Conventional and torque magnetometry on disc-shaped high-T c superconductor samples : I. A steady-state dynamical theory

Abstract

A nonlinear, macroscopic electrodynamic theory is given to explain the irreversible part of the magnetic momentum m irr and the torque momentum Γ irr observed in conventional (CM) and torque magnetometry (TM) on HTSC discs and thin films with oblique external time-dependent magnetic field H 0( t) and off-plane rotation of H 0( t), respectively. This theory relates m irr and Γ irr with the nonlinear conductivity tensor σ of the mixed state, and with microstructure-dependent material parameters entering σ, which govern the thermally activated vortex motion under anisotropic pinning. In the steady state, m irr and Γ irr is understood to result from a current j excited by an “applied” electrical field E 0 induced by the external inductance B 0 ( t) = H 0( t). The limiting case of discs with large aspect ratio and thickness much smaller than the nonlinear skin depth is studied in detail. It is shown that, except of some singular cases, j and m irr becomes strictly azimuthal and axial, respectively, while | δB| ⪡ | B 0| where B = B o + δB is the total inductance. The boundary value problem is solved in a self-consistent approximation making use of the strong sublinear characteristic of j versus the total electrical field E under CM and TM conditions, which allows to replace σ by an effective pseudo-linear quantity ḡs governed by the dominating azimuthal E -mode. Formulae or m irr and Γ irr are given, showing, in spite of the simple configuration of E and B , a complicated nonlinear dependence upon the components of σ. To interpret CM and TM experiments, a phenomenological description of σ( E, B ) is presented based upon symmetry arguments, as well as theoretical and experimental facts, which is valid for anistropic and layered HTSC, including the isotropic, and the anisotropic intrinsic and twin-boundary pinning. The possibility to determine σ and related material parameters from CM and TM results is discussed in detail.