Frustrated magnetism in superconducting hexagonal Fe: Calculation of inter-atomic pair exchange interactions S. Khmelevskyi a, * , A.V. Ruban b , P. Mohn a a Center for Computational Materials Science, Vienna University of Technology, Getreidemarkt 9/134, A-1060 Vienna, Austria b Applied Material Physics, Department of Materials Science and Engineering, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Available online 22 April 2007 Abstract We calculate magnetic exchange interaction parameters in hcp Fe using magnetic force theorem in density functional theory in a range of volumes, which covers the region of stability of the superconducting state. The calculations are done for a paramagnetic state using disordered local moment model within a local fixed spin-moment constraint. It is found that exchange interaction parameters strongly favor antiferromagnetic inter-plane stacking of the basal hcp planes. At the same time, the nearest neighbor in-plane exchange interac- tion parameters are also strongly antiferromagnetic, which should lead to magnetic frustrations in the planar triangular lattice. Eventual consequences of the magnetic frustration effects on the interplay between magnetism and superconductivity in hcp Fe under pressure are discussed. Ó 2007 Elsevier B.V. All rights reserved. Keywords: hcp Fe; Magnetic frustrations; Exchange interactions Immediately after the remarkable discovery of super- conductivity (SC) under high pressure in pure hcp Fe [1], a still unresolved question about its mechanism has aroused. Superconductivity exists in the volume interval of 132 < V < 145 (Bohr 3 ) appearing just at the border of a–e pressure induced structural transition. It has been argued on the basis of calculations of electron–phonon coupling [2] that a conventional mechanism can be respon- sible for SC in hcp Fe, but such a mechanism cannot explain rapid disappearance of the SC with increasing pressure. Earlier density functional theory (DFT) calculations [3], based on the general gradient approximation (GGA), have predicted an antiferromagnetic (AF) ground state of hcp Fe at the volumes, where the SC is stable. Owing to the slight overestimate of magnetism by the GGA, this result has suggested that hcp Fe may be very close to a magnetic instability and thus an unconventional pairing mechanism due to strong spin-fluctuations (SF) has been proposed [2,4]. In this scenario the vanishing of SC at higher pressure is naturally explained by a weakening of SF with decreas- ing volume. Thakor et al. [5] have calculated the wave vector depen- dent spin-susceptibility in hcp Fe in the paramagnetic state and found a dominating AF component of the SF. Since the basal planes of the hcp structure form geometrically frus- trated 2D triangular lattices for the AF interactions, one can expect a non-trivial magnetic behavior in the hcp Fe. To investigate this point in detail we calculate exchange interaction parameters J ij of the magnetic Hamiltonian H = ÀRJ ij S i S j , where S i is spin-moment of Fe on site i. To this end we apply Korringa–Kohn–Rostocker (KKR) method in atomic sphere approximation [6], using GGA/ DFT [7], and the magnetic force theorem technique as described in [8]. In this short paper we present only the results for hcp Fe with ideal c/a ratio and for the paramag- netic state with finite local spin-moment amplitude. A more detailed study will be presented elsewhere. 0921-4534/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physc.2007.04.182 * Corresponding author. Tel.: +43 1 58801 15838; fax: +43 1 58801 15898. E-mail address: sk@cms.tuwien.ac.at (S. Khmelevskyi). www.elsevier.com/locate/physc Physica C 460–462 (2007) 647–648