Lattice relaxations in disordered Fe-based materials in the paramagnetic state from first principles

The first-principles calculation of many material properties, in particular related to defects and disorder, starts with the relaxation of the atomic positions of the system under investigation. This procedure is routine for nonmagnetic and magnetically ordered materials. However, when it comes to magnetically disordered systems, in particular the paramagnetic phase of magnetic materials, it is not clear how the relaxation procedure should be performed or which geometry should be used. Here we propose a method for the structural relaxation of magnetic materials in the paramagnetic regime, in an adiabatic fast-magnetism approximation within the disordered local moment (DLM) picture in the framework of density functional theory. The method is straightforward to implement using any ab initio code that allows for structural relaxations. We illustrate the importance of considering the disordered magnetic state during lattice relaxations by calculating formation energies and geometries for an Fe vacancy and C insterstitial atom in body-centered cubic (bcc) Fe as well as bcc Fe1-xCrx random alloys in the paramagnetic state. In the vacancy case, the nearest neighbors to the vacancy relax toward the vacancy of 0.14 angstrom (-5% of the ideal bcc nearest-neighbor distance), which is twice as large as the relaxation in the ferromagnetic case. The vacancy formation energy calculated in the DLM state on these positions is 1.60 eV, which corresponds to a reduction of about 0.1 eV compared to the formation energy calculated using DLM but on ferromagnetic-relaxed positions. The carbon interstitial formation energy is found to be 0.41 eV when the DLM relaxed positions are used, as compared to 0.59 eV when the FM-relaxed positions are employed. For bcc Fe0.5Cr0.5 alloys, the mixing enthalpy is reduced by 5 meV/atom, or about 10%, when the DLM state relaxation is considered, as compared to positions relaxed in the ferromagnetic state.