The first experimental verification of Snell's law for spin waves has been carried out by an international team of researchers. By imaging the incident, refracted and reflected waves at interfaces in thin ferromagnetic films, the team has shown how the law is different for spin waves as compared to light. According to the researchers, their work is a step forward for the emerging field of "magnonics", whereby information could be encoded in spin waves.

In optics, Snell's law predicts the path taken by a beam of light travelling from one medium to another. The formula outlines the relationship between the angles of incidence and refraction, when light or other waves pass through a boundary between two different isotropic media. Passing through such boundaries causes the waves to change their speed, causing reflection and refraction.

Spin boundaries

Spin waves occur in magnetic materials where a disturbance changes the magnetic ordering within the material. These collective excitations can be described as quasiparticles known as magnons and occur in magnetic lattices with continuous symmetry. The field of magnonics aims to use these propagating spin waves to transmit information from one medium to another and store data in nanoscale devices. Therefore researchers developing such devices need to know how these waves will reflect and refract at boundaries.

It is currently a challenge to efficiently manipulate such waves, and understanding Snell's law could point to new ways of steering magnons. Miniaturization is also a problem because spin waves are currently generated using microwave antennas, which create magnons with relatively long wavelengths. Passing such magnons through different media could offer a way of reducing their wavelength.

Now, Christian Back and Johannes Stigloher at the University of Regensburg in Germany have measured how Snell's law applies to spin waves. While there have been previous theoretical studies, this is the first experiment that involves the complete imaging of spin waves impinging onto an interface between two media of different thickness.

Back told physicsworld.com that the team's main aims were to demonstrate spin-wave steering and to study the reduction of wavelength when transmitting a spin wave into a medium with different refractive index. "This may help in reducing the wavelength while keeping the spin wave amplitude large," he says, adding that "one could imagine a series of 'thickness steps' thus steering to more extreme angles while reducing the wavelength for each step."

Smaller wavelengths

For its experiments, the team used a thin magnetic film – which has two regions with different thicknesses that allow the waves to refract – made up of a nickel-iron permalloy (Ni81Fe19). This material has a particularly low damping for magnetic excitations, and allows the researchers to observe the spin waves as they travel over a large distance. The researchers then use electron beam lithography to pattern a microwave-antenna structure onto the film. This produces time-varying magnetic fields that launch spin waves into the film. The film itself is placed in an external magnetic field, which is aligned in parallel to the antenna, to ensure that it is uniformly magnetized. At the thickness step, all of the spin waves suddenly experience a different dispersion relation – which relates the wavelength of the wave to its frequency – and are refracted and reflected.

The researchers then performed temporally and spatially resolved magnetic imaging to observe the wave propagation, reflection and refraction. "In essence, we record a time-resolved movie of the travelling spin waves," says Back, explaining that the data are then used to extract the wavelength and the refracted angles of the waves. This is then used to deduce Snell's law.

The team observed that the spin-waves' wavelength and amplitude both changed at the step and that reflected and refracted spin waves formed – just as happens with light. But some deviations were also seen that are related to magnetization of the film, the externally applied magnetic field, and dipolar interactions between spins. They found that the angle between the spin waves and the applied magnetic field alters the wave dispersion, making it directionally dependent.

Deviations from the law

"We observe that there are deviations from Snell's law in optics due to the anisotropic dispersion relation of dipolar spin waves," says Back. He adds that these deviations become obvious when looking at refracted angles of the spin waves, which increase as a function of the incoming angle to a maximum around 40° and then decreases again. This behaviour is very different from light, which does not see the decrease. By taking all of their observations into consideration, the researchers could develop Snell's law for spin waves that correctly predicted their experimental observations. "The new ingredient for a magnetic thin film is the highly anisotropic dispersion relation for dipole-exchange spin waves which is at the heart of our observations," says Back.

Bruce Gaulin at McMaster University in Canada, who was not involved in the study, is impressed with the team's work. "I think this very quantitative study sets the groundwork for manipulating spin waves in the type of architectures that are likely to be important for applications." More specifically, Gaulin believes that the research "clearly demonstrates an elegant solution to reducing spin-wave wavelengths on transmission across an interface, and shows just how quantitative an understanding of 'spin wave optics' can be".

The research is described in Physical Review Letters.