Looking at the paper, I don't think these particular magnetite nanoparticles (or any similar small crystal) would be compatible with the Ad26 (J&J/AZ) vaccines, nor the mRNA (P/M) vaccines (at least not as presented in this paper).

These magnetite nanoparticles, due to a slight negative charge on their surface, as well as compatible hydrophobicity attract positively charged slightly hydrophobic polymers (a lot of amine groups and carbon chains) as a sort of coat. This polymeric coating then attracts the negatively charged backbone of the genetic material to be transfected (RNA/DNA). The magnetic nature is then exploited for transfection.

Neither the lipid nanoparticles (mRNA vaccines) nor the adenovirus vaccines have these types of positively charged polymers as listed ingredients, nor would they, as they are self contained with the genetic material inside and employ different methods of transfection. I am not seeing (at least from this paper) how these types of systems would aid directly in delivery of these technologies; unless they aren't what they say they are (like at all).

I'm still trying to rectify the anecdotal evidence of the magnetic effect of the vaccines though. It really makes no sense from the ingredients as listed in any of the vaccines I looked at (J&J/Pfizer/Moderna).

Idk but this sure as hell does... https://www.theguardian.com/science/neurophilosophy/2016/mar/24/magneto-remotely-controls-brain-and-behaviour

This is eating-Tide-Pods level stupid.

SPIONs, you can't make this shit up.

People are missing the forest for the trees over the magnet issue.

It doesn't matter that most vaxxed people can't make a magnet stick to their injection site.

The fact that some vaxxed people can stick a magnet to their injection site seems to indicate that all vaxxed people were injected with magnetic material of some kind.

If the magnet doesn't stick, that may mean that the magnetic material was successfully introduced deeper into the person's bloodstream. Perhaps the sticking magnets are merely an indicator of an injection that didn't go quite right.

From wikipedia:

The typical time between two flips is called the Néel relaxation time. In the absence of an external magnetic field, when the time used to measure the magnetization of the nanoparticles is much longer than the Néel relaxation time, their magnetization appears to be in average zero; they are said to be in the superparamagnetic state. In this state, an external magnetic field is able to magnetize the nanoparticles, similarly to a paramagnet. However, their magnetic susceptibility is much larger than that of paramagnets.

https://en.wikipedia.org/wiki/Superparamagnetism

Can anyone explain, if this could be related?

I tried it on someone who got the J&J vaccine.

His arm was not magnetic at all and every magnet fell to the floor on multiples attempts.