The most widely taught example of a magnetic transition is that of Fe at 1043 K. Despite the high temperature most discussions of this transition focus on the magnetic states of a fixed spin lattice with lattice vibrations analyzed separately and simply added. We propose a model of α iron that fully couples spin and displacement degrees of freedom. Results demonstrate a significant departure from models that treat these coordinates independently. The success of the model rests on a first principles calculation of changes in energy with respect to spin configurations on a bcc-iron lattice with displacements. Complete details of environment-dependent exchange interactions that augment the Finnis-Sinclair potential are given and comparisons to measurements are made. We find that coupling has no effect on critical exponents, a small effect on the transition temperature, T c , and a large effect on the entropy of transformation.The magnetic moment associated iron atoms and the interactions between them (Fig. 1) have a strong dependence on atomic environment, e.g., the interatomic distances which affect the overlap of atomic orbitals. 1 Other local environmental parameters, such as the magnitude and shape of the atomic volume, the number of atoms within the first peak distance of the radial distribution function, etc, also come into play. 2 Due to the magnon-phonon interactions 3 the instantaneous local magnetic moments become very inhomogeneous in the presence of displacements. Figure 1 shows that at T c the displacements are large, e.g., fluctuations in first nearest neighbor separations exceed the separation of second nearest neighbors, resulting in exchange parameters that depend on the local environment in a complicated manner that cannot be captured by a simple separation dependent interaction. How can this be reconciled with the fact that the classical Heisenberg model already provides a surprisingly reasonable description of the magnetic phase transition in bcc iron, 4 including critical exponents that are close to the measured values? [5][6][7][8] In this paper, we take a close look at the role of lattice vibrations in magnetic interactions.A few studies of the magnon-phonon interaction have been reported. 3,9 In Ref. 3, a model with a distance-dependent exchange parameter J (r) is proposed, where the dependence for both the first-and second-neighbors in bcc iron is found to be linear; hence, there is no contribution from the magnon-phonon coupling. On the other hand, recent studies 10 indicate that J (r) has a rather complex functional form, and an environment-independent pairwise representation is inadequate. The J (r) models fail to capture the longitudinal degrees of freedom in the local magnetic moments, 11 which are an important property of itinerant systems. We introduce local environmental parameters, such as atomic volume, that reflect the change in magnitude of local moments. The environmental parameters go beyond pair interactions in the sense that change in the position of an atom alters the J valu...
One-electron Green's functions play a central role in multiple-scattering theory (MST) based electronicstructure methods. Robust methods exist for calculating the Green's function for crystal potentials that are spherically symmetric about atomic centers. When applied to potentials of general shape, these same techniques result in pathologies in the small-r behavior of the electronic charge density because a portion of the Green's function can become singular at the origin for that case. We propose an algebraic method that eliminates the singular behavior by making use of the equivalence of two terms that involve poles in the inverse of the sine matrix. Our accurate calculations illustrate the limitations of previous methods for treating this problem that rely on extrapolating the solutions near the origin.
Density functional calculations have proven to be a useful tool in the study of ground state properties of many materials. The investigation of finite temperature magnetism, on the other hand, has to rely usually on the usage of empirical models that allow the large number of evaluations of the systems Hamiltonian that are required to obtain the phase space sampling needed to obtain the free energy, specific heat, magnetization, susceptibility, and other quantities as function of temperature. We have demonstrated a solution to this problem that harnesses the computational power of today’s large massively parallel computers by combining a classical Wang–Landau Monte-Carlo calculation [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)] with our first principles multiple scattering electronic structure code [Y. Wang et al., Phys. Rev. Lett. 75, 2867 (1995)] that allows the energy calculation of constrained magnetic states [M. Eisenbach et al., Proceedings of the Conference on High Performance Computing, Networking, Storage and Analysis (ACM, New York, 2009)]. We present our calculations of finite temperature properties of Fe and Fe3C using this approach and we find the Curie temperatures to be 980 and 425K, respectively.
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