Quantum Barkhausen noise induced by domain wall cotunneling.

Most macroscopic magnetic phenomena (including magnetic hysteresis) are typically understood classically. Here, we examine the dynamics of a uniaxial rare-earth ferromagnet deep within the quantum regime, so that domain wall motion, and the associated hysteresis, is initiated by quantum nucleation, which then grows into large-scale domain wall motion, which is observable as an unusual form of Barkhausen noise. We observe noncritical behavior in the resulting avalanche dynamics that only can be explained by going beyond traditional renormalization group methods or classical domain wall models. We find that this "quantum Barkhausen noise" exhibits two distinct mechanisms for domain wall movement, each of which is quantum-mechanical, but with very different dependences on an external magnetic field applied transverse to the spin (Ising) axis. These observations can be understood in terms of the correlated motion of pairs of domain walls, nucleated by cotunneling of plaquettes (sections of domain wall), with plaquette pairs correlated by dipolar interactions; this correlation is suppressed by the transverse field. Similar macroscopic correlations may be expected to appear in the hysteresis of other systems with long-range interactions.

Quantum interference in superposed lattices.

Charge transport in solids at low temperature reveals a material's mesoscopic properties and structure. Under a magnetic field, Shubnikov-de Haas (SdH) oscillations inform complex quantum transport phenomena that are not limited by the ground state characteristics and have facilitated extensive explorations of quantum and topological interest in two- and three-dimensional materials. Here, in elemental metal Cr with two incommensurately superposed lattices of ions and a spin-density-wave ground state, we reveal that the phases of several low-frequency SdH oscillations in [Formula: see text] and [Formula: see text] are no longer identical but opposite. These relationships contrast with the SdH oscillations from normal cyclotron orbits that maintain identical phases between [Formula: see text] and [Formula: see text] . We trace the origin of the low-frequency SdH oscillations to quantum interference effects arising from the incommensurate orbits of Cr's superposed reciprocal lattices and explain the observed [Formula: see text]-phase shift by the reconnection of anisotropic joint open and closed orbits.

Linear magnetoresistance in the low-field limit in density-wave materials.

The magnetoresistance (MR) of a material is typically insensitive to reversing the applied field direction and varies quadratically with magnetic field in the low-field limit. Quantum effects, unusual topological band structures, and inhomogeneities that lead to wandering current paths can induce a cross-over from quadratic to linear MR with increasing magnetic field. Here we explore a series of metallic charge- and spin-density-wave systems that exhibit extremely large positive linear MR. By contrast to other linear MR mechanisms, this effect remains robust down to miniscule magnetic fields of tens of Oersted at low temperature. We frame an explanation of this phenomenon in a semiclassical narrative for a broad category of materials with partially gapped Fermi surfaces due to density waves.

Direct Observation of Collective Electronuclear Modes about a Quantum Critical Point.

We directly measure the low energy excitation modes of the quantum Ising magnet LiHoF_{4} using microwave spectroscopy. Instead of a single electronic mode, we find a set of collective electronuclear modes, in which the spin-1/2 Ising electronic spins hybridize with the bath of spin-7/2 Ho nuclear spins. The lowest-lying electronuclear mode softens at the approach to the quantum critical point, even in the presence of disorder. This softening is rapidly quenched by a longitudinal magnetic field. Similar electronuclear structures should exist in other spin-based quantum Ising systems.

Using thermal boundary conditions to engineer the quantum state of a bulk magnet.

The degree of contact between a system and the external environment can alter dramatically its proclivity to quantum mechanical modes of relaxation. We show that controlling the thermal coupling of cubic-centimeter-sized crystals of the Ising magnet LiHo(x)Y(1-x)F4 to a heat bath can be used to tune the system between a glassy state dominated by thermal excitations over energy barriers and a state with the hallmarks of a quantum spin liquid. Application of a magnetic field transverse to the Ising axis introduces both random magnetic fields and quantum fluctuations, which can retard and speed the annealing process, respectively, thereby providing a mechanism for continuous tuning between the destination states. The nonlinear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways.

Emergence of long-range order in sheets of magnetic dimers.

Quantum spins placed on the corners of a square lattice can dimerize and form singlets, which then can be transformed into a magnetic state as the interactions between dimers increase beyond threshold. This is a strictly 2D transition in theory, but real-world materials often need the third dimension to stabilize long-range order. We use high pressures to convert sheets of Cu(2+) spin 1/2 dimers from local singlets to global antiferromagnet in the model system SrCu2(BO3)2. Single-crystal neutron diffraction measurements at pressures above 5 GPa provide a direct signature of the antiferromagnetic ordered state, whereas high-resolution neutron powder and X-ray diffraction at commensurate pressures reveal a tilting of the Cu spins out of the plane with a critical exponent characteristic of 3D transitions. The addition of anisotropic, interplane, spin-orbit terms in the venerable Shastry-Sutherland Hamiltonian accounts for the influence of the third dimension.

Incommensurate antiferromagnetism in a pure spin system via cooperative organization of local and itinerant moments.

Materials with strong correlations are prone to spin and charge instabilities, driven by Coulomb, magnetic, and lattice interactions. In materials that have significant localized and itinerant spins, it is not obvious which will induce order. We combine electrical transport, X-ray magnetic diffraction, and photoemission studies with band structure calculations to characterize successive antiferromagnetic transitions in GdSi. GdSi has both sizable local moments and a partially nested Fermi surface, without confounding contributions from orbital effects. We identify a route to incommensurate order where neither type of moment dominates, but is rooted in cooperative feedback between them. The nested Fermi surface of the itinerant electrons induces strong interactions between local moments at the nesting vector, whereas the ordered local moments in turn provide the necessary coupling for a spin-density wave to form among the itinerant electrons. This mechanism echoes the cooperative interactions between electrons and ions in charge-density-wave materials, and should be germane across a spectrum of transition-metal and rare-earth intermetallic compounds.

Breakdown of the Bardeen-Cooper-Schrieffer ground state at a quantum phase transition.

Advances in solid-state and atomic physics are exposing the hidden relationships between conventional and exotic states of quantum matter. Prominent examples include the discovery of exotic superconductivity proximate to conventional spin and charge order, and the crossover from long-range phase order to preformed pairs achieved in gases of cold fermions and inferred for copper oxide superconductors. The unifying theme is that incompatible ground states can be connected by quantum phase transitions. Quantum fluctuations about the transition are manifestations of the competition between qualitatively distinct organizing principles, such as a long-wavelength density wave and a short-coherence-length condensate. They may even give rise to 'protected' phases, like fluctuation-mediated superconductivity that survives only in the vicinity of an antiferromagnetic quantum critical point. However, few model systems that demonstrate continuous quantum phase transitions have been identified, and the complex nature of many systems of interest hinders efforts to more fully understand correlations and fluctuations near a zero-temperature instability. Here we report the suppression of magnetism by hydrostatic pressure in elemental chromium, a simple cubic metal that demonstrates a subtle form of itinerant antiferromagnetism formally equivalent to the Bardeen-Cooper-Schrieffer (BCS) state in conventional superconductors. By directly measuring the associated charge order in a diamond anvil cell at low temperatures, we find a phase transition at pressures of approximately 10 GPa driven by fluctuations that destroy the BCS-like state but preserve the strong magnetic interaction between itinerant electrons and holes. Chromium is unique among stoichiometric magnetic metals studied so far in that the quantum phase transition is continuous, allowing experimental access to the quantum singularity and a direct probe of the competition between conventional and exotic order in a theoretically tractable material.

Continuous and discontinuous quantum phase transitions in a model two-dimensional magnet.

The Shasty-Sutherland model, which consists of a set of spin 1/2 dimers on a 2D square lattice, is simple and soluble but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry-Sutherland material, SrCu(2)(BO(3))(2), in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution X-ray measurements exploit what emerges as a remarkably strong spin-lattice coupling to both monitor the magnetic behavior and the absence or presence of structural discontinuities. In the low-pressure spin-singlet regime, the onset of magnetism results in an expansion of the lattice with decreasing temperature, which permits a determination of the pressure-dependent energy gap and the almost isotropic spin-lattice coupling energies. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure.

Order parameter fluctuations at a buried quantum critical point.

Quantum criticality is a central concept in condensed matter physics, but the direct observation of quantum critical fluctuations has remained elusive. Here we present an X-ray diffraction study of the charge density wave (CDW) in 2H-NbSe(2) at high pressure and low temperature, where we observe a broad regime of order parameter fluctuations that are controlled by proximity to a quantum critical point. X-rays can track the CDW despite the fact that the quantum critical regime is shrouded inside a superconducting phase; and in contrast to transport probes, allow direct measurement of the critical fluctuations of the charge order. Concurrent measurements of the crystal lattice point to a critical transition that is continuous in nature. Our results confirm the long-standing expectations of enhanced quantum fluctuations in low-dimensional systems, and may help to constrain theories of the quantum critical Fermi surface.

A ferromagnet in a continuously tunable random field.

Most physical and biological systems are disordered, even though the majority of theoretical models treat disorder as a weak perturbation. One particularly simple system is a ferromagnet approaching its Curie temperature, T(C), where all of the spins associated with partially filled atomic shells acquire parallel orientation. With the addition of disorder by way of chemical substitution, the Curie point is suppressed, but no qualitatively new phenomena appear in bulk measurements as long as the disorder is truly random on the atomic scale and not so large as to eliminate ferromagnetism entirely. Here we report the discovery that a simply measured magnetic response is singular above the Curie temperature of a model, disordered magnet, and that the associated singularity grows to an anomalous divergence at T(C). The origin of the singular response is the random internal field induced by an external magnetic field transverse to the favoured direction for magnetization. The fact that ferromagnets can be studied easily and with high precision using bulk susceptibility and a large variety of imaging tools will not only advance fundamental studies of the random field problem, but also suggests a mechanism for tuning the strength of domain wall pinning, the key to applications.

Direct measurement of antiferromagnetic domain fluctuations.

Measurements of magnetic noise emanating from ferromagnets owing to domain motion were first carried out nearly 100 years ago, and have underpinned much science and technology. Antiferromagnets, which carry no net external magnetic dipole moment, yet have a periodic arrangement of the electron spins extending over macroscopic distances, should also display magnetic noise. However, this must be sampled at spatial wavelengths of the order of several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present a direct measurement of the fluctuations in the nanometre-scale superstructure of spin- and charge-density waves associated with antiferromagnetism in elemental chromium. The technique used is X-ray photon correlation spectroscopy, where coherent X-ray diffraction produces a speckle pattern that serves as a 'fingerprint' of a particular magnetic domain configuration. The temporal evolution of the patterns corresponds to domain walls advancing and retreating over micrometre distances. This work demonstrates a useful measurement tool for antiferromagnetic domain wall engineering, but also reveals a fundamental finding about spin dynamics in the simplest antiferromagnet: although the domain wall motion is thermally activated at temperatures above 100 K, it is not so at lower temperatures, and indeed has a rate that saturates at a finite value-consistent with quantum fluctuations-on cooling below 40 K.

Switchable hardening of a ferromagnet at fixed temperature.

The intended use of a magnetic material, from information storage to power conversion, depends crucially on its domain structure, traditionally crafted during materials synthesis. By contrast, we show that an external magnetic field, applied transverse to the preferred magnetization of a model disordered uniaxial ferromagnet, is an isothermal regulator of domain pinning. At elevated temperatures, near the transition into the paramagnet, modest transverse fields increase the pinning, stabilize the domain structure, and harden the magnet, until a point where the field induces quantum tunneling of the domain walls and softens the magnet. At low temperatures, tunneling completely dominates the domain dynamics and provides an interpretation of the quantum phase transition in highly disordered magnets as a localization/delocalization transition for domain walls. While the energy scales of the rare earth ferromagnet studied here restrict the effects to cryogenic temperatures, the principles discovered are general and should be applicable to existing classes of highly anisotropic ferromagnets with ordering at room temperature or above.

Signatures of quantum criticality in pure Cr at high pressure.

The elemental antiferromagnet Cr at high pressure presents a new type of naked quantum critical point that is free of disorder and symmetry-breaking fields. Here we measure magnetotransport in fine detail around the critical pressure, Pc approximately 10 GPa, in a diamond anvil cell and reveal the role of quantum critical fluctuations at the phase transition. As the magnetism disappears and T-->0, the magnetotransport scaling converges to a non-mean-field form that illustrates the reconstruction of the magnetic Fermi surface, and is distinct from the critical scaling measured in chemically disordered CrV under pressure. The breakdown of itinerant antiferromagnetism only comes clearly into view in the clean limit, establishing disorder as a relevant variable at a quantum phase transition.

Discovery of quantum phases in the Shastry-Sutherland compound SrCu2(BO3)2 under extreme conditions of field and pressure.

The 2-dimensional layered oxide material SrCu2(BO3)2, long studied as a realization of the Shastry-Sutherland spin topology, exhibits a range of intriguing physics as a function of both hydrostatic pressure and magnetic field, with a still debated intermediate plaquette phase appearing at approximately 20 kbar and a possible deconfined critical point at higher pressure. Here, we employ a tunnel diode oscillator (TDO) technique to probe the behavior in the combined extreme conditions of high pressure, high magnetic field, and low temperature. We reveal an extensive phase space consisting of multiple magnetic analogs of the elusive supersolid phase and a magnetization plateau. In particular, a 10 × 2 supersolid and a 1/5 plateau, identified by infinite Projected Entangled Pair States (iPEPS) calculations, are found to rely on the presence of both magnetic and non-magnetic particles in the sea of dimer singlets. These states are best understood as descendants of the full-plaquette phase, the leading candidate for the intermediate phase of SrCu2(BO3)2.

A continuous metal-insulator transition driven by spin correlations.

While Mott insulators induced by Coulomb interactions are a well-recognized class of metal-insulator transitions, insulators purely driven by spin correlations are much less common, as the reduced energy scale often invites competition from other degrees of freedom. Here, we demonstrate a clean example of a spin-correlation-driven metal-insulator transition in the all-in-all-out pyrochlore antiferromagnet Cd2Os2O7, where the lattice symmetry is preserved by the antiferromagnetism. After the antisymmetric linear magnetoresistance from conductive, ferromagnetic domain walls is removed experimentally, the bulk Hall coefficient reveals four Fermi surfaces of both electron and hole types, sequentially departing the Fermi level with decreasing temperature below the Néel temperature, TN = 227 K. In Cd2Os2O7, the charge gap of a continuous metal-insulator transition opens only at T ~ 10 K << TN. The insulating mechanism parallels the Slater picture, but without a folded Brillouin zone, and contrasts sharply with Mott insulators and spin density waves, where the electronic gap opens above and at TN, respectively.

Supercapacitance and superinductance of TiN and NbTiN films in the vicinity of superconductor-to-insulator transition.

We investigate the low-temperature complex impedance of disordered insulating thin TiN and NbTiN films in the frequency region 400 Hz-1 MHz in close proximity to the superconductor-insulator transition (SIT). The frequency, temperature, and magnetic field dependencies of the real and imaginary parts of the impedance indicate that in full accord with the theoretical predictions and earlier observations, the films acquire self-induced electronic granularity and become effectively random arrays of superconducting granules coupled via Josephson links. Accordingly, the inductive component of the response is due to superconducting droplets, while the capacitive component results from the effective Josephson junctions capacitances. The impedance crosses over from capacitive to inductive behavior as films go across the transition.

Entangled quantum state of magnetic dipoles.

Free magnetic moments usually manifest themselves in Curie laws, where weak external magnetic fields produce magnetizations that vary as the reciprocal of the temperature (1/T). For a variety of materials that do not display static magnetism, including doped semiconductors and certain rare-earth intermetallics, the 1/T law is replaced by a power law T(-alpha) with alpha < 1. Here we show that a much simpler material system-namely, the insulating magnetic salt LiHo(x)Y(1-x)F(4)-can also display such a power law. Moreover, by comparing the results of numerical simulations of this system with susceptibility and specific-heat data, we show that both energy-level splitting and quantum entanglement are crucial to describing its behaviour. The second of these quantum mechanical effects-entanglement, where the wavefunction of a system with several degrees of freedom cannot be written as a product of wavefunctions for each degree of freedom-becomes visible for remarkably small tunnelling terms, and is activated well before tunnelling has visible effects on the spectrum. This finding is significant because it shows that entanglement, rather than energy-level redistribution, can underlie the magnetic behaviour of a simple insulating quantum spin system.

Optical Raman measurements of low frequency magnons under high pressure.

The application of giga-Pascal scale pressures has been widely used as a tool to systematically tune the properties of materials in order to access such general questions as the driving mechanisms underlying phase transitions. While there is a large and growing set of experimental tools successfully applied to high-pressure environments, the compatibility between diamond anvil cells and optical probes offers further potential for examining lattice, magnetic, and electronic states, along with their excitations. Here, we describe the construction of a highly efficient optical Raman spectrometer that enables measurements of magnetic excitations in single crystals down to energies of 9 cm-1 (1.1 meV or 13 K) at cryogenic temperatures and under pressures of tens of GPa.