A team of European researchers recently demonstrated a phenomenon known as magnetic fragmentation in a rare-earth pyrochlore iridate. As they report in a recent issue of Nature Communications, this suggests that fragmentation can be induced in so-called spin ice materials by the creation of magnetic monopoles via a staggered magnetic field. This mechanism would provide a new way to study and perhaps influence the exotic magnetic properties of these materials.

Spin ice materials are magnetic substances without a unique minimum energy ground state. The atoms in spin ice are arranged in triangular pyramids that form crystalline structures called pyrochlores. Of the four atoms that form the vertices of a pyramid, two have magnetic moments (spin) that point inward and two point outward. Spin ice is so named because the structure is analogous to how hydrogen atoms are arranged around oxygen atoms in one form of ice. 

Flipping a spin at the center of two neighboring tetrahedra in spin ice creates excitations called magnetic monopoles. Monopoles are quasiparticles that act like magnetic charges, following laws analogous to those of electrostatics and interacting through Coulomb’s law. After flipping a spin, the tetrahedron with three spins pointing inward creates a monopole with an effective magnetic charge of +1 while its neighbor creates a monopole with an effective magnetic charge of -1.

In 2014, Brooks-Bartlett and colleagues predicted in an article in Physical Review X that in the presence of dipole interactions, spin ice with a high density of monopoles would undergo magnetic-moment fragmentation and split into two parts contributing to different phases. The fragmentation results from the collective behavior of the magnetic moments and gives rise to a stable crystal of effective charges as well as a fluctuating, spin-disordered magnetic background.

In this new work, the researchers proposed inducing magnetic fragmentation by creating monopoles in spin ice. Led by PhD students Emilie Lefrançois from the Institut Laue Langevin, Grenoble Alps University (UGA), and the French National Centre for Scientific Research (CNRS), and Vadim Cathelin from UGA and CNRS, they employed a staggered magnetic field that alternates direction in space, following the local direction of the magnetic moments. This magnetic field plays the role of a particle injector, allowing for control of the concentration of monopoles.

Performing Monte Carlo simulations on a pyrochlore lattice after minimizing the energy of a tetrahedron in this environment, the team saw ground states emerge that varied with the local magnetic field. For intermediate-range magnetic fields, they saw a stable monopole crystal emerge and signs of fragmentation.  

The researchers then explored this approach experimentally. They used a sample of Ho₂Ir₂O₇, a member of the pyrochlore iridate family containing the rare element holmium. The holmium in this compound has the same geometric structure and expected magnetic behavior as spin ice. Below 140 K, the iridium sublattice in the compound exerts a magnetic field on the holmium that is equivalent to the staggered magnetic field proposed in the model.

Experiments showed that as the temperature of the system decreased, the magnetic interactions between holmium atoms started becoming more pronounced. Below 2 K, neutron scattering measurements displayed signature characteristics of fragmentation in the material.

Together, this theoretical and experimental work presents strong evidence that generating magnetic monopoles in spin ice produces fragmentation. “This is the exact realization of the prediction of Brooks-Bartlett in a three-dimensional magnetic lattice,” says one of the senior authors of this research, Virginie Simonet from Grenoble Alps University and CNRS.

There is still much to learn about the strange and contradictory states of fragmentation. “We hope that there will be other demonstrations of this fragmentation even beyond the field of magnetism. All the properties of this novel state are still to be discovered,” says Simonet.

According to Peter Holdsworth, an author on the 2014 Brooks-Bartlett article who is not associated with this new research, “The moments map onto the elements of a generalized electrostatic field with great precision, opening the door to experimental studies of topological phases and transitions with high charge density.” Holdsworth, of the École Normale Supérieure in France, specializes in frustrated systems, phase transitions in confined geometry, and models of spin ice. He calls this result “a fabulous example of emergence in condensed-matter systems.”

Read the article in Nature Communications.