- Here is a feature article in Science that talks about the experimental quest for detecting Majorana fermions in solid state systems, bookended by the story of Majorana's disappearance.
This brief column is a good starting point with references if you want to learn about altermagnetism. For a lengthier, more technical discussion, see this PRX paper. Quickly: in local-moment ferromagnetism, the spins (and therefore magnetic moments) of electrons on lattice sites in a material spontaneously align (at least, in a single domain). Shifting over one lattice site leads to the same pattern of magnetic moments, so the ferromagnetic ordered state is "invariant under a lattice translation". In a local moment antiferromagnet, the spins alternate up and down on neighboring sites. Shifting over one lattice site + a 180 degree rotation gets back the same pattern of magnetic moments, so the antiferromagnetic ordered state is invariant under a one lattice site translation plus 180 degree rotation. It turns out, there is a third possibility: in an "altermagnet", neighboring spins alternate up and down, but their local environments are rotated by 90 degrees, so that the ordered state is invariant under a spin flip plus a 90 degree rotation. This has neat consequences for band structure and could lead to technological applications.
Adapted from PRX 12, 045501 (2022) - A statement in the press this week caused me to realize that I've never written a nicely accessible post about magnetism and how it works. Thinking about how to do that brought me back to this classic video with Richard Feynman, explaining why this can be very challenging. It seems necessary to ask a general reader simply to accept certain postulates - for example, that electrons, which are nominally point particles, have angular momentum called "spin", and that associated with that spin is a magnetic moment, so that electrons act in some sense like little magnetic dipoles. That really is remarkable, and in trying to find a way to think about this that is more accessible, I found this classic paper (pdf here) by Ohanian. My conclusion: I still need to think about this further, particularly the connection between the classical dipolar \(1/r^{3}\) field from a magnetic dipole and the fact that spin for an electron is a quantum mechanical quantity that follows its particular rules.
- N. David Mermin posted a neat little autobiographical essay on the arxiv yesterday. Fun to read, especially if you are familiar with his writing.
Wednesday, January 10, 2024
Items of interest
For the first post of the new calendar year, here are a few items that I thought were interesting:
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7 comments:
... as I'm sure you know, magnetism can also be orbital moment rather than spin moment!
Hi Steve, sure. I may have oversimplified in my wording, and I also was avoiding talking about itinerant magnets and the Stoner instability. Please let me know if you have suggested reading, though, for clear exposition about how spin leads to magnetic moment. (I hope all is well over there - sounds like you may get some real winter weather!)
Majorana: it's nice to hear about brilliant physicists who actually don't care about getting credit for their discoveries.
It's nice to see that, after all these years, FQHE research is still alive and well, but the fundamental practical problem with the effect is that any patterning of the near-perfect 2D host materials will inevitably add disorder and destroy the state - researchers who work with these materials know this all too well. So how would you pattern the qubits, then? I agree with Kouwenhoven in his assessment.
Those superconducting qubits seem to strike the balance between ease of fabrication, controllability, and qubit quality. You can make better qubits out of cold atoms in vacuum chambers, but solid-state devices are much more amenable to scaling.
It's interesting to compare Ohanian's view about the origin of spin with that of Kirk McDonald, which can be found here: http://kirkmcd.princeton.edu/examples/spin.pdf
Perhaps the most interesting thing about altermagnetism is that it's phenomenology is completely different; see the table in https://journals.aps.org/prx/abstract/10.1103/PhysRevX.12.040002 for a nice review. See https://www.youtube.com/playlist?list=PLS3nw8GL8hAVO03hJA_AGH3x9QKRijICY for a nice set of lectures.
Victor, I think Kirk McDonald (who generations of Princeton physics undergrads recall as the instructor of a famously challenging mechanics course) did a great job with writing up how one gets spin and orbital angular momentum out of classical electromagnetic fields, which seems similar in spirit to part of Ohanian's paper. I think the conceptual challenge for me is, beyond asserting it as true, how does one go from a charged point particle with intrinsic angular momentum to having a magnetic dipole moment. Ohanian sets up a calculation thinking about a gaussian blob of Dirac equation-obeying stuff with a certain state of the spinor degree of freedom and goes from there, but it still seems a bit like magic to me.
Here's something that's tangential related, an excellent lecture by Ilya Kuprov about "What exactly is Spin?"
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