Topological Spin Structures

Establishing a sustainable society is our century’s grand challenge. A key goal is to harvest, store and use clean energy efficiently. One of the largest energy-consuming sectors is information technology, where data centers and networks are consuming staggering amounts of power, projected to constitute ∼21% of the global electricity supply [1] and responsible for ∼23% of the global greenhouse gas emissions by 2030.

To meet this demand without devastating environmental costs, scientists are turning to quantum materials, where electrons are not only used for their charge, but also their quantum properties like spin.  The significance of a quantum revolution cannot be emphasised enough. Suppose we switch all current ICT (information and communication technology) for quantum devices by 2030, then we will save approximately 90% electricity, corresponding to the total energy produced by all coal power plants globally.

This article delves into one such quantum material–topological spin structures.

What is spin?

In 1922, a group of physicists discovered that electrons possess an intrinsic magnetic moment in the famous Stern Gerlach experiment. 

You can think of the magnetic moment as a vector pointing from the south to north pole of the presumably spherical electron, which tends to align with an external magnetic field, much like a compass needle.  However, unlike a compass needle, the vector can be measured to point in two directions–up or down relative to the direction of measurement/applied field. To explain this, early physicists modelled the electron as a uniformly charged sphere spinning on its axis, which is why this property adopted the name “spin”. But this model implied that the electron’s surface spun faster than the speed of light, which is impossible. Today spin is understood as a quantum number, belonging to the realm of quantum mechanics where atomic properties take on discrete, quantized values.

What are TSSs?

In magnetic materials such as iron and steel, which are common in paperclips and refrigerator doors, there is a “sea” of electrons whose spins interact with each other and external magnetic fields. Under the right combination of interactions, the spins form miniature vortices called topological spin structures (TSSs). A TSS consists of a region of spins continuously varying in direction and is characterized by a quantity called the winding number. To visualise this, imagine placing the ends of all the spins in the structure at the center of a sphere–the winding number counts how many times their heads cover the surface of the sphere.

One might wonder: if electron spins can only point “up” or “down” along a measurement axis, how can they form continuous vortices? The answer is that the spins in these structures represent the local spin density—an average orientation of many electron spins at a given point—rather than the measured spin of a single electron.

The winding number of TSSs cannot change under smooth, continuous deformations of the spin field and only takes integer values provided two conditions are met:

1. The spin field is continuous and smooth

2. The spins at the boundary of the vortex are uniform

Physically, this implies that the TSS is created and destroyed as a unit, so it can be deemed a fixed particle. Topology is the study of properties that survive continuous deformations, thus this property of TSSs is called topological protection.

Some Examples of TSSs [4]:

Skyrmions:

 Named after T.H.Skyrme, the pioneer of TSSs, skyrmions are the most well-known examples of TSSs.  They are characterised by a winding number of +1, with spins at the center pointing perpendicular to the plane of the structure. As one traces a circle centered on the skyrmion, the spin field twists continuously in the direction of traversal. And as one moves radially outwards towards the boundary, spins gradually end up pointing in the direction opposite to that at the center.

Antiskyrmions:

Antiskyrmions, in contrast, are characterised by a winding number of -1. Like skyrmions, spins in the center point opposite to those at the boundary, but the way spins twist is reversed: one traces a circle around the core, the spin field rotates in the opposite direction of traversal. When skyrmions and antiskyrmions collide, the spins “cancel each other” and annihilate.

Merons:  

Merons have a winding number of ½.  The spin field only covers half a sphere so the spins at the boundary are not uniform. This breaks the assumption needed for integer winding numbers, and thus merons are not topologically protected singly, but in pairs. Because in pairs, they can make a uniformly polarized boundary.

Hedgehogs:

Instead of being confined to a plane like previous examples, hedgehogs are three-dimensional. Any disk obtained by slicing through the center of the hedgehog is similar to a skyrmion–spins twist in the direction of traversal around the rings of the disk.

How are TSSs formed?

There are three crucial interactions that allows the formation of TSSs in magnetic materials:

In the quantum world, electrons are “fuzzy”-they aren’t tiny spheres but have a field of influence–wavefunctions–that spread out and interact with each other.

Heisenberg exchange arises from electron wave function overlap between neighboring atoms. It favors spin alignment in the absence of an external field and is responsible for long-range order. In a material with only Heisenberg exchange, all spins will point in the same direction.

The Zeeman effect describes the tendency for magnetic moments to align with an external magnetic field. This pins spins at the TSS boundary to align parallel to the field, which is necessary for topological protection. Adding the Zeeman effect to Heisenberg exchange, spins will transition to a helical state, wound like the single strands in DNA.

Last but not least, the Dzyaloshinskii-Moriya interaction (DMI) favors perpendicular spin alignment, enabling twisted structure, which is indispensable for the formation of TSSs. The origin is spin-orbit coupling combined with broken inversion symmetry.

How are TSSs used?

TSSs can be as small as a few nanometers in diameter—comparable to just a few dozen atoms across—making them promising candidates for ultra-dense information storage, potentially exceeding 10¹² bits per square inch, far beyond current magnetic hard drives. Their stability through topological protection ensures that once created, they cannot be easily destroyed without overcoming a significant energy barrier, while their ability to move under ultra-low current densities makes them highly energy-efficient carriers of information. Together, these features lay the groundwork for next-generation quantum and spintronic devices that are smaller, faster, and far more energy efficient than current semiconductor technologies.

One of the most prominent proposals is skyrmion-based racetrack memory, in which skyrmions act as mobile data bits within narrow magnetic nanowires (“racetracks”) [2]. Information is encoded digitally—e.g., a “1” represented by the presence of a skyrmion and a “0” by its absence—and shifted along the wire by short current pulses.

Beyond memory, TSSs also hold promise in neuromorphic computing, where information is processed in ways analogous to the brain. [3] Skyrmion motion, collisions, and interactions can naturally mimic neuron-like firing and synaptic plasticity (strengthening or weakening of connections). This enables the representation of both spiking dynamics and adaptive learning within a single physical medium. Combined with their nanoscale size, high propagation velocities (up to several hundred meters per second), and robust stability against defects, skyrmions offer a powerful alternative to traditional silicon-based circuits for building energy-efficient, brain-inspired computing architectures.

References 

[1] N. Jones et al., “How to stop data centres from gobbling up the world’s electricity,” Nature, vol. 561, no. 7722, pp. 163–166, 2018.

 [2] X. Zhang, G. P. Zhao, H. Fangohr, J. P. Liu, W. X. Xia, J. Xia, and F. J. Mor van, “Skyrmion-skyrmion and skyrmion-edge repulsions in skyrmion-based racetrack memory,” Scientific Reports, vol. 5, Jan. 2015

[3] S. Li, W. Kang, X. Chen, J. Bai, B. Pan, Y. Zhang, and W. Zhao, “Emerging neuromorphic computing paradigms exploring magnetic skyrmions,” in 2018 IEEE Computer Society Annual Symposium on VLSI (ISVLSI), pp. 539–544, 2018

[4] Y. Tokura and N. Kanazawa, “Magnetic skyrmion materials,” Chemical Reviews, vol. 121, no. 5, pp. 2857–2897, 2020