Strong impact of lattice vibrations on electronic and magnetic properties of paramagnetic Fe revealed by disordered local moments molecular dynamics

We study the impact of lattice vibrations on magnetic and electronic properties of paramagnetic bcc and fcc iron at finite temperature, employing the disordered local moments molecular dynamics (DLM-MD) method. Vibrations strongly affect the distribution of local magnetic moments at finite temperature, which in turn correlates with the local atomic volumes. Without the explicit consideration of atomic vibrations, the mean local magnetic moment and mean field derived magnetic entropy of paramagnetic bcc Fe are larger compared to paramagnetic fcc Fe, which would indicate that the magnetic contribution stabilizes the bcc phase at high temperatures. In the present study we show that this assumption is not valid when the coupling between vibrations and magnetism is taken into account. At the $\gamma \text{–}\delta$ transition temperature (1662 K), the lattice distortions cause very similar magnetic moments of both bcc and fcc structures and hence magnetic entropy contributions. This finding can be traced back to the electronic densities of states, which also become increasingly similar between bcc and fcc Fe with increasing temperature. Given the sensitive interplay of the different physical excitation mechanisms, our results illustrate the need for an explicit consideration of vibrational disorder and its impact on electronic and magnetic properties to understand paramagnetic Fe. Furthermore, they suggest that at the $\gamma \text{–}\delta$ transition temperature electronic and magnetic contributions to the Gibbs free energy are extremely similar in bcc and fcc Fe.

Figure 1

(a) Mean magnitude of local magnetic moments $\overline{M}$ per atom as a function of temperature in paramagnetic (DLM) bcc and fcc Fe. All data points are calculated at the respective experimental volumes. Electronic contributions are considered for the static and the MD calculations by the corresponding Fermi smearing. The shown MD calculations include effects of vibrationally distorted local geometries on the magnetic moments. For comparison, static FM calculations for bcc are shown. (b) Electronic and magnetic free energy contributions to the bcc-fcc competition in Fe as a function of temperature, with and without explicit vibrational effects.

Figure 2

Contour plots of the distribution of local magnetic moments versus the corresponding local Voronoi polyhedra volumes of the atoms of bcc (left) and fcc (right) Fe at different temperatures obtained with DLM-MD (FM-MD for bcc at 300 K) simulations. In all cases, the corresponding temperature-dependent experimental data is used to determine the total volume of the supercell. The mean local moment of static DLM (FM) bcc and fcc Fe as a function of volume is shown as solid (dashed) lines for comparison.

Figure 3

The calculated total (spin-up + spin-down) electronic DOS of fcc (red shaded) and bcc (black) Fe. (a) Ferromagnetic state in a static lattice, (b) ferromagnetic MD at 1085 K, (c) disordered local moments in static lattice, (d) disordered local moments MD at 1662 K. Calculations are performed at an electronic temperature of $T=0$ K in order to be able to clearly distinguish magnetic from vibrational disorder which could otherwise be hidden by electronic smearing.