Magnetic viscosity and the field rate dependence of the magnetization

This paper is concerned with the relation between the experimental measurements obtained under a steady external field and the measurements for the same ferromagnetic material obtained by varying the field at a constant rate R. We define conditions of equivalence that allow the measurement of the coefficient of magnetic viscosity, the irreversible susceptibility and the fluctuation field to be made from swept-field experimental data, using the relations S = - partial derivative M-irr/partial derivative ln R\(H), chi(irr) = partial derivative M(irr/)partial derivative H\(R) and H-f= partial derivative H/partial derivative ln R/(Mirr), respectively. The theory is applied on an ensemble of magnetic moments with easy axes aligned to the direction of the applied field. The relation between the time and rate dependence of the coercivity is derived as dH(c)/d ln t = H-f(R)(1 - dH(f)(R)/dH)(-1), where H-f(R) = dH(c)/d ln R. The effect of sweeping the field is shown to be equivalent to applying a constant field for a time interval t(R) = H-f(R)/R. If the magnetic reversal is coherent, the conditions of equivalence are satisfied for long measurement times, when the energy of activation E-B much greater than kT. At high-sweep rates, however, when the effective time is of the order of nanoseconds, a substantial difference is predicted between the time and the rate dependence of the coercivity and the magnetization. (C) 1999 Elsevier Science B.V. All rights reserved.