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Title: Scaling of hysteresis dispersion in a model spin system
Authors: Liu, J
Chan, HLW 
Choy, CL 
Ong, CK
Issue Date: 3-Dec-2001
Source: Physical review. B, Condensed matter and materials physics, 3 Dec. 2001, v. 65, 014416, p. 1-9
Abstract: We present a calculation of the magnetic hysteresis and its area for a model continuum spin system based on three-dimensional (Φ²)² model with O(N) symmetry in the limit N→∞, under a time-varying magnetic field. The frequency dependence of the hysteresis area A(f), namely, hysteresis dispersion, is investigated in detail, predicting a single-peak profile which grows upwards and shifts rightwards gradually with increasing field amplitude H[sub 0]. We demonstrate that the hysteresis dispersion A(f) over a wide range of H[sub 0] can be scaled by scaling function W(η)∝τ₁A(f,H[sub 0]), where η= log[sub 10](fτ₁) and τ₁ is the unique characteristic time for the spin reverse, as long as H[sub 0] is not very small. The inverse characteristic time τ₁ˉ¹ shows a linear dependence on amplitude H[sub 0], supported by the well-established empirical relations for ferromagnetic ferrites and ferroelectric solids. This scaling behavior suggests that the hysteresis dispersion can be uniquely described by the characteristic time for the spin reversal once the scaling function is available.
Keywords: Magnetic hysteresis
Dielectric hysteresis
Spin dynamics
Publisher: American Physical Society
Journal: Physical review. B, Condensed matter and materials physics 
ISSN: 1098-0121
EISSN: 1550-235X
Rights: Physical Review B © 2001 American Physical Society. The Journal's web site is located at
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