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Zoology of Spin and Valley Skyrmions in Graphene

While skyrmions have recently been observed in magnetic films, they are equally expected to occur in two-dimensional electron systems exposed to a strong perpendicular magnetic field. Theoreticians from LPS have now predicted a novel manifestation in graphene, where skyrmions can be formed not only with the electrons’ physical spin but also by using the valley pseudospin.

Skyrmions appear in ferromagnetic films as complex spin textures. They may be represented as a spin flip at a certain spatial point, the skyrmion core, with respect to the global spin polarization far from the skyrmion core. In contrast to a simple spin flip, the minority spin forces other spins in its neighbourhood to be flipped as well, as shown in figure 1. Here, the global spin polarization is pointing upwards, whereas the spin in the skyrmion core is oriented downwards. At a certain distance from the skyrmion core, the spins are all oriented in the plane. If one considers only these spins with an in-plane orientation, it is clear from figure 1 that they reside on a closed circle encompassing the skyrmion core and that they turn once when following this closed path. Similarly to a Moebius strip, this twist prevents the global texture from being deformed continuously into a homogeneous ferromagnet – it is a topologically stable object.

Skyrmion Figure 1 – Skyrmions. While the global magnetization is pointing upwards, the spin at the core of the texture points downwards and encourages its neighbours to do the same. When only the spins pointing in the plane are taken into account, one notices that they perform a complete tour on a closed path around the skyrmion core. (© CC BY-SA 3.0 K. Everschor-Sitte and M. Sitte)

Beyond magnetic films, theoreticians from LPS, in collaboration with A. Rosch from the University of Cologne, Germany, have studied skyrmions in less common systems : electrons in graphene in a strong magnetic field. Under certain circumstances, the spins of these electrons are spontaneously ordered to form a ferromagnet as well as skyrmions. Contrary to magnetic films, graphene electrons carry an additional type of spin, called valley pseudospin. In analogy with the true spin, this pseudospin has also a tendency to align spontaneously and form a pseudospin ferromagnet. In a recent publication in PRL, the LPS researchers have shown that novel types of skyrmions can be formed with this pseudospin or, more exotically, with both the true spin and the valley pseudospin, as both can in principle be entangled. This gives rise to a rich zoology of skyrmions.

Apart from this theoretical classification, one may ask how to visualize these exotic skyrmions. While it seems natural to probe spin skyrmions by their local magnetization, the situation is more complex when the pseudospin is involved. At this point, enters a remarkable property of graphene electrons – for the case under scrutiny, it is sufficient to simply measure the electronic occupation of the two triangular sublattices that form the graphene lattice. If the pseudospin points upwards, the first sublattice is occupied ; if it points downwards, it is the other sublattice that matters, as shown in figure 2. One thus needs only to measure, at the atomic scale, the charge and spin densities to access the valley pseudospin and thus to identify the different theoretically studied skyrmion types. This can, for example, be achieved with the help of spin-resolved scanning tunneling spectroscopy. Stimulated by the theoretical results from LPS, this type of spectroscopic experiments is being planned at the University of Aachen in Germany.

Figure 2 – Atomic-scale representation of a valley-pseudospin skyrmion. The colour indicates the charge and spin densities, on the left and right panels, respectively, on each lattice site. While only one triangular sublattice is occupied at distances far from the skyrmion core (see left inset, where the occupied sites form an inverted Y), the other sublattice is occupied at the core (right inset, where the occupied sites form the letter Y) at the centre of each image.

Reference :

SU(4) Skyrmions in the ν = ±1 Quantum Hall State of Graphene
Y. Lian, A. Rosch and M. O. Goerbig
Physical Review Letters 117, 056806 (2016)

Contact :

Mark Goerbig