I am collecting drivers for my next build, and I now got Ciare 15” bass driver and an 18Sound 10” midrange.
Only the tweeter is missing.

I have fallen in love witht the ESS Heil Air Motion Transformer….I simply must try it.

My question, is regarding the minimum cross over frequence: I have seen various specs, some says 800 Hz, and some 1500 Hz.
If I look at the specs of the AMT 1 speakers, they cross at 700 Hz….?

I need a cross over frequence areound 1200 Hz.

Any thoughts

The silly Dane is confused ☺️
I would err on the higher side, the few distortion measurements I've seen did not look like crossing as low as ESS suggested was a great idea. Also, the FR looked like it needed some massaging to get close to flat or smoothly downward-sloping.

With all of that in mind, I'd be inclined to first prototype with DSP; start with crossover at the highest point directivity match will allow, and see how much FR massaging is needed to get to target curve. Then start walking the XO frequency down in steps until you get to the lowest XO that has acceptable power handling for your application while maintaining acceptable distortion. Then if you're going passive, build out a passive equivalent.

To be honest, looking at your other drivers, I would be more inclined to use one of the Beyma waveguided AMTs, they seem like a better fit directivity wise, and can likely handle more power with lower distortion. IMO they are among the best, possibly the very best, AMT on the market currently. But they are substantially more expensive.
I use mine as a tweeter from 7khz and up. I am building another pair of speakers use the AMTs from 3500hz and up.

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My question is regarding the minimum cross over frequency...I need a cross over frequency around 1200 Hz.

Any thoughts?
It turns out that the answer to your question is a function of whether or not you provide side walls, i.e., "wings", for the driver. Above ~2 kHz, the driver acts as a 90 degree horizontal horn-loaded AMT (unlike other flat AMTs on the market).

Below 2 kHz, the first 1/4 wavelength of extends beyond the edges of the side magnet assembly, thus allowing the ESS AMT horizontal polar output to expand without bound, i.e., it begins to lose polar control below ~2 kHz. By 1.2 kHz, it's basically lost most polar control horizontally (the vertical dimension is still controlled due to the line array height--which is the reason why the AMT-1 is still good on-axis down to 610 Hz).

If you look at the harmonic distortion of the AMT-1 vs. amplitude output (SPL), you will see that it begins to lose harmonic distortion control below 2 kHz and above 100 dB at 1m due to its loss of horizontal polar control. If you simply provide wings on the sides of the AMT-1, you can easily extend the low end polar directivity down to 600 Hz and below (depending on the size of the wings employed). Voila!

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About 15 years ago or so I did a blind test with a pair. I set up an active 2-way system using a PC and kX Driver. This allowed me to use a slider to adjust a 24dB LR crossover. I would adjust it with my eyes closed until it sounded good and it always landed around 1.8kHz.

Still have the AMTs. Never did anything with them. Not because I didn't like them; I'm just lazy. I really do like their sound.
Additional question.

I will have limited space behind the driver.
In fact, I plan, to put them in a 35x35cm box, 45cm deep.
The box will be open at the front, still 35x35cm, but lots of space around the driver.

The wall behind the driver will be inclined.

My plan is to put damping material on the back wall, as well as the side walls.