Dynamics of flux lines studied by modulated microwave absorption

The solution of the coupled differential equations of motion of a flux line in the pinning potential is obtained under the condition of a swept de field, modulation field and microwave field. It can explain the hysteresis which is observed when lock-in detected signal is recorded in forward and reverse field sweeps. The width of the hysteresis is proportional to the pinning potential. From the measurements in laser grown the films of YBa₂Cu₃O_7-δ, we have deduced field and temperature dependences of the pinning potential. The irreversibility line fits to the formB∞ (T _c-T)^β with β=2.3±0.3.