On the energetics of transversal and longitudinal fluctuations of atomic magnetic moments

An extended atomistic spin model allowing for studies of the finite temperature magnetic properties of alloys is proposed. The model is obtained by extending the Heisenberg Hamiltonian via a parameterization from a first principles basis, interpolating from both the low temperature ferromagnetic and the high temperature paramagnetic reference states. This allows us to treat magnetic systems with varying degree of itinerant character within the model. Satisfactory agreement with both previous theoretical studies and experiments are obtained in terms of Curie temperatures and paramagnetic properties. The proposed model is not restricted to elements but is also applied to binary alloys, such as the technologically important material Permalloy, where significant differences in the finite magnetic properties of Fe and Ni magnetic moments are found. The proposed model strives to find the right compromise between accuracy and computational feasibility for accurate modelling, even for complex magnetic alloys and compounds.

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“…The longitudinal part of the partition function over which a functional integration is performed can be written as 15,[40][41][42][43][44] …”

Section: Details Of the Calculationsmentioning

confidence: 99%

“…Evaluation of thermodynamic properties for a model including longitudinal fluctuations involves technically intricate details. The longitudinal part of the partition function over which a functional integration is performed can be written as 15,[40][41][42][43][44]…”

Section: Details Of the Calculationsmentioning

confidence: 99%

Extended spin model in atomistic simulations of alloys

et al. 2017

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“…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.…”

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confidence: 99%

Effect of lattice vibrations on magnetic phase transition in bcc iron

et al. 2012

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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...

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“…(8)] to the FMA [Eq. (9)]. In all cases, the results were obtained at T = 1400 K and corresponding w Fe 1400 K .…”

Section: Pm Fcc Fementioning

confidence: 99%

“…Magnetic thermodynamics in real metallic magnets is, however, significantly more complicated and in addition characterized by fluctuations of the longitudinal magnetic component of the local moments, depending on the degree of electron localization. In Fe, Co, and Ni, the exchange splitting is of the same order as the electronic bandwidth, making the energy scale of longitudinal spin fluctuations (LSFs) already accessible at temperatures below the magnetic phase transition [9][10][11]. To improve the predictions of the localized (Heisenberg) limit, one may account for LSFs in such phenomenological models, and extended model Hamiltonians have indeed been proposed in recent years [7,8,12,13].…”

Section: Introductionmentioning

confidence: 99%

Elastic properties of paramagnetic austenitic steel at finite temperature: Longitudinal spin fluctuations in multicomponent alloys

et al. 2017

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We propose a first-principles framework for longitudinal spin fluctuations (LSFs) in disordered paramagnetic (PM) multicomponent alloy systems and apply it to investigate the influence of LSFs on the temperature dependence of two elastic constants of PM austenitic stainless steel Fe15Cr15Ni. The magnetic model considers individual fluctuating moments in a static PM medium with first-principles-derived LSF energetics in conjunction with describing chemical disorder and randomness of the transverse magnetic component in the single-site alloy formalism and disordered local moment (DLM) picture. A temperature-sensitive mean magnetic moment is adopted to accurately represent the LSF state in the elastic-constant calculations. We make evident that magnetic interactions between an LSF impurity and the PM medium are weak in the present steel alloy. This allows gaining accurate LSF energetics and mean magnetic moments already through a perturbation from the static DLM moments instead of a tedious self-consistent procedure. We find that LSFs systematically lower the cubic shear elastic constants c and c 44 by ∼6 GPa in the temperature interval 300-1600 K, whereas the predominant mechanism for the softening of both elastic constants with temperature is the magneto-volume coupling due to thermal lattice expansion. We find that non-negligible local magnetic moments of Cr and Ni are thermally induced by LSFs, but they exert only a small influence on the elastic properties. The proposed framework exhibits high flexibility in accurately accounting for finite-temperature magnetism and its impact on the mechanical properties of PM multicomponent alloys.

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On the energetics of transversal and longitudinal fluctuations of atomic magnetic moments

Cited by 17 publications

References 14 publications

Extended spin model in atomistic simulations of alloys

Extended spin model in atomistic simulations of alloys

Effect of lattice vibrations on magnetic phase transition in bcc iron

Elastic properties of paramagnetic austenitic steel at finite temperature: Longitudinal spin fluctuations in multicomponent alloys

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