Remanent magnetization of a simple ferromagnet

Abstract

We have measured the remanent magnetization of single-crystal EuS from 10""* to 10'' sec after removing an applied field. Using a recent model for magnon relaxation on finite domains, the data yield size-scaling exponents of ^=-0.10 ±0.02 and f=0.669 ±0.004, in excellent agreement with exact theoretical predictions. As a function of temperature, the remanent magnetization is a maximum above the Curie transition, and, for some thermal histories, becomes negative in the ferromagnetic regime. The behavior is consistent with a percolation backbone that is negatively coupled to the finite domains.PACS numbers: 75.50. Dd, 64.60.Ak, 75.40.Gb, 75.60.Lr Relaxation of the remanent magnetization in ferromagnetic materials has previously been attributed to rotation of individual domains, wall motion between domains, or relaxation of a continuum of internal degrees of freedom. Most models of domain rotation [1,2] consider activation over a smooth distribution of barrier heights, resulting in logarithmic time dependences, for which the 1949 measurements of Street and Woolley [3] remain the most cited evidence [4,5]. Power-law behavior is predicted by scaling theories for domain growth [6] and internal dynamics [7]. Other treatments yield Kohlrausch-Williams-Watts stretched-exponential relaxation [8]. All of these empirical formulas have divergent slope at short times, and hence they can only be approximations valid over a limited range. Complete numerical solution of semiclassical Ising [9] and Heisenberg [10] models generally exhibit relaxation times that increase with domain size. We have measured the magnetic relaxation of ferromagnetic EuS from 10""* to 10"^ sec after removing an applied field. The quality and range of the data are suflficient to demonstrate significant deviations from all of these previously proposed relaxation mechanisms.A recent model for relaxation of quantized excitations (magnons, phonons, polaritons, etc.) on a distribution of finite domains has been shown to give excellent agreement with observed magnetic relaxation in spin glasses [11], stress relaxation in ionic glasses [12,13], and dielectric susceptibility of glass-forming liquids [14,15]. The model is based on standard domain-size distributions and elementary finite-size quantization, thus providing a common link between fundamental excitations and observed dynamic response. Here we show that the remanent magnetization of single-crystal EuS is dominated by finite-size quantized magnons.Macroscopic ferromagnetic samples segregate into mesoscopic domains to reduce their magnetic dipolar energy. The lowest-energy domains (Goldstone modes), which form as metastable droplets in an otherwise ordered system, generally have a positive surface tension and a negative energy term proportional to volume.Minimizing the free energy leads to a domain-size distribution of the form [16-18] ris^-s'^&xp( -s^). The size-scaling exponents, 0=~^and f=T, are exact theoretical predictions for isotropic low-energy excitations, regardless of local structure or natur...

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“…We discuss various models that might apply to the relaxation process associated with the applied field. In particular, our data are well described by a percolation model for relaxation that has recently been applied to other disordered systems, such as spin glasses [9].…”

“…These include a power law, simple exponential, double exponential, stretched exponential, and a fit based on a percolation model that has been used to describe several different dynamical systems [9]. A constant background was used in all cases.…”

“…In principle, we might observe phase slip at short times (any relaxational response associated with phase slip should be fast compared to phase deformation), until the CDW reorients and the slow deformation process becomes the "bottleneck" for the response. Since there is no clear rationale for only two time scales, we were prompted to attempt a different type of fit that has been used to study the relaxation in disordered magnetic systems, including spin glasses [9]. The physical picture is that of a domain structure with the relaxation rate of each domain occurring independently.…”

Topological theory of magnetism in nanostructured ferromagnets

“…50 In particular, the authors of the latter paper have developed an interesting theory of relaxation processes, based on percolation theory and mesoscopic domains, which applies rather successfully to EuS. Their basic formula for the time dependence of remanent magnetization is -s) is assumed, they take BE.…”

Relaxation of thermo-remanent magnetization in Fe–Cr GMR multilayers

“…Power-law behavior is predicted by scaling theories for domain growth and internal dynamics [5]. Calculations based on Sherrington-Kirkpatrick mean-field model suggest that the magnetization decays algebraically as…”