The researchers in Roderich Moessner’s group have attempted to discover as yet unknown principles according to which complex physical systems organize in space and time. One object of their research is topological quantum liquids. In a quantum liquid, matter is present in a special state that exists in addition to the solid, liquid and gaseous phases. An example is the Bose-Einstein condensate, in which, at very low temperatures, small clouds of atoms enter a common quantum state. A quantum liquid is topological when certain of its properties are determined by its geometry. “These topological quantum liquids are currently playing an important role in the research into quantum computers,” says Moessner.
The hidden organizing principles are, in a sense, the laws of nature of complex systems, and thus the foundation of new insights. Roderich Moessner and his colleagues only predicted the appearance of the magnetic monopoles after they had observed a new form of order in spin ice.
This new type of order concerns the magnetism in the material. The magnetic order of spin ice is much less evident than, for example, that in ferromagnetic metals, which can be permanently magnetized. “In ferromagnets, the magnetic moments of all atoms tend to be aligned,” says Moessner. The arrangement of the moments can be compared to a picket fence. “To see this order, it would be sufficient to observe the alignment of the moments of a few discrete atoms,” he explains. We would then discover that most of the magnetic moments point in a certain direction. This order is local.
“In spin ice, by contrast, there is no local order,” says Moessner. But the fact that spin ice is not simply random becomes evident only when all magnetic moments in a larger region are observed. “First, however, we must consider the individual tetrahedra of which spin ice is composed,” says Moessner. Each tetrahedron is subject to the ice rule, which dictates that the magnetic moments at two of its corners have one orientation, the opposite to that of the moments at the other two corners. This permits six combinations for the orientation of the four magnetic moments at the corners of the tetrahedron, and thus six different total magnetic moments. The magnetic moments of multiple tetrahedra combine to form the magnetization of a region under consideration. Even when the ice rule is observed, different regions in spin ice may vary widely in their magnetization.
“In spin ice, one revealing quantity is the magnetization of lattice planes that run through the crystal like floors through a building,” says Moessner. The magnetization of these planes turns out to be the same as long as the ice rule is observed.
“This shows that a certain order is still present,” he says. And only where an order exists can it be violated. A magnetic monopole is nothing other than such an infringement. Initially, Roderich Moessner’s interest lay not in the magnetic monopole, but in the departure from such an order. He considered how the magnetization of the entire crystal changes when an external magnetic field acts on spin ice in the laboratory.