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Magnetic knots suggest a pathway to energy-efficient computers

Related publication: Chmiel F. P., Waterfield Price N., Johnson R. D., Lamirand A. D., Schad J., Van Der Laan G., Harris D. T., Irwin J., Rzchowski M. S., Eom C. B. & Radaelli P. G. Observation of magnetic vortex pairs at room temperature in a planar α-Fe2O3/Co heterostructure. Nat. Mater. 17, 581–585 (2018). DOI: 10.1038/s41563-018-0101-x

Publication keywords: Absorption; Spectra; Vortices

Computers based on silicon are energy-hungry, and the search for energy-efficient alternatives is increasingly important. Electronic components based on insulating magnetic oxides should be much more efficient at storing and manipulating information. In order to operate at room temperature, such devices would rely on the presence of ‘magnetic knots’ (vortices), which would protect stored information from thermal fluctuations.

A team of researchers from Diamond Light Source, the University of Oxford, and the University of Wisconsin-Madison predicted that magnetic vortices could exist in a very simple form of iron oxide, known as haematite, which is abundant in common rust. Vortices are amongst the simplest topological structures, but in some systems (such as crystals) long-range interactions hamper their formation. This is true for microscopic magnetic vortices, which are not commonly found in ferromagnetic materials. Haematite is an antiferromagnet; it has the same magnetic moments as a ferromagnet, combined in a way that does not produce a long-range effect.

The team also expected to be able to ‘imprint’ the vortices found in haematite onto a ferromagnetic material - cobalt. On the Nanoscience beamline (I06) they were able to use X-ray Photoemission Electron Microscopy (X-PEEM) to visualise vortices in both the haematite and cobalt simultaneously but independently, with a resolution of a few tens of nm. They also managed to manipulate the vortices with a magnetic field, and observed the presence of what could be interpreted as ‘bits’ of magnetic information in the cobalt layer, in the form of a different type of magnetic knot known as a ‘meron’.

: Figure 1: Map of the antiferromagnetic spins in the Fe2O3 layer. Colour represents the axis of the antiferromagnetic moments
(colour bar bottom right). The two insets (left and right) highlight a vortex and anti-vortex respectively. The three colours (red,
green, blue) represent the three possible spin directions allowed by the magnetic symmetry of Fe2O3.

In spite of its extraordinary success in fuelling the IT revolution, silicon (CMOS) technology is intrinsically energy-inefficient. The heat flux generated by microprocessors is comparable to that on the Sun’s surface, and their clock speeds stopped growing a decade ago to prevent complete meltdown. At the core of the problem is the fact that CMOS relies on the movement of electrical charge, which is associated with Joule heating. Although its commercial success seems unstoppable, power-hungry CMOS is ultimately doomed, and IT companies are actively scouting for new energy-efficient technologies to replace it. A nominal target of 1 attojoule/operation ought to be possible – after all, the human brain uses up approximately 1.5 attojoule/operation, and the ultimate physical limit (dictated by the so-called Landauer principle) is ~0.003 attojoule/operation at room temperature. However, we would have to improve by a factor of 1,000,000 to reach this target.

Several novel technologies are being investigated to address this crucial issue. One of the front runners among these ‘beyond-CMOS’ technologies is spintronics, which relies on spins rather than charges to process information. However, much of the energy-efficiency of spintronics is lost if spin flipping – the elementary spintronic operation – must itself be performed by electrical currents. For this reason, voltage control of magnetic components is widely considered to be the key to large-scale commercialisation of spintronics. The field of oxide electronics emerges precisely from the consideration that oxides can display a multitude of intriguing multi-functional properties in their insulating states. Moreover, oxides are already integrated with CMOS, are generally stable, and are compatible with other spintronic components. Insulating oxides of magnetic transition metals such as iron, cobalt, and manganese, have many of the required properties to achieve voltage control of spins, since their charge, orbital, and magnetic states are intertwined. This can be further enhanced by exploiting the power of topology. It is well known that ordinary magnetic ‘bits’ are thermally unstable when very small in size, but this can be overcome, quite literally, by tying the spins into ‘magnetic knots’. Very recently, topological structures such as skyrmions, vortices, and 'merons' (see below) have shown enormous potential to enhance the performances of both spintronics and oxide materials, since they can be stable at room temperature and above even when very small, and can be manipulated at very low energy cost.

: Figure 2: Map of the ferromagnetic spins of the Co layer. Colour and arrows represents the direction of the ferromagnetic moments (colour
bar bottom right). The two insets (left and right) highlight a vortex and anti-vortex respectively.

Work recently published in Nature Materials¹ presented what could be a major breakthrough in this field²: for the first time, small-scale hybrid oxide/metal topological magnetic objects were created, consisting of spin vortices in antiferromagnetic iron oxide (Fe₂O₃), tightly coupled with spin ‘merons’ in ferromagnetic metallic cobalt (Co). One particularly appealing feature of this system is that it employs cheap and readily available materials – Fe₂O₃ is the most abundant constituent of common rust! Moreover, the film fabrication method was relatively simple, raising hopes that it could be deployed on a commercial scale.

The journey towards this discovery illustrates the power of analogies and generalisations in physics. Vortices are common in nature at all length scales, from galaxies (~105 light years), through to hurricanes and ordinary sink whirlpools, down to sub-micron objects. The visual similarity between all these objects belies a much deeper topological analogy – for example, all vortices ‘swirl’ around a one-dimensional singularity (a core), regardless of what exactly is the swirling field. In the early 70s, the famous British physicist Tom Kibble discussed in great detail the topology of vortices, and also pointed out that these structures can often be described by an ‘effective’ phenomenological theory³. Although primarily concerned with the formation of cosmic strings (thereby providing inspiration to countless science fiction stories), Kibble’s theory was later applied to describe the tiny quantum vortices that form in superfluid helium.

As Kibble remarked, vortices are generally destroyed by long-range interactions, so they would be extremely difficult to stabilise in ordinary magnets. The only known method to create magnetic vortices is to fabricate tiny (sub-micron) magnetic disks – an expensive process that is difficult to scale up commercially. One possible solution is to use an antiferromagnet, in which spins are exactly compensated at the atomic scale, and do not generate a long-range field. As it turns out, Fe₂O₃ is almost perfect in this respect, because it can be described by a phenomenological theory that is very close to Kibble’s ‘cosmic strings’ theory. However, the advantage of Fe₂O₃s, and all antiferromagnets, comes with a major drawback: they do not have a net magnetic moment that can be detected or modified with external magnetic fields, and therefore their vortices are extremely difficult to observe. To overcome this issue, the ideal technique is synchrotron X-ray Photoemission Electron Microscopy (X-PEEM), which is able to resolve magnetic structures as small as a few tens of nanometres by measuring the light polarisation dependency of the X-ray Absorption (XAS) coefficient of a material. An added bonus of this method is that it is element-specific, and can measure ferromagnets and antiferromagnets independently, even when they are stacked on top of each other. This led to the idea of depositing a very thin layer of ferromagnetic Co on top of Fe₂O₃, in a sense mimicking a typical spintronic device configuration.

: Figure 3: Artistic rendering of a 'meron'. A spin 'meron' is characterised by a swirling of
magnetic spins, which rise out of their plane of rotation at the 'meron' core. Finite-element
simulations indicate that vortices observed in the Co core are likely to be 'merons'.

The experiments were performed using the I06 beamline at Diamond, reconstructing a single spin map by merging polarisation dependent X-PEEM images recorded across a range of different sample orientations. This technique, known as vector mapping, takes advantage of the anisotropic nature of XAS in ferromagnets or antiferromagnets. This method was first applied to image the antiferromagnetic spin map of the Fe₂O₃ layer (Fig. 1) revealing a network of whirling magnetic vortices hundreds of nanometres in size, as well as more exotic anti-vortices. Based on Kibble’s theory, vortices and anti-vortices can annihilate, and they were seen occasionally to do so in the experiment (perhaps under the influence of the X-ray beam), although most of the vortex-antivortex network remained very stable. Later, the instrument configuration was switched to observe the Co over-layer. What was seen confirmed the team’s predictions: the Fe₂O₃ had ‘imprinted’ itself onto the adjacent metallic layer, forming tiny ferromagnetic vortices/antivortices exactly on top of the antiferromagnetic counterparts (Fig. 2). But – one may ask – what happens at the exact centre of the vortex? Once again, the power of analogy – helped by powerful finite-element simulations – provided the answer. The analogy here is with the ‘eye of the storm’ in a hurricane: whereas throughout the storm the wind whirls parallel to the ground, in the eye the flow is downwards towards the ground, whence the high pressure and clear skies. Likewise, at the centre of a ferromagnetic vortex, the spins are expected to lift out of the plane of the film, forming a topological structure known as a 'meron' (Fig. 3). Hints of 'meron' cores could be seen in the data, although the resolution of the measurements was not quite sufficient to confirm them unambiguously. Finite-element simulations confirmed that 'merons' with very small cores (10 nm) should form in these conditions. If corroborated by higher-resolution data, the existence of 'merons' would be extremely exciting; a 'meron' ‘core’ would in effect act as an extremely small memory bit, which would be topologically protected against thermal fluctuations by the surrounding vortex. Further beamtime at Diamond has been allocated for a new experimental campaign to control the density of magnetic vortices, and to investigate their presence in other materials and architectures.

References:

Chmiel F. P. et al. Observation of magnetic vortex pairs at room temperature in a planar α-Fe2O3/Co heterostructure. Nat. Mater. 17, 581–585 (2018). DOI: 10.1038/s41563-018-0101-x
Fiebig M. Symmetry and magnetism allied. Nat. Mater. 17, 567–568 (2018). DOI: 10.1038/s41563-018-0113-6
Kibble T. W. B. Topology of cosmic domains and strings. J. Phys. A Gen. Phys. 9, 1387–1398 (1976). DOI: 10.1088/0305-4470/9/8/029

Funding acknowledgement:

The work done at the University of Oxford was funded by EPSRC grant no. EP/M020517/1, entitled Oxford Quantum Materials Platform grant, and by a Royal Society University Research Fellowship. The work at University of Wisconsin-Madison was supported by the Army Research Office through grant nos W911NF-13-1-0486 and W911NF-17-1-0462.

Corresponding author:

Prof Paolo G. Radaelli, University of Oxford, p.g.radaelli@physics.ox.ac.uk

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Magnetic knots suggest a pathway to energy-efficient computers