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In this work we propose a method for the structural relaxation of magneticmaterials in the paramagnetic regime, in an adiabatic fast-magnetismapproximation within the disordered local moment (DLM) picture in the frameworkof density functional theory (DFT). The method is straight forward to implementusing any $ab$ $initio$ code that allows for structural relaxations. Weillustrate the importance of considering the disordered magnetic state duringlattice relaxations by calculating formation energies and geometries for an Fevacancy and C insterstitial atom in bcc Fe as well as bcc Fe$_{1-x}$Cr$_x$random alloys in the paramagnetic state. In the vacancy case, the nearestneighbors to the vacancy relax towards the vacancy of 0.16 {\AA} (-5% of theideal bcc nearest neighbor distance), which is twice as large as the relaxationin the ferromagnetic case. The vacancy formation energy calculated in the DLMstate on these positions is 1.60 eV, which corresponds to a reduction of about0.1 eV compared to the formation energy calculated using DLM but onferromagnetic-relaxed positions. The carbon interstitial formation energy isfound to be 0.41 eV when the DLM relaxed positions are used, as compared to0.59 eV when the FM-relaxed positions are employed. For bccFe$_{0.5}$Cr$_{0.5}$ alloys, the mixing enthalpy is reduced by 5 meV/atom, orabout 10%, when the DLM state relaxation is considered, as compared topositions relaxed in the ferromagnetic state.

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