Steven T. Bramwell

Magnetic Coulomb Phase in the Spin Ice Ho2Ti2O7

Magnetic Monopoles Magnets come with a north and a south pole. Despite being predicted to exist, searches in astronomy and in high-energy particle physics experiments for magnetic monopoles (either north or south on their own) have defied observation. Theoretical work in condensed-matter systems has predicted that spin-ice structures may harbor such elusive particles (see the Perspective by Gingras). Fennell et al. (p. 415, published online 3 September) and Morris et al. (p. 411, published online 3 September) used polarized neutron scattering to probe the spin structure forming in two spin-ice compounds—Ho2Ti2O7 and Dy2Ti2O7—and present results in support of the presence of magnetic monopoles in both materials. Neutron scattering measurements on two spin-ice compounds show evidence for magnetic monopoles. Spin-ice materials are magnetic substances in which the spin directions map onto hydrogen positions in water ice. Their low-temperature magnetic state has been predicted to be a phase that obeys a Gauss’ law and supports magnetic monopole excitations: in short, a Coulomb phase. We used polarized neutron scattering to show that the spin-ice material Ho2Ti2O7 exhibits an almost perfect Coulomb phase. Our result proves the existence of such phases in magnetic materials and strongly supports the magnetic monopole theory of spin ice.

Measurement of the charge and current of magnetic monopoles in spin ice

The transport of electrically charged quasiparticles (based on electrons or ions) plays a pivotal role in modern technology as well as in determining the essential functions of biological organisms. In contrast, the transport of magnetic charges has barely been explored experimentally, mainly because magnetic charges, in contrast to electric ones, are generally considered at best to be convenient macroscopic parameters, rather than well-defined quasiparticles. However, it was recently proposed that magnetic charges can exist in certain materials in the form of emergent excitations that manifest like point charges, or magnetic monopoles. Here we address the question of whether such magnetic charges and their associated currents—‘magnetricity’—can be measured directly in experiment, without recourse to any material-specific theory. By mapping the problem onto Onsagers theory of electrolytes, we show that this is indeed possible, and devise an appropriate method for the measurement of magnetic charges and their dynamics. Using muon spin rotation as a suitable local probe, we apply the method to a real material, the ‘spin ice’ Dy2Ti2O7 (refs 5–8). Our experimental measurements prove that magnetic charges exist in this material, interact via a Coulomb potential, and have measurable currents. We further characterize deviations from Ohms law, and determine the elementary unit of magnetic charge to be 5 μB Å-1, which is equal to that recently predicted using the microscopic theory of spin ice. Our measurement of magnetic charge and magnetic current establishes an instance of a perfect symmetry between electricity and magnetism.It has recently been predicted that certain magnetic materials contain mobile magnetic charges or ‘monopoles’. Here we address the question of whether these magnetic charges and their associated currents (‘magnetricity’) can be directly measured in experiment, without recourse to any material-specific theory. By mapping the problem onto Onsager’s theory of weak electrolytes, we show that this is possible, and devise an appropriate method. Then, using muon spin rotation as a convenient local probe, we apply the method to a real material: the spin ice Dy2Ti2O7. Our experimental measurements prove that magnetic charges exist in this material, interact via a Coulomb interaction, and have measurable currents. We further characterise deviations from Ohm’s Law, and determine the elementary unit of magnetic charge to be 5 μBÅ −1 , which is equal to that predicted by Castelnovo, Moessner and Sondhi using the microscopic theory of spin ice. Our demonstration of magnetic charge transport has both conceptual and technological implications.

Universality of rare fluctuations in turbulence and critical phenomena

A statistical treatment of three-dimensional turbulent flow continues to pose a challenge to theorists,. One suggestion invokes an analogy with equilibrium phase transitions. Here we approach this idea experimentally, presenting evidence of a strong analogy between the statistical behaviour of a confined turbulent flow andthat of a model of the critical behaviour of a ferromagnet. Both systems experience large fluctuations limited only by the system size. We find that the power consumption measured in turbulent-flow experiments and the magnetization at the critical point of the ferromagnet have probability distributions of the same functional form, irrespective of Reynolds number on the one hand and system size on the other. The distributions both have non-gaussian tails that characterize the large-amplitude fluctuations. In this region, the scaled distributions for the two systems collapse onto a single universal curve over at least four orders of magnitude. This suggests a basic similarity in the finite-size corrections to the fluctuation statistics in the limit of infinite system size (for the magnetic system) or infinite Reynolds number (for turbulent flow).

Universal fluctuations in correlated systems

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated equilibrium and nonequilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sandpiles, avalanches, and granular media in a self-organized critical state. We discuss the relationship with both Gaussian and extremal statistics.

Pressure-induced crystallization of a spin liquid

Liquids are expected to crystallize at low temperature. The only exception is helium, which can remain liquid at 0 K, owing to quantum fluctuations. Similarly, the atomic magnetic moments (spins) in a magnet are expected to order at a temperature scale set by the Curie–Weiss temperature θCW (ref. 3). Geometrically frustrated magnets represent an exception. In these systems, the pairwise spin interactions cannot be simultaneously minimized because of the lattice symmetry. This can stabilize a liquid-like state of short-range-ordered fluctuating moments well below θCW (refs 5–7). Here we use neutron scattering to observe the spin liquid state in a geometrically frustrated system, Tb2Ti2O7, under conditions of high pressure (∼9 GPa) and low temperature (∼1 K). This compound is a three-dimensional magnet with θCW = -19 K, where the negative value indicates antiferromagnetic interactions. At ambient pressure Tb2Ti2O7 remains in a spin liquid state down to at least 70 mK (ref. 8). But we find that, under high pressure, the spins start to order or ‘crystallize’ below 2.1 K, with antiferromagnetic order coexisting with liquid-like fluctuations. These results indicate that a spin liquid/solid mixture can be induced by pressure in geometrically frustrated systems.

Magnetic fluctuations in the classical XY model: The origin of an exponential tail in a complex system

We study the probability density function for the fluctuations of the magnetic order parameter in the low-temperature phase of the XY model of finite size. In two dimensions, this system is critical over the whole of the low-temperature phase. It is shown analytically and without recourse to the scaling hypothesis that, in this case, the distribution is non-Gaussian and of universal form, independent of both system size and critical exponent eta. An exact expression for the generating function of the distribution is obtained, which is transformed and compared with numerical data from high-resolution molecular dynamics and Monte Carlo simulations. The asymptotes of the distribution are calculated and found to be of exponential and double exponential form. The calculated distribution is fitted to three standard functions: a generalization of Gumbels first asymptote distribution from the theory of extremal statistics, a generalized log-normal distribution, and a chi(2) distribution. The calculation is extended to general dimension and an exponential tail is found in all dimensions less than 4, despite the fact that critical fluctuations are limited to D=2. These results are discussed in the light of similar behavior observed in models of interface growth and for dissipative systems driven into a nonequilibrium steady state.

Melting artificial spin ice

Artificial spin ice arrays of micromagnetic islands are a means of engineering additional energy scales and frustration into magnetic materials. Here we demonstrate a magnetic phase transition in an artificial square spin ice and use the symmetry of the lattice to verify the presence of excitations far below the ordering temperature. We do this by measuring the temperature-dependent magnetization in different principal directions and comparing it with simulations of idealized statistical mechanical models. Our results confirm a dynamical pre-melting of the artificial spin ice structure at a temperature well below the intrinsic ordering temperature of the island material. We thus create a spin ice array that has the real thermal dynamics of artificial spins over an extended temperature range.

Dy2Ti2O7 Spin Ice: a Test Case for Emergent Clusters in a Frustrated Magnet

Dy2Ti2O7 is a geometrically frustrated magnetic material with a strongly correlated spin ice regime that extends from 1 K down to as low as 60 mK. The diffuse elastic neutron scattering intensities in the spin ice regime can be remarkably well described by a phenomenological model of weakly interacting hexagonal spin clusters, as invoked in other geometrically frustrated magnets. We present a highly refined microscopic theory of Dy2Ti2O7 that includes long-range dipolar and exchange interactions to third nearest neighbors and which demonstrates that the clusters are purely fictitious in this material. The seeming emergence of composite spin clusters and their associated scattering pattern is instead an indicator of fine-tuning of ancillary correlations within a strongly correlated state.

Influence of sample quality on the magnetic properties of URU2Si2

Abstract The influence of the sample quality on the magnetic properties of the heavy-fermion superconductor URu 2 Si 2 has been studied by neutron scattering, specific heat, electrical resistivity, and magnetic susceptibility measurements. Two single crystals prepared under identical conditions received different heat treatments. One crystal was annealed, the other was used as-grown. While the macroscopic properties and the magnetic excitations are essentially the same for the two crystals, the magnetic Bragg peak intensity have completely different temperature dependences. Despite this, the low-temperature magnetic moment is identical for the two samples, showing that the small moment of 0.023(3) μ B is intrinsic. The finite correlation length (∼ 500 A) appears to be related to defects. We discuss the relevance of itinerant versus localized behavior of the 5f electrons responsible for the magnetism, and the possibility of two successive phase transitions.

Neutron scattering investigation of the spin ice state in Dy2Ti2O7

Dy2Ti2O7 has been advanced as an ideal spin ice material. We present a neutron scattering investigation of a single-crystal sample of (Dy2Ti2O7)-Dy-162. The scattering intensity has been mapped in zero applied field in the h,h,l and h,k,0 planes of reciprocal space at temperatures between 0.05 and 20 K. The measured diffuse scattering has been compared with that predicted by the dipolar spin ice model. The comparison is good, except at the Brillouin-zone boundaries where extra scattering appears in the experimental data. It is concluded that the dipolar spin ice model provides a successful basis for understanding Dy2Ti2O7, but that there are issues which remain to be clarified.