Magnetism and chemical ordering in icosahedral Al-Pd-Mn quasicrystal

Abstract

Even after nearly two decades of research efforts, the origin of the outstanding magnetic properties of icosahedral quasicrystals containing Mn remains unclear. Experiments have demonstrated that only a rather small fraction of the Mn atoms carry rather large magnetic moments, but it remains unclear whether these sites are intrinsic to the quasicrystalline structure or represent defects. We present ab initio density-functional calculations of the magnetic properties of a large 2/1 approximant to icosahedral $(i)$ Al-Pd-Mn, performed in the semilocal generalized gradient approximation. Structures for rational approximants to the quasicrystalline structure of bulk $i$-Al-Pd-Mn have been constructed using the cut-and-projection technique in six-dimensional (6D) hyperspace according to the Katz-Gratias-Boudard model. We studied magnetism in models of the 2/1 approximant with idealized coordinates obtained by projection from 6D hyperspace in models with coordinates relaxed using Hellmann-Feynman forces and in models simulating the structure of the quasicrystal at high temperature. In some idealized structural models a majority of the Mn atoms carry a large magnetic moment. Although this contradicts experiments demonstrating that only a very small fraction of the Mn atoms are magnetic, this provides the opportunity to investigate in detail the mechanisms leading to the formation of magnetic moments on the Mn atoms. We identify two major mechanisms: a loosely packed environment of the Mn atoms and a direct Mn-Pd interactions leading to a shift of the Mn $d$ band toward the Fermi level. The dominant contribution is the Mn-Pd interaction. A large magnetic moment on a Mn atom is formed at special sites where the Mn atom has two or three Pd nearest neighbors. These special sites are located at those regions of the quasiperiodic lattice where the pseudo-Mackay and Bergman clusters building the structure are linked along the threefold axes. At these sites, the building principles of the Mackay and Bergman clusters are in conflict: from the side of the Mackay cluster, occupation with an Al atom is required, whereas the symmetry of the Bergman cluster suggests occupation by a Pd atom. We have found that a small modification of the chemical decoration of these sites (corresponding to a slight modification of the internal shell structure of the occupation domains in the 6D hyperspace) can lead to a complete disappearance of magnetism in $i$-Al-Pd-Mn. Total energy calculations show that models with a chemical ordering disfavoring formation of magnetic moments on Mn atoms have the lowest energies. This re-establishes agreement with experiment. The ground state of $i$-Al-Pd-Mn is nonmagnetic; but at these specific sites, Al atoms can be replaced by Pd at low energetic cost and without strong violation of the building principles of the quasicrystalline structure, resulting in the formation of large local magnetic moments.