already beyond the stability limit of Ni films on fcc (111) substrates due to very large lattice mismatch. 21 Highly trigonally deformed states can be unstable for the same reason and are experimentally hardly accessible. Nevertheless, the study of these states can bring 184424-1 1098-0121/2011/83(18)/184424(7) ©2011 American Physical Society