NMR is usually conducted by first aligning nuclei to a strong, constant magnetic field, so that you can apply RF radiation with a magnetic component directly perpendicular to the constant field. However, it seems to be that Larmor precession could be induced by any kind of RF radiation, because there will (almost) always be a component that is perpendicular to the effective magnetic field generated by fine and hyperfine interactions. As a result, why is the constant magnetic field so important to NMR? And have there been studies done into inducing Larmor precession with radio waves alone?
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The frequency of Larmor precession is directly proportional to the magnitude of the static magnetic field applied. It is not the rf radiation that induces Larmor precession the static magnetic field lifts the degeneracy of the Zeeman sublevels, the rf radiation couples the Zeeman sublevels, causing spin flips to other Zeeman states.
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Yes - this can be done and is known as ZULF NMR (Zero to Ultra Low Field).
The ZULF experiments can be tricky to interpret - in conventional NMR you know that the dominant interaction is between the nuclear spin and the (strong) applied field. Everything else is a small correction which makes the your life somewhat easier.
The strong constant field is important for another reason - sensitivity. The signal you detect is proportional to the nuclear magnetisation which in turn is proportional to the magnetic field. And the local fields in diamagnetic molecules are very weak. Typically before doing a ZULF experiment you have to polarize your nuclei - either by equilibriating them in a strong magnetic field or by some hyperpolarization technique (for example using para hydrogen). (One exception would be magnetically ordered materials - these can have local fields on the order of tens of Tesla - more than enough to do NMR. But that is a niche within a niche:)
