The Development of a New Method for Generating and Controlling Orbital Angular Momentum Beams

Eniola Elizabeth Fase

X-ray photons scattered from an artificial spin ice (ASI), a patterned array of nanoscale magnets, acquire orbital angular momentum. The X-ray beams can be switched on and off with temperature and magnetic field. Inset: Experimental X-ray diffraction pattern. Credit: Woods et al.

Artificial spin ices (ASIs) are known as magnetic metamaterials with unique properties dependent on their geometries. Many physicists have been studying these materials in recent years because their peculiar properties may be useful in a variety of applications.

A mechanism for achieving switchable X-ray orbital angular momentum (OAM) in ASI magnetic systems has recently been proposed by researchers at the University of Kentucky, Lawrence Berkeley National Laboratory, Argonne National Laboratory, and other institutions in the United States. Their process, which they describe in a paper published in Physical Review Letters, could lead to new research into ferroelectrics, chiral systems, magnetic systems, and nanostructures.

In a recent article published in Nature Photonics, Roy and his colleagues demonstrated that by fabricating a specialized grating with a fork dislocation, they could successfully produce OAM-carrying soft X-ray beams. As a result of their work on 2D square ASIs, they began looking into the generation of OAM beams in cases where a material’s square lattice has a fork defect.

ASIs are known as patterned arrays of nanomagnets with properties similar to water ice. ASIs are always “frustrated,” which means that the magnets inside them are unable to align themselves with their neighbors in such a way that their interactions consume the least amount of energy. Hydrogen atoms in water ice are usually structured similarly, as Linus Pauling discovered in 1935.

Around a decade ago, physicists discovered that square ASIs, which were first observed by a Penn State University research team, do not become “frustrated,” but instead join a well-ordered antiferromagnetic ground state. Möller and Moessner first predicted this in 2006, and Christopher Marrows and his colleagues at the University of Leeds experimentally demonstrated it in 2011. The magnets in the lattice are focused in such a way that they cancel out in an antiferromagnetic ground state, resulting in no net magnetization of the ASI.

The topological charge (number of fork defects) in the ASI studied by Roy, Hastings, and their colleagues are 2, while the antiferromagnet is 1, resulting in two separate topological charges in a single system. The researchers investigated how the inclusion and exclusion of frustration can affect the charge of a single defect in square ASI systems, as well as how X-rays scatter from these structures.

By applying an external magnetic field to square ASIs, a research team led by the Paul Scherrer Institute and Laura Heyderman at ETH Zurich showed that they could be placed in a ferromagnetic state, where all nanomagnets are focused in the same direction. Roy and Hastings proposed that an applied magnetic field might also switch off magnetically dispersed OAM beams, which would then turn back on when the device returned to its ground state, based on previous work.

“With this, the entire picture came together of a system that could produce X-ray beams with different order orbital angular momenta and in which the magnetically scattered beams could be switched on and off,” Hastings said.

The density of a substance is usually sensitive to X-rays, but the magnetic moment is not. The researchers used a method called Resonant X-ray Magnetic Scattering (RXMS) with a coherent beam to create X-rays that are sensitive to magnetic signals (for instance, one with a well-defined phase and amplitude). By adjusting the energy of the incident beam to an element’s absorption edge, they were able to achieve better magnetic sensitivity.

When researchers use RXMS techniques to conduct a diffraction experiment, they can observe strong peaks at specific angles that meet the Bragg condition, in which scattered X-rays interfere constructively. Antiferromagnets’ lattice spacing is twice that of structural lattices, so the antiferromagnetic peak occurs in various positions. Researchers can differentiate between charge and magnetic diffraction peaks thanks to this difference in position.

The nanomagnets utilized by Roy, Hastings, and their colleagues in the ASIs were made of permalloy, an alloy of iron and nickel. The researchers used electron-beam lithography to write a pattern in a polymer on a silicon wafer to build the device they studied.

The researchers discovered that the ASI system they studied reached an antiferromagnetic ground state when X-ray beams were diffracted at the correct angle and tuned to the magnetic L3 edge of iron. They later verified the existence of this condition by using X-ray magnetic circular dichroism photoemission electron microscopy to specifically view the magnetization of the nanomagnets in the device (XMCD-PEEM). They used this method to illuminate the ASI with X-rays and use an electron microscope to detect the electrons released by the nanomagnets.

The researchers also used a magnetic field to align all of the magnets in the ASI. The nanomagnets changed their magnetization orientation internally rather than rotating in the external magnetic field. The magnetically scattered X-ray OAM beams vanished as soon as the ASI was no longer in the antiferromagnetic ground state, according to the researchers.

Roy, Hastings, and their colleagues invented a method for producing a switchable X-ray OAM from ASIs, which could have a wide range of applications. It could open up new possibilities for the use of X-rays in quantum information technology, in addition to informing new studies analyzing different materials. Furthermore, physicists could identify other materials that could be utilized to produce tailored X-ray beams using the methods used by this research team.

Roy, Hastings, and their colleagues are now attempting to determine whether the beams generated in their experiments are sensitive to specific properties of other materials. If this is true, their findings could open up new avenues and horizons for research into various material systems


  • Shixing Yu and Long Li, “New method for generating Orbital Angular Momentum vortex beams in the radio frequency domain,” 2016 Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 4121-4121, doi:10.1109/PIERS.2016.7735547.


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