One thing is clear from the start, the higher the strength of the magnetic field, the lower the resonance frequency. Via the energy relationship formula for photons, we find that the lower the frequency, the lower the energy of the photon is.
So for lower external magnetic fields, we need higher energy photons to get rid of the asymmetry.
This must mean that the lower magnetic fields do not compensate the intrinsic magnetic field as well as the higher magnetic fields. Or the external magnetic field and the internal magnetic field do not strengthen each other, but work against each other.
Therefore the intrinsic magnetic field must have a negative sign (compared to the external magnetic field).