Nonlinear transverse magnetic moment in anisotropic superconductors

We consider the nonlinear transverse magnetic moment that arises in the Meissner state of superconductors with a strongly anisotropic order parameter. We compute this magnetic moment as a function of applied field and geometry, assuming $d$-wave pairing, for realistic samples, finite in all three dimensions, of high-temperature superconducting materials. Return currents, shape effects, and the anisotropy of the penetration depth tensor are all included. We numerically solve the nonlinear Maxwell-London equations for a finite system. Results are discussed in terms of the relevant parameters. The effect, which is a probe of the order parameter symmetry in the bulk, not just the surface, of the sample should be readily measurable if pairing is in a $d$-wave state. Failure to observe it would set a lower bound to the $s$-wave component.