Hysteresis and temperature-induced transitions in ferromagnetic materials

Abstract

In this paper we present two basic one-dimensional models for the temperature-induced phase-changes in a ferromagnetic material. In the framework of the Ginzburg-Landau theory, we construct suitable thermodynamic potentials from which thermodynamically-consistent evolution equations for the magnetization are derived. For both soft and hard materials these models account for saturation and provide an effective description of the transition from paramagnetic to ferromagnetic regimes by displaying the onset of hysteresis loops when the temperature decreases below the Curie critical value. The temperature enters the model as a parameter by way of the magnetic susceptibility. Such a dependence is discussed in order to comply with both Bloch's law (below the critical value) and Curie-Weiss law (far above the critical value). Focusing on uniform processes, numerical simulations of the magnetic responses at different temperatures are performed

A thermodynamic approach to rate-type models in deformable ferroelectrics

“…where S, E, P). We report that constitutive assumptions (27) are similar to eqns. (13) and (25) in [9] where P is referred to as ferroelectric polarization vector, a vector-valued order parameter whose evolution is ruled a priori by a Ginzburg-Landau equation.…”

“…Since the hysteretic behaviour cannot take place when ξ = 0 and the dissipation function vanishes, ξ is referred to as hysteretic function. Although the major hysteresis cycle can even be described by a phase-field approach (see, for instance, [27,28]), the scheme devised here has the advantage of being able to model even minor loops, as will be highlighted by means of examples. Some assumptions are now made in order to ease the comparison with electrolasticity.…”

“…Under the assumption of small deformations, a linearization procedure such as that performed in Sect. 3.1 provides the stress charge equations P = ΛS + σ E + P, T = CS − Λ T E − E ⊗ P. (27) where S := 1 2 (∇u +(∇u) T ). Unlike (16), however, here P = ρ R P is not a function of θ , but is an independent variable whose evolution equation is obtained from (24) by taking its small strain approximation.…”

Accurate mean-field modeling of the Barkhausen noise power in ferromagnetic materials, using a positive-feedback theory of ferromagnetism

“…14 All these show interesting similarities, suggesting a common principle at work. Yet, in spite of >100 years of investigation, there has been little mention of this fact in the context of ferromagnetism.…”

The Harrison Model as a Tool to Study Phase Transitions in Magnetocaloric Materials

“…The study of phase transitions in magnetocaloric materials requires that new computational tools able to capture the effect of varying temperature on the shape of magnetization curve be developed [7][8][9][10]. In our opinion a convenient description for this purpose could be the Harrison model [11][12][13].…”