Ab initiostudy of energetics and magnetism of Fe, Co, and Ni along the trigonal deformation path

Abstract

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 ($c/a=2.83$).