Numerical Simulations of the Invar Effect in Fe-Ni, Fe-Pt, and Fe-Pd Ferromagnets

Abstract

The Invar effect in ferromagnetic Fe-Ni, Fe-Pt, and Fe-Pd alloys is investigated theoretically by means of a computationally efficient scheme. The procedure can be divided into two stages: study of magnetism and calculations of structural properties. In the first stage, an Ising model is considered and fractions of Fe moments which point up as a function of temperature are determined. In the second stage, density-functional theory calculations are performed to evaluate free energies of alloys in partially disordered local moment states as a function of lattice constant for various temperatures. Extensive tests of the scheme are carried out by comparing simulation results for thermal expansion coefficients of Fe1−xNix with x = 0.35, 0.4, . . . , 0.8, Fe0.72Pt0.28, and Fe0.68Pd0.32 with measurements. The scheme is found to perform well, at least qualitatively, throughout the whole spectrum of test compounds. For example, the significant reduction of the thermal expansion coefficient of Fe1−xNix as x decreases from 0.55 to 0.35 near room temperature, which was discovered by Guillaume, is reliably reproduced. As a result of the overall qualitative agreement between theory and experiment, it appears that the Invar effect in Fe-Ni alloys can be investigated within the same computational framework as Fe-Pt and Fe-Pd.

First-principles modeling of the Invar effect in Fe65Ni35 by the spin-wave method

“…In Fig. 9, we show the SWM results, which include the MSRO effects, and the PDLM-CPA results by Liot and Hooley 26 where the effect of the MSRO is absent. Clearly, the MSRO leads to a substantial shift of the lattice constant.…”

“…Similar first-principles-based modeling of the Invar effect, using 0 K total energies of alloys with different spin configurations representing the finite-temperature magnetic state of the Invar alloy, was successfully applied by Khmelevskyi et al to a number of different Invar systems, [20][21][22][23][24] A more elaborate approach was adopted by Liot and co-authors [25][26][27] who actually calculated the finite temperature lattice constant and thermal expansion coefficient of some Invar alloys using the Debye-Grüneisen model. 28 It is obvious, that the above mentioned computational schemes are approximate in many details.…”

Magnetization, magnetostriction, and their relationship in Invar Fe$_{1-x}A_{x}$ ($A={\rm Pt},{\rm Ni}$)

“…Another approach based on ab initio density functional theory (DFT) emphasizes the importance of non-collinearity of the local magnetic moments on iron sites [10,11], though experiments undertaken to detect such non-collinearity have not found it [12]. A third class of models relies on the disordered local moment (DLM) approach [13,14,15,16,17,18], in which a binary alloy Fe 1−x A x with complete positional disorder of 'up-and down-moments' on Fe sites is simulated, within the coherent potential approximation (CPA), as a three-component alloy Fe ↑…”

“…In two recent exciting papers [16,18], alloys in equilibrium at temperature T in the range 0 ≤ T /T C < 1 have been modelled by random substitutional alloys in homogeneous ferromagnetic (FM) states, partially disordered local moment (PDLM) states, or DLM states depending on the fraction of Fe moments which are antiferromagnetically aligned with the spontaneous magnetization at T , x Fe↓ (T ). The general procedure can be divided into three stages.…”

“…Even though simulation agrees qualitatively with experiment, the discrepancy between the calculated reduced magnetization at T /T C = 1/2 and the corresponding experimental value exceeds 0.1. In [18], the linear thermal expansion coefficient in Fe 0.72 Pt 0.28 and Fe 1−x Ni x with x = 0.35, 0.4, • • • , 0.8 has been investigated. The finding that Fe 0.72 Pt 0.28 and Fe 0.65 Ni 0.35 display the Invar effect perfectly matches experimental observation.…”