The exciting discovery of an exotic new form of magnetism in stacked, atomic-thin sheets of carbon (a.k.a graphene) reminded me of a somewhat related piece of work done half a decade ago, which happened to be my first ever research project! Contrary to the exquisite control needed to observe the exotic ‘orbital’ magnetic state, you can actually get regular old magnetism in graphene rather simply — by punching a hole in the sheet of carbon atoms. That isn’t the whole story though. Here, I write about why this simple theoretical prediction couldn’t be observed experimentally, and how we found a way to fix it.

Rummaging through some old notebooks, I found notes from my first ever research project, done as an undergraduate researcher. Once I recovered from the burst of nostalgia, with the added perspective of six years of graduate school, I realized that I was then oblivious to how cool this problem actually was! The question we were trying to answer was rather simple; can you make a magnet out of something that is — not magnetic?

The building blocks of a magnet are microscopic objects called ‘spins’, which are an attribute of electrons, present in all matter. In most materials, such as copper, gold, water, or wood, these spins are ‘paired up’, and cancel each other out. In some materials though, such as iron, steel, nickel, and many more, these spins remain ‘unpaired’, giving rise to what we know as magnetism. It is these unpaired spins that make compasses point north, magnets stick to your refrigerator, and motors and generators run. So, scientists were naturally surprised when they discovered that graphene, a form of carbon that is most certainly non-magnetic, with no unpaired spins, can show signs of magnetism. This is quite remarkable — it’s like finding a piece of wood that mysteriously sticks to your refrigerator!

Graphene, as you may have heard, is quite the star in the world of materials. It is literally a single, two-dimensional sheet of carbon atoms, bonded in a honeycomb structure. Behind this incredibly simple structure lies a plethora of unexpected physical phenomena, such as extremely fast-moving electrons, tensile strength a hundred times larger than steel, and as recently discovered, an exotic form of superconductivity. These properties are a consequence of the honeycomb lattice, which is held together by two kinds of forces — (i) ‘local’ chemical bonds made of electrons trapped between carbon atoms, and (ii) a ‘delocalized’ cloud of free electrons, spread out on either side of the atomic sheet. It is the latter that gives rise to the unique phenomena shown above, and as we’ll see, the unexpected magnetic behavior.

All you have to do to make graphene magnetic is to literally make a hole in the sheet of carbon atoms. You can do this by, say, bombarding a graphene sheet with fast-moving ions, which kicks out carbon atoms, leaving holes. Each departing carbon atom, breaking the chemical bonds holding it in place, leaves behind two ‘dangling’ bonds — one (i) associated with the local chemical bond, and the other (ii) associated with the delocalized electron cloud. The local dangling bond is rather boring, since it remains ‘local’, and doesn’t talk with the rest of the material. On the other hand, theoretical models showed that when the delocalized electron cloud loses a carbon atom, it can host unpaired spins — just what is needed for magnetism! The models made exciting predictions, such as the formation of a beautiful, alternating magnetic motif of unpaired spins on the honeycomb lattice, and importantly, that they would spread over a large area, allowing them to talk with neighboring unpaired spins so they could conspire to create magnetic order.

Theoretical prediction for magnetism in graphene.

There was one problem though — it was seemingly impossible to see this experimentally.

At the time, I hadn’t yet developed the experimental skills needed to solve such a challenging problem, but working with my research advisor, I had access to sophisticated codes that allowed us to simulate, with great precision, the quantum mechanical details of every chemical bond in graphene. While simple theoretical models predicted a magnetic state, the discrepancy with experiments meant that there was something wrong — perhaps a faulty assumption, or a missing piece of the puzzle. One of the central assumptions of the previous theory was that the two dangling bonds left behind by the carbon vacancy, i. e. the local dangling bond and the delocalized dangling bond, did not interact with each other. This assumption was quite reasonable, since graphene was two-dimensional — in some ways, the local bonds lived within the two-dimensional sheet of atoms, and the delocalized bonds lived on either side of the sheet of atoms, in a sense, in a different dimension. Here’s the twist though — what if the graphene wasn’t truly two-dimensional? This was the insight we had through our simulations. While pristine graphene is two-dimensional, when you create a hole in it by bombarding it with energetic ions, the process is so violent that along with the hole, you additionally create subtle ripples in the sheet, in effect making graphene three-dimensional rather than two-dimensional! This means the original assumption no long holds — the local and delocalized dangling bonds can now talk to each other.

Graphene with a hole. Expected 2D structure (left) vs. actual 3D structure (right).

Our simulations showed that when you included this literal wrinkle, the delocalized dangling bond was no longer magnetic, i. e. the spins paired up, cancelling each other out. It was no wonder then that it was impossible to detect any delocalized magnetism when experiments were done on graphene sheets bombarded with ions. If you wanted to see delocalized magnetism, you had to find a way to create a hole in the atomic sheet, while also ensuring that the sheet remained two-dimensional.

We eventually wrote up these findings in a paper and published it in April 2016. However, theoretical predictions are merely castles in the sky if they are not validated by experiments. You can imagine then that I was delighted when an experimental paper came out just six months later, confirming our predictions! In this work, instead of creating holes in graphene by bombarding it with ions, the authors synthesized graphene in a unique way that ensured it had naturally occurring holes in it, thereby preserving the two-dimensional nature of the atomic sheet. Using a tool called a scanning tunneling microscope, the researchers found evidence for unpaired, delocalized spins — magnetism!

Scanning tunneling microscopy experiments on graphene with a hole, showing signatures of magnetism. Plots from Physical Review Letters 117, 166801.

This is all old news though. I have since gone onto become an experimentalist. Meanwhile, graphene has not done too badly for itself either. It started with the astonishing discovery of superconductivity in twisted bilayer graphene in 2018, which led to a flood of research on this material by some of the smartest researchers in the world. Among the many remarkable fruits of these efforts is the recent discovery of a rare, exotic form of magnetism that comes not from unpaired spins, but from the orbital motion of electrons. It’s safe to say that the story of magnetism in graphene is far from finished.

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