Calculating the spontaneous magnetization and defining the Curie temperature using a positive-feedback model

Abstract

A positive-feedback mean-field modification of the classical Brillouin magnetization theory provides an explanation of the apparent persistence of the spontaneous magnetization beyond the conventional Curie temperature-the little understood "tail" phenomenon that occurs in many ferromagnetic materials. The classical theory is unable to resolve this apparent anomaly. The modified theory incorporates the temperature-dependent quantum-scale hysteretic and mesoscopic domain-scale anhysteretic magnetization processes and includes the effects of demagnetizing and exchange fields. It is found that the thermal behavior of the reversible and irreversible segments of the hysteresis loops, as predicted by the theory, is a key to the presence or absence of the "tails." The theory, which permits arbitrary values of the quantum spin number J, generally provides a quantitative agreement with the thermal variations of both the spontaneous magnetization and the shape of the hysteresis loop.

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

“…More general calculations using arbitrary J-values are also possible. 19 This type of hysteresis, also seen in other physical contexts, has two "vertical" irreversible jumps (directed arrows), separated by a physically inaccessible negative slope region, as in Fig. 1(a).…”

“…1(a) depicts a fundamental S-shaped M(H) magnetization curve originating from an atomic-scale PFB process and leading to hysteresis. [16][17][18][19] This field component is termed H q in recognition of its quantum-mechanical (QM) origin. 44 Typical ferromagnets such as Ni and Fe have spatially quantized spin orientations J ¼ 1 = 2 and J ¼ 1, respectively, corresponding to tanh(x)-type or B 1 (x)-type magnetization functions, 19 where B J (x) is the Brillouin function.…”

“…According to the PFB theory of ferromagnetism, [15][16][17][18][19] hysteresis originates in an atomic-scale quantum-mechanical (QM) PFB process resulting in an S-shaped M(H) magnetization curve. Analogously to processes in numerous other nonlinear physical systems, 1-14 as the field H traverses such a curve in a positive-or negative-going direction, the magnetization M experiences a sudden unidirectional jump as soon as the negative-slope part of the S-curve H(M) is reached: this is the origin of irreversibility.…”

“…19. Here, we use the simple but useful expressions for the field components that result when J ¼ 1 = 2 , appropriate for several ferromagnetic materials.…”

“…Yet, in spite of >100 years of investigation, there has been little mention of this fact in the context of ferromagnetism. However, recent work has demonstrated its applicability in explaining and accurately modeling several mean-field aspects of ferromagnetism, such as hysteretic reversibility and irreversibility; 15 major and minor loops including first-order return curves (FORCs), 16 recoil loops, 17 and high-order closed loops and spirals; 18 spontaneous magnetization; 19 the returnpoint memory and Madelung's rules; 16 and the effect of temperature on all of these.…”