## Research highlights

**Evidence of impurity and boundary effects on magnetic monopole dynamics in spin ice **

H. Revell, L. Yaraskavitch, J. Mason, K. Ross, H. Noad, H. Dabkowska, B. Gaulin, P. Henelius, and J. Kycia, Nature Physics Letters

Electrical resistance is a crucial and well-understood property of systems ranging from computer microchips to nerve impulse propagation in the human body. Here we study the motion of magnetic charges in spin ice and find that extra spins inserted in Dy2Ti2O7 trap magnetic monopole excitations and provide the first example of how defects in a spin-ice material obstruct the flow of monopoles—a magnetic version of residual resistance. We measure the time-dependent magnetic relaxation in Dy2Ti2O7 and show that it decays with a stretched exponential followed by a very slow long-time tail. In a Monte Carlo simulation governed by Metropolis dynamics we show that surface effects and a very low level of stuffed spins (0.30%)—magnetic Dy ions substituted for non-magnetic Ti ions—cause these signatures in the relaxation. In addition, we find evidence that the rapidly diverging experimental timescale is due to a temperature-dependent attempt rate proportional to the monopole density.

### Universal signatures of fractionalised quantum critical points.

Sergei Isakov, Roger Melko, Matthew Hastings, Science 335, 193 (2012)

Ground states of certain materials can support exotic excitations with a charge equal to a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive unusual quantum phase transitions. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly nonclassical critical exponent η = 1.493 and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z2 gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.

### Spin Ice: Magnetic Excitations without Monopole Signatures Using Muon Spin Rotation.

Theory predicts the low-temperature magnetic excitations in spin ices, magnetic analogue of common water ice, consist of deconfined magnetic charges, or monopoles, that interact at long distance with an emerging magnetic Coulomb force. A recent high-profile transverse-field (TF) muon spin rotation (muSR) experiment [S T Bramwell et al, Nature 461, 956 (2009)] reported esults claiming to be consistent with the temperature and magnetic field dependence anticipated for monopole nucleation -- the so-called second Wien effect explained by Lars Onsager. In an experimental-theory collaboration, Gingras and his GWPI PhD students, Behnam Javanparast and Taoran Lin, recently published a Physical Review Letter in which they demonstrated, through calculations and a new series of muSR experiments in Dy2Ti2O7, that such a Wien effect is not observable in a TF muSR experiment. Rather, as found in many highly frustrated magnetic materials, they reported spin fluctuations which become temperature independent at low temperatures, behaviour which dominates over any possible signature of thermally nucleated monopole excitations.

### Topological entanglement entropy of a Bose–Hubbard spin liquid

Sergei V. Isakov, Matthew B. Hastings & Roger G. Melko

Nature Physics: 7,772 (2011)

Spin liquids are states of matter that reside outside the regime where the Landau paradigm for classifying phases can be applied. This makes them interesting, but also hard to find, as no conventional order parameters exist. The authors demonstrate that topologically ordered spin-liquid phases can be identified by numerically evaluating a measure known as topological entanglement entropy.