# Evidence of topological excitations in a quantum magnet

8 May 2017

Condensed matter physics is the study of the multitude of ways in which matter can organise itself. Conventional phases, such as a ferromagnet, metal or superconductor, can be characterised by looking at the system locally in space. However, topological phases of matter require a different approach and in a recent Nature Physics paper we show the importance of topology for the excitations in a quantum magnet.

Over the last ten years, following on from crucial insights made in the 70's and 80's there has been a revolution in our understanding of matter through the realisation that there are states of matter that cannot be distinguished by measurements performed only at a particular point in the system. Instead one must, in some sense, know something about the system as a whole. The distinction between such phases is encoded in so-called topological numbers, which are precise measures of the nature of these phases. To make an analogy, we might ask how you could tell that the Earth is roughly spherical rather than being shaped like a pretzel. By standing at any point on the Earth you would not be able to tell. Instead you need a global observation, say a photograph from space. Or one may assemble together the observations of many people dotted across the surface. Or you may notice that the shadow during a lunar eclipse does not have holes. In this case, the topology is reflected in the number of holes. In so-called topological insulators, the topological number is computed from the quantum mechanical wave function of the electrons.

Such topological phases have experimental signatures even though we cannot distinguish them locally from more conventional phases. This is because, when there is a boundary between a topological insulator and a trivial insulator, the boundary conducts electricity like a metal - the presence of this surface state being determined by the topology of the solid.

In a recent Nature Physics paper from a team of theorists and experimentalists at Oxford, UCL and the Rutherford-Appleton Laboratory, the topological revolution in condensed matter physics is advanced in three ways. Firstly experimental evidence is found in a particular quantum magnet SrCu_{2}(BO_{3})_{2} (SCBO) for the existence of the importance of topology. The material has magnetic copper ions sitting on a lattice (see figure) such that the magnetic interactions bind the magnetic moments together into pairs of total spin zero. One implication of the reported experiment is that, in contrast to usual topological insulators which have metallic surface states, SCBO instead has magnetic surface states. Secondly, the signatures of topology are found to live in the excitations about a very simple non-topological state. Thirdly, it is found that interactions are a crucial ingredient to our understanding of these systems whereas in ordinary topological insulators interactions may essentially be neglected. In short, this paper paves the way to the exploration of a completely new set of topological insulating materials with novel properties. It raises new questions such as the extent to which such systems appear in nature and whether they may lead to new technologies.

Topological triplon modes and bound states in a Shastry–Sutherland magnet,

P.A. McClarty, F. Krüger, T. Guidi, S.F. Parker, K. Refson, A. W. Parker, D. Prabhakaran, and R. Coldea

Nature Physics, published online 8 May 2017 doi:10.1038/nphys4117

**Figure**. The top panel shows the orthogonal arrangement of “dimers” in SCBO. The dimers consist of pairs of magnetic copper ions that are in a quantum mechanical superposition with zero total magnetic moment. It requires a finite energy to break-up this superposition and induce a net moment. These excitations are called “triplons”, in order to express that they behave as quantum mechanical particles. The coupling between spins of adjacent dimers is responsible for the peculiar motion of triplons as well as for the strong interactions between them. In a small magnetic field perpendicular to the dimer planes, the magnetic excitation acquire a topological character. This goes hand-in-hand with the appearance of excitations that circulate around the edges of the sample. The bottom panel shows the comparison between the excitation spectrum measured by inelastic neutron scattering at the Rutherford Appleton Laboratory and theoretical calculations based on a model of interacting triplons. The high resolution and sensitivity of the inelastic neutron scattering data were crucial in order to observe the magnetic excitations in unprecedented detail and to reveal fingerprints of strong interactions. The large single crystals used in the neutron experiments were grown using an optical floating zone image furnace in the Clarendon Laboratory.