Magnetostriction of a Superconductor: -Results from the Critical-State Model

In many cases, the critical-state theory can be treated as a suffi ciently accurate approximation for the modelling of the magnetic properties of superconductors. In the present work, the magnetostrictive hysteresis is computed for a quite general case of the modified Kim-Anderson model. The results obtained reproduce many features of the giant magnetostriction (butterfly-shaped curves) reported in the literature for measurements made on single-crystal samples of the high-temperature superconductor $Bi_2Sr_2CaCu_2O_8$. It is shown that addition of a contribution to the magnetostriction in the superconducting state which is of similar origin as in the normal state, offers a broader phenomenological interpretation of the complex magnetostriction hysteresis found in such heavy-fermion compounds as $UPt_3$, $URu_2Si_2$ or $UBe_{13}$.