Longitudinal spin fluctuations in bcc and liquid Fe at high temperature and pressure calculated with a supercell approach
Investigating magnetic materials at realistic conditions with first-principles methods is a challenging task due to the interplay of vibrational and magnetic degrees of freedom. The most difficult contribution to include in simulations is represented by the longitudinal magnetic degrees of freedom [longitudinal spin fluctuation (LSF)] due to their inherent many-body nature; nonetheless, schemes that enable to take into account this effect on a semiclassical level have been proposed and employed in the investigation of magnetic systems. However, assessment of the effect of vibrations on LSF is lacking in the literature. For this reason, in this work we develop a supercell approach within the framework of constrained density functional theory to calculate self-consistently the size of local-environment-dependent magnetic moments in the paramagnetic, high-temperature state in the presence of lattice vibrations and for liquid Fe in different conditions. First, we consider the case of bcc Fe at the Curie temperature and ambient pressure. Then, we perform a similar analysis on bcc Fe at Earths inner-core conditions, and we find that LSFs stabilize nonzero moments which affect atomic forces and the electronic density of states of the system. Finally, we employ the present scheme on liquid Fe at the melting point at ambient pressure and at Earths outer-core conditions (p approximate to 200 GPa, T approximate to 6000 K). In both cases, we obtain local magnetic moments of sizes comparable to the solid-state counterparts. ; Funding Agencies|Swedish Research Council (VR) through International Career GrantSwedish Research Council [2014-6336, 2019-05403]; Marie Sklodowska Curie Actions [INCA 600398]; Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linkoping University [2009 00971]; Knut and Alice Wallenberg Foundation (Wallenberg Scholar Grant) [KAW-2018.0194]; Swedish Foundation for Strategic Research through the Future Research Leaders 6 program [FFL 15-0290]