Measurements of the lower critical field of superconductors using NV centers in diamond optical magnetometry

The lower critical magnetic field, $H_{c1}$, of superconductors is measured by using ensembles of NV-centers-in-diamond optical magnetometry. The technique is minimally invasive, and has sub-gauss field sensitivity and sub-$\mu$m spatial resolution, which allow for accurate detection of the vector field at which the vortices start penetrating the sample from the corners. Aided by the revised calculations of the effective demagnetization factors of actual cuboid - shaped samples, $H_{c1}$ and the London penetration depth, $\lambda$, derived from $H_{c1}$ can be obtained. We apply this method to three well-studied superconductors: optimally doped Ba(Fe$_{1-x}$Co$_{x}$)$_2$As$_2$, stoichiometric CaKFe$_4$As$_4$, and high-$T_c$ cuprate YBa$_2$Cu$_3$O$_{7-\delta}$. Our results are well compared with the values of $\lambda$ obtained using other techniques, thus adding another non-destructive and sensitive method to measure these important parameters of superconductors.