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In an NMR experiment, I the local magnetic flux density of an iron sample was found to be roughly 33 T, by checking for a resonance frequency of the magnetic dipoles. How can it be that such a high field is measured, when the sample itself doesn't have a magnetic field of its own?

The spins precess around the z-axis in an applied field, which would explain how the x- and y-components of the magnetic momenta are cancelled out in such a large number of nuclei. The z-components don't seem to cancel though, and also assuming a Boltzmann distribution on the two possible energy states (for Fe-57, spin up and down), almost all occupy the lower state, so there is also no balance. enter image description here

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A piece of iron has ferromagnetic domains:

iron and other ferromagnets are often found in an "unmagnetized" state. The reason for this is that a bulk piece of ferromagnetic material is divided into tiny regions called magnetic domains[13] (also known as Weiss domains). Within each domain, the spins are aligned, but (if the bulk material is in its lowest energy configuration, i.e. unmagnetized), the spins of separate domains point in different directions and their magnetic fields cancel out, so the object has no net large scale magnetic field

NMR explores atomic behavior in the presence of a magnetic field,

A key feature of NMR is that the resonance frequency of a particular substance is directly proportional to the strength of the applied magnetic field.

and in this case it is the field in the magnetic domains.

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