Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Physics and Astronomy

First Advisor

John R. Clem


This dissertation is divided into five sections, each dealing with an aspect of the response of type-II superconductors to applied magnetic fields;In Section I, a generalized variational model of a single vortex is presented, valid in the anisotropic case when the applied magnetic field H is along one of the principal axes. The effects of the anisotropy on pinning forces of individual vortices and on the vortex lattice form are discussed;In Section II, a variational model of the mixed state is proposed, which permits an analytic calculation of the free energy density F in the Ginzburg-Landau regime. A formula for the reversible magnetization is obtained, valid for the entire field region H[subscript]c1 ≤ H ≤ H[subscript]c2. The model is further extended to include anisotropy by introducing an effective mass tensor for the case when H is parallel to one of the principal axes. The method permits an accurate determination of H[subscript]c2 versus temperature T from reversible magnetization measurements, and dH[subscript]c2/dT = -1.65 ± 0.23 T/K is found for a YBa[subscript]2Cu[subscript]3O[subscript]7 single crystal for H parallel to the c axis near T[subscript] c, implying [xi][subscript]ab(0) = 17 ± 1 A;In Section III, the reversible magnetization of anisotropic superconductors is considered for the case that H is along an arbitrary direction with respect to the principal axes. When H is not parallel to one of the principal axes, the average magnetic flux density B is not parallel to H, and a torque associated with the transverse magnetization exists, tending to orient the sample so that the value of ~[kappa] is the largest. Analytic expressions for the magnetization and the torque are obtained for H \gg H[subscript]c1 by making use of the model of Section II and their dependences upon H and T are discussed;In Section IV, it is pointed out that the London model for the reversible magnetization M of high-[kappa] type-II superconductors in the intermediate-field region is quantitatively incorrect. It is also shown that the apparently linear dependence of M versus lnH in the intermediate-field region, a behavior that has been observed experimentally, can be obtained from the model of Section II;In Section V, it is found that the reversible magnetization M can be written to good approximation as -4[pi] M = (H[subscript]spc2/H[subscript]c2)[phi](h) for H \gg H[subscript]c1 and [kappa] \gg 1, where h = H/H[subscript]c2 is the reduced field and [phi] is a function of h. This property can be used to estimate the anisotropy ratio [gamma] from the reversible magnetization measurement, and [gamma] ~eq 18 as a lower bound is found for a Bi[subscript]2Sr[subscript]2CaCu[subscript]2O[subscript]8 single crystal.



Digital Repository @ Iowa State University,

Copyright Owner

Zhidong Hao



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122 pages