Direct measurement of the magnetic penetration depth by magnetic force microscopy

We present an experimental approach using magnetic force microscopy for measurements of the absolute value of the magnetic penetration depth $\lambda$ in superconductors. $\lambda$ is obtained in a simple and robust way without introducing any tip modeling procedure via direct comparison of the Meissner response curves for a material of interest to those measured on a reference sample. Using a well-characterized Nb film as a reference, we determine the absolute value of $\lambda$ in a Ba(Fe$_{0.92}$Co$_{0.08}$)$_{2}$As$_{2}$ single crystal and a MgB$_2$ thin film through a comparative experiment. Our apparatus features simultaneous loading of multiple samples, and allows straightforward measurement of the absolute value of $\lambda$ in superconducting thin film or single crystal samples.