  Sensitive and accurate diagnostic technologies with magnetic sensors are of
great importance for identifying and localizing defects of rechargeable solid
batteries in a noninvasive detection. We demonstrate a microwave-free AC
magnetometry method with negatively charged NV centers in diamond based on a
cross-relaxation feature between NV centers and individual substitutional
nitrogen (P1) centers occurring at 51.2 mT. We apply the technique to
non-destructive solid-state battery imaging. By detecting the
eddy-current-induced magnetic field of the battery, we distinguish a defect on
the external electrode and identify structural anomalies within the battery
body. The achieved spatial resolution is $360\,\mu\rm m$. The maximum magnetic
field and phase shift generated by the battery at the modulation frequency of 5
kHz are estimated as 0.04 mT and 0.03 rad respectively.
