Stoner Magnetism

My latest story at Physical Review Focus describes experimental evidence that a missing atom in a chicken-wire-like sheet of carbon can hold a single extra electron.

Theorists have long expected this to be the case, and that unpaired electrons on such vacancies might join up to make an entire single-atom-thick graphene sheet magnetic at relatively high temperatures. Many researchers are excited about the rapid and unusual motion of electrons in these sheets, and IBM researchers recently described a graphene field-effect transistor, grown on silicon carbide, whose expected frequency (f_T) exceeds 100GHz. If the layers are also magnetic at normal temperatures, this material could be fun and potentially practical for spintronics, which manipulates both the charge and magnetic properties of electrons.

The actually experiment didn't directly show magnetism, though, just a state that looked like it should hold only one electron. The researchers used scanning-tunneling microscopy to look at a clean, cold graphite surface, which includes many stacked graphene-like layers. In fact, the authors suggest that magnetism may exist in graphite, but not in graphene, because in the latter the effects of two equivalent carbon positions for a vacancy may cancel each other out.

It turns out to be a little bit tricky to explain the connection between local spins, which naturally carry a magnetic moment, and magnetism in a bulk material.

The usual story is straightforward: some types of atoms (or vacancies) naturally have a magnetic moment, "like a tiny bar magnet." Nearby moments exert forces that tend to align their neighbors, either the same way or oppositely. If it's the same, then the moments on many different atoms can all line up to form a net magnetization in a large sample, if the temperature is not so high that they get jostled out of position.

This description is correct--but only for some magnets.

For other magnets, it's just not accurate to say that the atoms each have magnetic moments that line up with each other. In these so-called "itinerant" magnets, the magnetization comes from the metallic electrons washing over all of the atoms. In this case, preference for one direction or another at a particular atom develops only as a part of the magnetization of the whole sample.

Mathematically, itinerant magnetism takes the form of an instability, in which the energy benefit of aligning the moments of the electrons overcomes the energy cost of doing so. A simple description was developed back in the 1940s by Edmund Stoner at the University of Leeds, and his name is still used to convey the ideas. (I apologize to anyone who expected this post to be about the natural charisma of pot-smokers.)

Of course, the distinction between the "local-moment" and "itinerant" magnetism is often somewhat fuzzy, and for the purpose of explanation to the general public it may not seem that important. But to people who understand the issues, getting it wrong is unforgivable, as I found out to my chagrin after using the above simple local picture in my Focus story on the 2007 Physics Nobel on Giant Magnetoresistance (GMR).

GMR read heads in disc drives can be seen as a simple type of spintronics device. In more sophisticated devices that people dream about, electrons will carry their magnetization to new locations, so it's important to be clear on the nature of that magnetism.