Effect of lattice vibrations on magnetic phase transition in bcc iron

Abstract

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...

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom

“…These discrepancies can be attributed to the anharmonic effects not being faithfully captured in the embedded atom potential and the pairwise functional representation of the exchange interaction. In fact, Yin et al [63] recently pointed out that the exchange parameters in bcc iron depend on the local atomic environment in a complicated manner that may not be properly characterized through a pairwise distance-dependent function. Thus, a more accurate depiction of magnetic interactions necessitates the development of sophisticated models of exchange interactions that effectively capture the contribution of the local environment.…”

“…In magnetic metals and alloys, the atomic magnetic moments and exchange interactions strongly depend on the local atomic environment [21][22][23] and therefore change dynamically as the local crystal structure is distorted by lattice vibrations [24]. On the other hand, magnetic interactions themselves are integral for maintaining the structural stability of such systems [25,26].…”

Magnetic phase transition in coupled spin-lattice systems: A replica-exchange Wang-Landau study

“…This demands sophisticated and improved magnetic models that are capable of providing a more realistic depiction of the material than that is possible with conventional spin models. A novel class of such improved models that continues to gain widespread attention are atomistic models that treat the dynamics of the translational (atomic) degrees of freedom on an equal footing with the spin (magnetic) degrees of freedom [1][2][3][4]. We will refer to such models as (coupled, dynamical) spin-lattice models.…”

“…A single study has been reported where parallel tempering Monte Carlo (MC) method was applied to relatively small system sizes to investigate the magnetic * dilinanp@physast.uga.edu phase transition in iron [4]. In addition to the obvious inflation of the phase space due to the inclusion of the extra spatial degrees of freedom, the coupling between the spin and lattice subsystems may also pose a significant challenge for the sampling due to the emergence of novel excitations such as coupled phonon-magnon modes [9].…”

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: A path for the optimization of low-energy many-body bases

“…21 But an adequate description of the electronic entropy in the subspace that preserves the spin is still lacking. 22 Finite temperatures benchmarks of a quality comparable to Ref. 10 are the key ingredients required to parametrize a finite temperature density functional.…”