Abstract
We show that, based on the Bean model for vortex pinning [Rev. Mod. Phys. 36, 31 (1964)] one can assess the relaxation of magnetic moment components in hard superconductors, induced by the oscillations of a perpendicular magnetic field. Our theory follows a recent proposal of using phenomenological two-dimensional modeling for the description of crossed field dynamics in high-${T}_{c}$ superconductors [Ph. Vanderbemden et al., Phys. Rev. B 75, 174515 (2007)]. Long thick strips of rectangular cross section, subjected to a uniform magnetic field, perpendicular to the strip axis are considered. One of the components of the applied field, ${H}_{x}$, oscillates with a given amplitude, while the other one, ${H}_{y}$, remains constant. By solving a variational statement of Bean's model, we obtain stationary regimes with either saturation of the magnetization component ${M}_{y}$ to metastable configurations or complete decay to the thermodynamic equilibrium. As a common feature, a steplike dependence in the time relaxation is predicted for both cases. The theory may be applied to long bars of arbitrary and nonhomogeneous cross section.
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