MRI/NMR doesn’t sense magnetic fields, so I don’t think that kind of sensor would help. You have to put your sample in a strong magnetic field for this method to work, but after that it’s just a matter of emitting some RF pulses and receiving some RF signals.

I thought they had to turn the magnet on and off. This would first align all the magnetic moments of the specific atoms and then as they randomize when the field is off, they interfere with a superimposed radio field creating peaks and troughs. Tomographic calculations are then applied to the collected radio signals to give an image. How can a permanent magnet be used?

There are a lot of NMR imaging techniques, and I'm not an expert, but my understanding (based on discussion with experts) is that the main magnetic field is static during all MRI scans. The gradient fields from electromagnets change, though, to alter the Larmor frequency across the thing being imaged.

The field is always on. Safety first. :)