Hmm. I'll keep researching too. Thanks for the help.

Alright, I guess I should post what I've learned.

Soft magnetic (that is, magnetic but not permanently so) thin films will align completely with a magnetic field normal to their surface if it's strong enough, and of course will lose their magnetisation to thermal fluctuations outside of any field. If the field is intermediate, there's two possible local states: aligned and anti-aligned, the latter of which is metastable. The thermal fluctuations will cause domain walls to wander naturally at most strengths, although they will have a sort of "surface tension" as the field becomes stronger, since anti-aligned is still the higher-energy state. If the field is just below that necessary to collapse the anti-aligned segments (bubbles) completely, they will be tightly constrained to circles with a diameter on the same order as the film thickness, which are suitable for manipulation.

I imagine to figure out the "collapse field" in a new material, you'd apply a gradually stronger magnetic field to a sample, and look for a discontinuity in instrument readings as the last bubbles collapse. I'd also guess there's a natural limit here as the thickness of domain walls becomes relevant, so you couldn't get sub-nm bubbles in an atomic monolayer, but I can't say for sure. In the 70's, they were working with films they considered to be 2D, but which are actually pretty thick by 2020s standards.

Bubbles are mobile just as their domain walls are, and slightly repel each other. To move them around, then, a pattern was printed on top of the film in another magnetic material, which would result in bubbles moving one unit one direction if the magnetic field was "wiggled" clockwise, and another if it was "wiggled" counterclockwise. To attract and repel the bubbles in such a way these patterns were asymmetrical, and Intel settled on a sort of chevron. Critically, the coils are much weaker than the permanent magnets in the assembly, so that the bubbles can be moved gently.

To remove bubbles, the field was locally increased with a wire hairpin, and to create a new one the field was weakened somewhat and a pattern was used to split the resulting giant bubble. It's also possible to use a very strong field in the opposite direction to directly create a bubble, but it was prohibitively energy expensive as a normal operation. I don't know how exactly the movement of bubbles around the 2D surface was handled, but I honestly bet you could implement a sort of billiard ball logic using the repulsion between bubbles if you wanted, so sky's the limit.

So, from a DIY perspective the patterning makes this not much better than another kind of solid-state memory, since you're still doing lithography. What I wonder about, is if you could make a 1D version, either by cutting grooves into a film or by using a thin filament wrapped onto a spool; basically a tape that moves itself in response to a "tilt" relative to the outside field that keeps it written. I have no specific reason to think bubbles would be disrupted by material edges, but there would still be a question about how to protect the bubble-free voids from closing up. I wonder about using more than one layer and exploiting interactions between them; we have a lot more materials to consider now.