Harmonic calculations and measurements of the irreversibility field using a vibrating sample magnetometer

The effect of the field inhomogeneity of the magnet on a vibrating sample magnetometer (VSM) measurement of a superconductor is calculated using Bean's model and Mallinson's principle of reciprocity. When the sample is centered in both the magnetic field and the VSM pick-up coils, the hysteretic signal obtained in a VSM measurement, associated with the critical current density (J(C)), is reduced to zero when the effective ac field caused by the sample movement penetrates the entire sample and not, as is commonly assumed, when the critical current density becomes zero. Under these conditions, an apparent phase transition is observed where the magnitude of the hysteresis drops to zero over a small field range. This apparent transition is solely an artifact of the measurement and cannot correctly be compared to theoretical calculations of the irreversibility field (B-IRR), which is the phase boundary at which J(C) is zero. Furthermore, the apparent reversible magnetization signal in high fields includes two contributions. In addition to the usual diamaagnetic contribution from the thermodynamic reversible magnetization of the superconductor, there is a reversible paramagnetic contribution from the nonzero J(C). Hence values of the Ginzburg-Landau parameter (kappa) cannot be reliably obtained from standard reversible magnetization measurements using a VSM unless it is confirmed that J(C) is zero. Harmonic measurements using a VSM are reported. They confirm the results of the calculations. By applying a large field gradient, the hysteresis in the magnetization signal at the drive frequency of the VSM is found to drop to zero more than 3 T below B-IRR We propose methods to improve measurements of B-IRR and kappa. The implications of results presented for superconducting quantum interference device measurements are also briefly discussed.