Spin ice has crystal lattices made up of tetrahedra of magnetic ions. In a ground state, two of the four spins on each tetrahedron point inward and two point outward. When an excitation called the magnetic monopole is created, this rule is broken as the monopole moves through the crystal. Monopole dynamics are reflected in quantities such as magnetic noise, the measurements of which have shown a different frequency dependence than the one predicted by the simplest model.

In a new study, scientists from the University of Cambridge, the Max Planck Institute for the Physics of Complex Systems, the University of Tennessee and the Universidad Nacional de La Plata identified an emerging dynamical fractal in a disturbance-free, stoichiometric and three-dimensional magnetic crystal in thermodynamic equilibrium. They discovered this new fractal type in a class of material called spin ice.

The novelty is due to two factors. First, fractal behavior is usually caused by disorder, while the phenomena take place in a clear, flawless three-dimensional crystal. Second, the unusual principles governing the temporal evolution of magnetization in these systems give rise to fractals in spin ice. These features led to the term “emerging dynamic fractal” being coined.

The peculiar topological structure of the magnetic properties of spin ice materials and their ability to support emergent monopole magnetic excitations have made them stand out in previous years. A fractal pattern appears for the first time in an almost perfect crystal with no disorder. This is caused by the dynamics of these magnetic monopoles and their interaction with the crystal structure.

In more technical terms, a quantum mechanical process that depends on the magnetic state of neighboring atoms supports the dynamical rules that guide monopole motion in spin ice. The procedure was implemented in extensive computer simulations and the results contrasted with high-resolution experimental observations at low temperatures. The fractals cannot be found by measurements of static attributes because they are dynamic in nature. However, they generate a distinctive measurable signal in the response and variations of the magnetization.

Jonathan N. Hallén, the first author and current Ph.D. student at the Cavendish Laboratory, said: “Indeed, signatures of these fractals had been observed in experiments, some dating back nearly two decades, and were poorly understood to date. Thus, in addition to the general interest and scientific curiosity of our findings, we also explain several puzzling results that explain the scientific community.”

“It will be interesting to see what other properties of these materials can be predicted or explained in light of the new insight provided by our work. The ability of spin ice to exhibit such striking phenomena holds the promise of further surprising discoveries in the cooperative dynamics of even simple multi-body topological systems.”

Professor Claudio Castelnovo, Theory of Condensed Matter Physics, Cavendish Laboratory, said: “One wonders if the slow relaxation observed in these systems – arising from the emerging dynamic fractal behavior – can be used to advance a possible new paradigm for the appearance of glassiness in systems without the disorder.”

Magazine reference:

  1. Jonathan Hallen et al. Dynamic fractal and anomalous noise in a clean magnetic crystal. Science. DOI: 10.1126/science.add1644