  Non-invasive magnetic field sensing using optically - detected magnetic
resonance of nitrogen-vacancy (NV) centers in diamond was used to study spatial
distribution of the magnetic induction upon penetration and expulsion of weak
magnetic fields in several representative superconductors. Vector magnetic
fields were measured on the surface of conventional, Pb and Nb, and
unconventional, LuNi$_2$B$_2$C, Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$,
Ba(Fe$_{0.93}$Co$_{0.07}$)$_2$As$_2$, and CaKFe$_4$As$_4$, superconductors,
with diffraction - limited spatial resolution using variable - temperature
confocal system. Magnetic induction profiles across the crystal edges were
measured in zero-field-cooled (ZFC) and field-cooled (FC) conditions. While all
superconductors show nearly perfect screening of magnetic fields applied after
cooling to temperatures well below the superconducting transition, $T_c$, a
range of very different behaviors was observed for Meissner expulsion upon
cooling in static magnetic field from above $T_c$. Substantial conventional
Meissner expulsion is found in LuNi$_2$B$_2$C, paramagnetic Meissner effect
(PME) is found in Nb, and virtually no expulsion is observed in iron-based
superconductors. In all cases, good correlation with macroscopic measurements
of total magnetic moment is found. Our measurements of the spatial distribution
of magnetic induction provide insight into microscopic physics of the Meissner
effect.
