Using magnetic dipolar chains as building blocks, researchers from Adolfo Ibáñez University (UAI) in Chile have demonstrated a way to design metamaterials with tailored responses to external magnetic fields. As reported in a recent issue of Physical Review Letters, they developed a prototype whose magnetic response can be modified by simply tuning its geometry and dipolar interactions. This work could pave the way for new materials with on-demand magnetic responses.

Researchers have identified magnetic response curves for many different materials by plotting induced magnetic flux against the strength of an external alternating magnetic field. In materials that display hysteresis, a response that depends on previous inputs, this curve becomes a loop. The shape of a hysteresis loop depends on its physical cause. The UAI researchers realized that a simple phenomenological model encompassing hysteresis loops of all shapes would help guide the engineering of magnetic responses.

To this end, Andrés Concha, David Aguayo, and Paula Mellado built and analyzed an elementary experimental model for engineering hysteresis loops. The base of the model was a nonmagnetic plate. At equal intervals along the surface of the plate, cylindrical neodymium magnets were hinged at their center of mass such that they could freely rotate in the plane parallel to the surface. The lowest energy state occurred when the dipoles were positioned head-to-tail (see Figure).

In the first experiment, 10 dipoles were positioned head-to-tail. The researchers applied a uniform magnetic field perpendicular to the chain and measured the rotational angle of each dipole as the magnetic field strength varied from zero to a maximum of b,  a minimum of -b and back to zero. The researchers repeated this experiment with the magnetic field oriented parallel to the chain. 

The two experiments resulted in hysteresis loops of different shapes, but in both cases, the chains displayed metastable magnetic states. In other words, the dipoles remained oriented either perpendicular or parallel to the applied field for a range of values until they collectively switched at a saturation value. This metastability occurred at every stage of the loop and according to molecular dynamics simulations, is primarily the result of interactions between the dipoles.

The researchers further characterized the system by systematically changing the number and spacing of the magnets and repeating the experiment. As the number of dipoles in a chain increased, the hysteresis loops moved toward larger field values and saturated more quickly. When space between dipoles was increased, the width of the loops and the saturation field decreased. When dipoles were randomly removed from the chain, the loops had smaller areas and the shape of the reversal curved changed.

“Once the magnetization loop of the chain is fully understood, it becomes the fundamental piece which allows us to design (and understand) loops of more complex structures,” Mellado says. To illustrate this approach, the researchers engineered a system from two dipolar chains to produce a specific hysteresis loop with complex features.  

Will Branford, an expert in magnetism and transport in nanostructures at Imperial College London, calls this an elegant demonstration. “This work shows that very simple structures of dipole chains have a large degree of tunability,” he says. “In the future the same effect could be realized with the magnetic moments on atoms or nanoparticles. Tuning the complex magnetic response of ferromagnets is critical to all sorts of applications from loudspeakers to new types of computation,” Branford says.

Read the abstract in Physical Review Letters.