Abstract
Investigation of 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 (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 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 Earth's inner core conditions, and we find that LSF stabilize non-zero moments which affect atomic forces and 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 Earth's outer core conditions ($p \approx 200$ GPa, $T \approx 6000$ K). In both cases, we obtain local magnetic moments of sizes comparable to the solid-state counterparts.
Highlights
Magnetic materials find widespread application in many technological sectors, for their obvious magnetic properties [1] and, for instance, as structural materials [2,3], the best example of which is steels
In this work we have developed a supercell approach for the derivation of the finite-temperature size of magnetic moments in magnetic materials based on the semiclassical theory of longitudinal spin fluctuations, which enables investigation of this degree of freedom in the presence of structural, vibrational, magnetic, and even liquid disorder in a self-consistent way
We found for bcc Fe at T ≈ TC that lattice vibrations affect the on-site energy landscape as a function of moment size, leading to some more itinerant moments compared to the usual localized behavior; increasing the degree of disorder in the system makes the average energy landscape shallower
Summary
Magnetic materials find widespread application in many technological sectors, for their obvious magnetic properties [1] and, for instance, as structural materials [2,3], the best example of which is steels. Since modern society needs always more efficient devices, the design of materials has recently started to be guided by theoretical calculations [4,5]. From this point of view, magnetism in solids poses a great challenge for modeling because of its many-body quantum nature and the difficulty in accurately representing thermal excitations, and for these reasons it has been and still is the subject of thorough theoretical investigations [6,7,8]. Solid-state magnetism is historically described within two limits: the localized moments and the itinerant electron models [9].
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