  The zero field splitting (ZFS) quantifies the energy difference for the
ground electron spin-triplet of a nitrogen-vacancy center in the absence of
external fields. The values of the ZFS play a key role in determining the
Larmor precession of the Bloch sphere and the Rabi oscillation of a spin
system. The ZFS is generally detected using coherent spin manipulation by
sweeping microwaves (MWs) at frequencies close to resonance with the ZFS. In
this letter, we report our experimental observations of the red-shift effect on
the ZFS as a function of the MW power for two different thermal environments of
a sample. We find an asymptotic property of the red shifts of the ZFS. Given
the identical initial thermal equilibrium states of the sample, the differences
in the raw values of the ZFS between the two cases randomly vary from 47 kHz to
1505 kHz over the entire experimental range. According to the asymptotic
approximation, the differences are reduced to 29-166 kHz with a standard
deviation of 49 kHz, suggesting a significant elimination of the red-shift
effect. To the best of our knowledge, no other study has addressed the
quantification and elimination of the red shift-effect of the MW field
dependence using the asymptotic approximation.
