I'm looking to learn about Air Motion Transformer technology

Ivan, thank you. You have really helped give me some knowledge to work with. I knew AMTs existed but have never confronted one. I like learning about what I don’t know.  

No sweat, I can answer all your ATM needs.... :>)

I own the Lawrence Audio Violin SE speakers which uses a front firing AMT tweeter and a rear firing ribbon tweeter for ambience.  I previously owned their earlier model which used a front firing ribbon tweeter only. The AMT tweeter is warmer and smoother sounding than the original ribbon tweeter. As stated above, ribbon tweeters, may have a higher range of detail but at times can sound fatiguing especially on poor recordings. I also experienced this with beryllium tweeters when I owned Focal speakers. Like all things, it comes down to equipment matching and your preferences. 

Hey there, I'm listening to some right now.

The potential is high, but not always realized. There are some damn awful sounding AMT speakers.

The one thing they all share is very low stored energy compared to dynamic tweets. However, their frequency response, and power handling can vary a great deal. The $2 Chinese units are not nearly as good as the top of the line European units. 
At the top end, AMT's are as good if not better than any other tweeter tech. At the low, they hurt.

Listen for yourself.
Best,
E

This review includes the highest level Beyma AMT on the market.

https://youtu.be/R9VeZOdatao