Not sure which NMR method is in discussion, but assuming we have a rotating battery to power the rotating instruments, will it still be possible to observe NMR?
Yes (in any NMR method).
In my naive understanding I am picturing NMR as a wobbling spinning toy, and in NMR we observe/measure that wobbling (the precession), though there's nothing really rotating inside atoms and there is no axle in an atom, so will NMR be seen as DC if we rotate the detector?
Yes, that's the classical model of NMR precession. The NMR signal is a rotating magnetic field, circularly polarized and rotating at the Larmor frequency.
In a stationary detection coil, we observe the NMR signal magnetic field induces a current, sine(Larmor frequency*time). And if we place a second stationary detection coil perpendicular to it, in it we observe a current
cosine(Larmor frequency*time). (This is actually done by, for example, a "birdcage" coil, which has two physically orthogonal outputs. By measuring whether the phase difference between them is +90 or -90 degrees, we can determine whether the NMR precession is occurring at a positive or negative frequency, thus directly determine the sign of the nuclear magnetogyric ratio.)
If the detection coil is rotating, the current induced in it will be the
difference between the rotation rate of the detection coil and the rotation rate (Larmor frequency) of the magnetic field (NMR signal) it is detecting. If rotating in opposite directions, this frequency will be higher. If rotating in the same direction, this frequency will be lower. If rotating at the same direction and rate, will be zero (DC).
This is exactly how an AC generator (an alternator) works. The rotor creates a rotating magnetic field, which induces a current in the stator windings. If it has multiple sets of windings, we can tell which direction the rotor is spinning by the phase difference between the currents from the windings. And if we were to begin to spin the stator in the same direction as the rotor, the frequency of the output current would fall. If the stator were spun at the same rate as the rotor, the output frequency would be zero (DC). So this is very simple. The rest of the universe is unaffected.
If yes, what will happen with the DC if we change the orientation of the spinning axle of the rotating instrument?
Ouch! Now my head is really spinning!
Hmm...
All the imaginary spinning we've done above is only of the detector, around the axis of the magnetic field produced by the NMR magnet, which defines the axis about which Larmor precession occurs. Whether the magnet has rotated or not, its magnetic field has remained static; we have rotated around it. So please clarify the question: by "rotating instrument", do you mean (1) rotating
only the detector (NMR probe), or (2) rotating
both the detector
and the magnet (the
entire instrument)?
If (1), then the detector, if still spinning at the Larmor frequency, will see
two magnetic fields, both at the Larmor frequency and whose magnitude is proportional to the sine of the angle between the two axes: one
enormous (produced by the magnet), and one
tiny (the NMR signal).
...and if you've ever pushed a conductor into a magnetic field of several Tesla, and felt it push back (due to the induced eddy currents), you can imagine what's about to happen... a huge current will be induced, quickly heating the conductor... converting the energy of the entire magnetic field into thermal energy in the detector, which becomes a rapidly expanding ball of plasma.
Poof! Ende gedankenexperiment!If (2), then the result depends on
how quickly we change the orientation of the magnetic field.
If the change is
slow compared to the Larmor frequency, the NMR magnetization simply follows it. This is called an "adiabatic" process (termed "adiabatic" in that it does not change the spin temperature by inducing transitions between NMR spin states).
If the change is
fast compared to the Larmor frequency, effectively instantaneous, the NMR magnetization does not move during this change, but suddenly sees the magnetic field appear in a
new direction, and simply begins to precess about it. This is termed a "nonadiabatic" process.
Both have been done in the laboratory (but by switching magnets on or off, not by rotating them). It is called an "adiabatic demagnetization in the laboratory frame" experiment. It has been described in many papers and several books. A very clear description is given by Melton and Pollack, "Condition for adiabatic passage in the earth’s-field NMR technique", JMR 158 (2002), 15
https://ur.booksc.eu/book/4940715/42cb27
In its Figure 2, the (a) nonadiabatic, (b) intermediate and (c,d) near-adiabatic cases are depicted. This is simple classical magnetodynamics, more easily understood in a rotating frame of reference, although we detect it in the stationary laboratory frame of reference.
...and the analogous experiment can be done with rotating magnetic fields, "adiabatic de- or re-magnetization in the rotating frame"... but that's enough for today!
How did we get
here from oscilloscopes, anyway?