S. A. Grigera

Dirac Strings and Magnetic Monopoles in the Spin Ice Dy2Ti2O7

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. Sources of magnetic fields—magnetic monopoles—have so far proven elusive as elementary particles. Condensed-matter physicists have recently proposed several scenarios of emergent quasiparticles resembling monopoles. A particularly simple proposition pertains to spin ice on the highly frustrated pyrochlore lattice. The spin-ice state is argued to be well described by networks of aligned dipoles resembling solenoidal tubes—classical, and observable, versions of a Dirac string. Where these tubes end, the resulting defects look like magnetic monopoles. We demonstrated, by diffuse neutron scattering, the presence of such strings in the spin ice dysprosium titanate (Dy2Ti2O7). This is achieved by applying a symmetry-breaking magnetic field with which we can manipulate the density and orientation of the strings. In turn, heat capacity is described by a gas of magnetic monopoles interacting via a magnetic Coulomb interaction.

Metamagnetism and Critical Fluctuations in High Quality Single Crystals of the Bilayer Ruthenate Sr3Ru2O7

We report the results of low temperature transport, specific heat, and magnetization measurements on high quality single crystals of the bilayer perovskite Sr3Ru2O7, which is a close relative of the unconventional superconductor Sr2RuO4. Metamagnetism is observed, and transport and thermodynamic evidence for associated critical fluctuations is presented. These relatively unusual fluctuations might be pictured as variations in the Fermi surface topography itself.

Metamagnetic Quantum Criticality in Metals

We present a renormalization group treatment of metamagnetic quantum criticality in metals. We show that for clean systems the universality class is that of the overdamped, conserving (dynamical exponent z = 3) Ising type. We obtain detailed results for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity, and specific heat. Our results are shown to be in quantitative agreement with data on Sr3Ru2O7 except very near to the critical point itself.

Multiple first-order metamagnetic transitions and Quantum oscillations in ultrapure Sr3Ru2O7

We present measurements on ultraclean single crystals of the bilayered ruthenate metal Sr3Ru2O7, which has a magnetic-field-tuned quantum critical point. Quantum oscillations of differing frequencies can be seen in the resistivity both below and above its metamagnetic transition. This frequency shift corresponds to a small change in the Fermi surface volume that is qualitatively consistent with the small moment change in the magnetization across the metamagnetic transition. Very near the metamagnetic field, unusual behavior is seen. There is a strong enhancement of the resistivity in a narrow field window, with a minimum in the resistivity as a function of temperature below 1 K that becomes more pronounced as the disorder level decreases. The region of anomalous behavior is bounded at low temperatures by two first-order phase transitions. The implications of the results are discussed.

Quantum oscillations near the metamagnetic transition in Sr3Ru2O7

We report detailed investigation of quantum oscillations in Sr3Ru2O7, observed inductively (the de Haas-van Alphen effect) and thermally (the magnetocaloric effect). Working at fields from 3 T to 18 T allowed us to straddle the metamagnetic transition region and probe the low- and high-field Fermi liquids. The observed frequencies are strongly field-dependent in the vicinity of the metamagnetic transition, and there is evidence for magnetic breakdown. We also present the results of a comprehensive rotation study. The most surprising result concerns the field dependence of the measured quasiparticle masses. Contrary to conclusions previously drawn by some of us as a result of a study performed with a much poorer signal to noise ratio, none of the five Fermi surface branches for which we have good field-dependent data gives evidence for a strong field dependence of the mass. The implications of these experimental findings are discussed.

Quantum Oscillations in the Anomalous Phase in Sr3Ru2O7

We report measurements of quantum oscillations detected in the putative nematic phase of Sr3Ru2O7. Improvements in sample purity enabled the resolution of small amplitude de Haas-van Alphen (dHvA) oscillations between two first order metamagnetic transitions delimiting the phase. Two distinct frequencies were observed, whose amplitudes follow the normal Lifshitz-Kosevich profile. Variations of the dHvA frequencies are explained in terms of a chemical potential shift produced by reaching a peak in the density of states, and an anomalous field dependence of the oscillatory amplitude provides information on domains.

Angular dependence of the magnetic susceptibility in the itinerant metamagnet Sr3Ru2O7

We report the results of a study of the differential magnetic susceptibility of Sr 3Ru2O7 as a function of temperature and magnetic fields applied at a series of angles to the ab plane. By analyzing the real and imaginary parts of the susceptibility, we conclude that the field angle acts as a continuous tuning parameter for the critical end point to a line of first-order metamagnetic phase transitions. The end point sits at ’1.25 K for fields applied in the ab plane, and is depressed to below 50 mK when the field is aligned within 10° of thec axis.

Quantum critical metamagnetism of Sr3Ru2O7 under hydrostatic pressure

Using ac susceptibility, we have determined the pressure dependence of the metamagnetic critical endpoint temperature T⊃* for a field applied in the ab plane in the itinerant metamagnet Sr3Ru2O 7. We find that T⊃* falls monotonically to zero as pressure increases, producing a quantum critical endpoint (QCEP) at P c~13.6±0.2kbar. New features are observed near the QCEP-the slope of T⊃* versus pressure changes at ~12.8 kbar, and weak subsidiary maxima appear on either side of the main susceptibility peak at pressures near Pc-indicating that some new physics comes into play near the QCEP. Clear signatures of a nematic phase, however, that were seen in field-angle tuning of T⊃* are not observed. As T⊃* is suppressed by pressure, the metamagnetic peak in the susceptibility remains sharp as a function of an applied magnetic field. As a function of temperature, however, the peak becomes broad with only a very weak maximum, suggesting that, near the QCEP, the uniform magnetization density is not the order parameter for the metamagnetic transition.

Phase Bifurcation and Quantum Fluctuations in Sr3Ru2O7

The bilayer ruthenate Sr3Ru2O7 has been cited as a textbook example of itinerant metamagnetic quantum criticality. However, recent studies of the ultrapure system have revealed striking anomalies in magnetism and transport in the vicinity of the quantum critical point. Drawing on fresh experimental data, we show that the complex phase behavior reported here can be fully accommodated within the framework of a simple Landau theory. We discuss the potential physical mechanisms that underpin the phenomenology, and assess the capacity of the ruthenate system to realize quantum tricritial behavior.

Thermodynamics of phase formation in the quantum critical metal Sr3Ru2O7

The behavior of matter near zero temperature continuous phase transitions, or “quantum critical points” is a central topic of study in condensed matter physics. In fermionic systems, fundamental questions remain unanswered: the nature of the quantum critical regime is unclear because of the apparent breakdown of the concept of the quasiparticle, a cornerstone of existing theories of strongly interacting metals. Even less is known experimentally about the formation of ordered phases from such a quantum critical “soup.” Here, we report a study of the specific heat across the phase diagram of the model system Sr3Ru2O7, which features an anomalous phase whose transport properties are consistent with those of an electronic nematic. We show that this phase, which exists at low temperatures in a narrow range of magnetic fields, forms directly from a quantum critical state, and contains more entropy than mean-field calculations predict. Our results suggest that this extra entropy is due to remnant degrees of freedom from the highly entropic state above Tc. The associated quantum critical point, which is “concealed” by the nematic phase, separates two Fermi liquids, neither of which has an identifiable spontaneously broken symmetry, but which likely differ in the topology of their Fermi surfaces.