Response of Ising systems to oscillating and pulsed fields: hysteresis, ac, and pulse susceptibility

Acharyya, Muktish ; Chakrabarti, Bikas K. (1995) Response of Ising systems to oscillating and pulsed fields: hysteresis, ac, and pulse susceptibility Physical Review B, 52 (9). pp. 6550-6568. ISSN 0163-1829

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We have studied, using Monte Carlo (MC) simulation for ferromagnetic Ising systems in one to four dimensions and solving numerically the mean-field (MF) equation of motion, the nature of the response magnetization m(t) of an Ising system in the presence of a periodically varying external field [h(t)=h0cos(ωt)]. From these studies, we determine the m-h loop or hysteresis loop area A(=?mdh) and the dynamic order parameter Q(=?mdt) and investigate their variations with the frequency (ω) and amplitude (h0) of the applied external magnetic field and the temperature (T) of the system. The variations in A are fitted to a scaling form, assumed to be valid over a wide range of parameter (ω,h0,T) values, and the best-fit exponents are obtained in all three dimensions (D=2,3,4). The scaling function is Lorentzian in the MF case and is exponentially decaying, with an initial power law, for the MC cases. The dynamic phase boundary (in the h0-T plane) is found to be frequency dependent and the transition (from Q≠0 for low T and h0 to Q=0 for high T and h0) across the boundary crosses over from a discontinuous to a continuous one at a tricritical point. These boundaries are determined in various cases. We find that the response can be generally expressed as m(t)=P(ω(t-Teff)) where P denotes a periodic function with the same frequency ω of the perturbing field and teff(h0,ω,T) denotes the effective delay. We established that this effective delay teff of the response is the crucial term and it practically determines all the above observations for A, Q, etc. Investigating the nature of the in-phase (X') and the out-of-phase (X") susceptibility, defined as X'=(m0/h0)cos(φ) and X"=(m0/h0)sin(φ); φ=ωteff [and m0 is the amplitude of m(t)], we find that the loop area A is directly given by X" and also the temperature variation of X", at fixed ω and h0, gives a prominent peak at the dynamic transition point. We have also studied the behavior of the response magnetization by the application of a short-duration (compared with the relaxation time) pulsed magnetic field. Here, we observed (both in the MC and MF cases) that the width ratio (of the half-width and the width of the response magnetization and of the pulsed field, respectively) and the susceptibility (the ratio of excess magnetization over its equilibrium value and the height of the pulsed field) both show sharp peaks at the order-disorder (ferromagnetic-paramagnetic) transition point. We have also studied similar response behavior of Ising systems in the presence of time-varying longitudinal and transverse fields, solving numerically the mean-field equation of motion. We have again studied here the nature of the dynamic phase transition and the behavior of the ac susceptibility (both longitudinal and transverse) across the dynamic phase boundary. For a short-duration pulse of the transverse field, the width ratio and the pulse susceptibility are again seen to diverge at the order-disorder transition point.

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Source:Copyright of this article belongs to American Physical Society.
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Deposited On:19 Oct 2010 10:57
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