Research case study: Graded index magnonics

Our research involves developing the theory of waves in magnetic structures. In particular, we're looking at 'graded index' structures, which have gradually changing magnetic properties that gradually change the behaviour of waves which pass through them. This work is inspired by the well-developed research area of graded-index optics, which uses a changing refractive index to manipulate the behaviour of light. In our recent publication, we also looked at how a particular graded index structure can act as a source of waves.

In a magnetic material, there are regions (called 'domains') where the magnetisation is aligned in the same direction - and so adjacent domains might have the magnetisation pointing in completely opposite directions. Between these domains exists a domain wall, where the magnetisation gradually rotates from one orientation to the other (see figure 1). These domains are tiny (about 10 times the spacing between atoms) and in recent experiments they have been found to generate waves of energy in the material, called 'spin waves', although the mechanism for this is unclear.

We have developed a theory which explains this mechanism. We find that, even when you apply a small magnetic field across a domain wall, which is uniform everywhere but oscillates in time, you can generate spin waves (see figure 2). Importantly, we find that it isn't the motion of the domain wall which generates spin waves (as many papers presume) - it is created simply because of the presence of the domain wall's graded index, along with the uniform external field.

If you move the domain wall around and then the domain wall generates spin waves, that would be a nonlinear effect - which is not what we (or many other papers) observe. We're hoping to research this in more detail in future, and also investigate other graded index profiles to generate and manipulate spin waves.

Figure 1. The 'Bloch' domain wall that we studied, where the magnetisation (indicated by the blue arrows) rotates out of the plane between two antiparallel domains. 

Figure 2. The oscillation of the magnetisation, showing the domain wall in the centre of each image and the ripples of the spin waves which move away from it. The main image shows the position of the magnetisation at phase = 0, and the inset is for the phase = ω.