# How does spin flip take place?

An electron in a constant magnetic field, say $B_z~ \hat{z}$ starts precessing about $\hat{z}$-direction. One can flip the spin by providing a time-varying field $B_x \sin(\omega t)~ \hat{x}$ in the $\hat{x}$-direction. The logic often given is that the linearly polarized field can be treated as a sum of the left and right circular field. The field component with is rotating in the same sense and same frequency as that of precession (Larmor frequency) is responsible for the spin flip. Could someone explain the actual mechanism behind the spin-flip in this context?

• If you hang a spinning gyroscope from a string, with its axis perpendicular to the string, you can watch it precess. Take note of the frequency and direction of its precession. Now swing the top end of the string in a small circle at about that same frequency, first in the same direction as the precession and then in the opposite direction to the precession. The gyroscope will orient itself either up of down depending on the direction of your circle. This is a consequence of classical mechanics. Pretty much the same happens when the spin of an electron is flipped by an applied RF field. Apr 14 '18 at 13:21
• Thanks, @S. McGrew. It seems a good analogy. Could you suggest some reference where I can find this gyroscope-flip phenomenon? Apr 14 '18 at 16:58
• I've posted an answer, mostly consisting of my last comment, but including links to a youtube video lecture about gyroscope precession, along with my own explanation. Apr 14 '18 at 20:55

## 1 Answer

If you hang a spinning gyroscope from a string, with its axis perpendicular to the string, you can watch it precess. Take note of the frequency and direction of its precession. Now swing the top end of the string in a small circle at about that same frequency, first in the same direction as the precession and then in the opposite direction to the precession. The gyroscope will orient itself either up of down depending on the direction of your circle. This is a consequence of classical mechanics. Pretty much the same happens when the spin of an electron is flipped by an applied RF field.

Here's what's going on. When the axis of the gyro is sticking out horizontally, it stays at pretty much the same vertical angle while precessing. The induced torque due to precession just balances the torque due to gravity. If you push a bit harder in the direction of precession, that induced torque is greater than the torque due to gravity, so the angle of the axis moves upward. If you push against the precession, the induced torque is reduced, so the angle of the axis moves downward.

Of course the quantum mechanical description is different, but you asked for a mechanism, and this is it. There are lots of explanations of gyro precession on Google, but I haven't found one yet that specifically mentions the experiment I described. There is a great video at [https://www.youtube.com/watch?v=1n-HMSCDYtM], which is marginally relevant and probably distracting. More to the point is [https://www.youtube.com/watch?v=1n-HMSCDYtM], but it doesn't seem to demonstrate the spin flip I described.

I've searched for written references to this, with no luck so far. In general, the classical mechanics treatments I've seen of this phenomenon have been pretty vague, though the math of classical mechanics is certainly adequate to explain it. Your best bet is to go to the nearest science toy store, buy a gyroscope, and play with it.