  We study the fluorescence of nanodiamond ensembles as a function of static
external magnetic field and observe characteristic dip features close to the
zero field with potential for magnetometry applications. We analyze the
dependence of the features width and contrast of the feature on the size of the
diamond (in the range 30 nm to 3 um) and on the strength of a bias magnetic
field applied transversely to the field being scanned. We also perform
optically detected magnetic resonance (ODMR) measurements to quantify the
strain splitting of the zero-field ODMR resonance across various nanodiamond
sizes and compare it with the width and contrast measurements of the zero-field
fluorescence features for both nanodiamonds and bulk samples. The observed
properties provide compelling evidence of cross-relaxation effects in the NV
system occurring close to zero magnetic fields. Finally, the potential of this
technique for use in practical magnetometry is discussed.
