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We measure the non-linear magnetic susceptibility $\chi^{(3)}$ of the disordered quantum Ising magnet, \lihofour, and demonstrate four-wave mixing due to coherent (anti-)Stokes Raman scattering at $\sim$ 100 Hz (p$e$V) energy scales. The temperature dependence of $\chi^{(3)}$ approximately follows a $\frac{1}{T}$ form, with a high-$T$ cutoff that can be linked to dissipation in the coherent spin clusters. $\chi^{(3)}$ also decreases monotonically with a transverse field, approaching a constant offset above a few kOe, suggesting the presence of both coherent, and spontaneous Raman scattering.

We examine the low-energy excitations in the vicinity of the quantum critical point in LiHoF$_4$, a physical realization of the Transverse Field Ising Model, focusing on the long-range fluctuations which soften to zero energy at the ferromagnetic quantum phase transition. Microwave spectroscopy in tunable loop-gap resonator structures identifies and characterizes the soft mode and higher-energy electronuclear states. We study these modes as a function of frequency and magnetic fields applied transverse and parallel to the Ising axis. These are understood in the context of a theoretical model of a soft electronuclear mode that interacts with soft photons as well as soft phonons. We identify competing infrared divergences at the quantum critical point, coming from the photons and the electronuclear soft mode. It is an incomplete cancellation of these divergences that leads to the muted but distinct signatures observed in the experiments. The application of a longitudinal magnetic field gaps the soft mode. Measurements well away from the quantum critical point reveal a set of ``Walker'' modes associated with ferromagnetic domain dynamics., Comment: 20 pages, 14 figures

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. 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 sigma_xx (rho_xx) and sigma_yy (rho_yy) are opposite, contrast with oscillations from normal cyclotron orbits that maintain identical phases. 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 pi-phase shift by the reconnection of anisotropic joint open and closed orbits.

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 dominated by large-scale quantum tunneling of spins, rather than classical thermal activation over a potential barrier. The domain wall motion is found to exhibit avalanche dynamics, observable as an unusual form of Barkhausen noise. We observe non-critical behavior in the 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 co-tunneling 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., Comment: 11 pages, 4 figures

We present a theory of magnon-polaritons in quantum Ising materials, and develop a formalism describing the coupling between light and matter as an Ising system is tuned through its quantum critical point. The theory is applied to Ising materials having multilevel single-site Hamiltonians, in which multiple magnon modes are present, such as the insulating Ising magnet LiHoF$_4$ . We find that the magnon-photon coupling strengths may be tuned by the applied transverse field, with the coupling between the soft mode present in the quantum Ising material and a photonic resonator mode diverging at the quantum critical point of the material. A fixed system of spins will not exhibit the diamagnetic response expected when light is coupled to mobile spins or atoms. Without the diamagnetic response, one expects a divergent magnon-photon coupling strength to lead to a superradiant quantum phase transition. However, this neglects the effects of damping and decoherence present in any real system. We show that damping and decoherence may block the superradiant quantum phase transition, and lead to weak coupling between the soft magnon mode and the resonator mode. The results of the theory are applied to experimental data on the model system LiHoF$_4$ in a microwave resonator., Comment: 22 pages, 6 figures

The transition metal monopnictide family of Weyl semimetals recently has been shown to exhibit anomalously strong second-order optical nonlinearity, which is theoretically attributed to a highly asymmetric polarization distribution induced by their polar structure. We experimentally test this hypothesis by measuring optical second harmonic generation (SHG) from TaAs across a pressure-tuned polar-to-nonpolar structural phase transition. Despite the high-pressure structure remaining noncentrosymmetric, the SHG yield is reduced by more than 60 % by 20 GPa as compared to the ambient pressure value. By examining the pressure dependence of distinct groups of SHG susceptibility tensor elements, we find that the yield is primarily controlled by a single element that governs the response along the polar axis. Our results confirm a connection between the polar axis and the giant optical nonlinearity of Weyl semimetals and demonstrate pressure as a means to tune this effect $in$ $situ$., Comment: 5 pages main text, 4 figures, 2 pages supplementary information

Protected by the interplay of on-site Coulomb interactions and spin-orbit coupling, Sr$_2$IrO$_4$ at high pressure is a rare example of a Mott insulator with a paramagnetic ground state. Here, using optical Raman scattering, we measure both the phonon and magnon evolution in Sr$_2$IrO$_4$ under pressure, and identify three different magnetically-ordered phases, culminating in a spin-disordered state beyond 18 GPa. A strong first-order structural phase transition drives the magnetic evolution at $\sim$10 GPa with reduced structural anisotropy in the IrO$_6$ cages, leading to increasingly isotropic exchange interactions between the Heisenberg spins and a spin-flip transition to $c$-axis-aligned antiferromagnetic order. In the disordered phase of Heisenberg $J_\mathrm{eff}=1/2$ pseudospins, the spin excitations are quasi-elastic and continuous to 10 meV, potentially hosting a gapless quantum spin liquid in Sr$_2$IrO$_4$.

Motivated by the intriguing properties of the Shastry-Sutherland compound SrCu2(BO3)2 under pressure, with a still debated intermediate plaquette phase appearing at around 20 kbar and a possible deconfined critical point at higher pressure upon entering the antiferromagnetic phase, we have investigated its high-field properties in this pressure range using tunnel diode oscillator (TDO) measurements. The two main new phases revealed by these measurements are fully consistent with those identified by infinite Projected Entangled Pair states (iPEPS) calculations of the Shastry-Sutherland model, a 1/5 plateau and a 10 x 2 supersolid. Remarkably, these phases are descendants of the full-plaquette phase, the prominent candidate for the intermediate phase of SrCu2(BO3)2. The emerging picture for SrCu2(BO3)2 is shown to be that of a system dominated by a tendency to an orthorhombic distortion at intermediate pressure, an important constraint on any realistic description of the transition into the antiferromagnetic phase.

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., Comment: 12 pages, 5 figures. Accepted for publication in Phys. Rev. Lett

Metal-insulator transitions involve a mix of charge, spin, and structural degrees of freedom, and when strongly-correlated, can underlay the emergence of exotic quantum states. Mott insulators induced by the opening of a Coulomb gap are an important and well-recognized class of transitions, but 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 fully preserved by the antiferromagnetism. After the antisymmetric linear magnetoresistance from conductive, ferromagnetic domain walls is carefully removed experimentally, the Hall coefficient of the bulk reveals four Fermi surfaces, two of electron type and two of hole type, sequentially departing the Fermi level with decreasing temperature below the N\'eel temperature, T_N. Contrary to the common belief of concurrent magnetic and metal-insulator transitions in Cd2Os2O7, the charge gap of a continuous metal-insulator transition opens only at T~10K, well below T_N=227K. The insulating mechanism resolved by the Hall coefficient parallels the Slater picture, but without a folded Brillouin zone, and contrasts sharply with the behavior of Mott insulators and spin density waves, where the electronic gap opens above and at T_N, respectively., Comment: Three figures

The random dipolar magnet LiHo$_x$Y$_{1-x}$F$_4$ enters a strongly frustrated regime for small Ho$^{3+}$ concentrations with $x<0.05$. In this regime, the magnetic moments of the Ho$^{3+}$ ions experience small quantum corrections to the common Ising approximation of LiHo$_x$Y$_{1-x}$F$_4$, which lead to a $Z_2$-symmetry breaking and small, degeneracy breaking energy shifts between different eigenstates. Here we show that destructive interference between two almost degenerate excitation pathways burns spectral holes in the magnetic susceptibility of strongly driven magnetic moments in LiHo$_x$Y$_{1-x}$F$_4$. Such spectral holes in the susceptibility, microscopically described in terms of Fano resonances, can already occur in setups of only two or three frustrated moments, for which the driven level scheme has the paradigmatic $\Lambda$-shape. For larger clusters of magnetic moments, the corresponding level schemes separate into almost isolated many-body $\Lambda$-schemes, in the sense that either the transition matrix elements between them are negligibly small or the energy difference of the transitions is strongly off-resonant to the drive. This enables the observation of Fano resonances, caused by many-body quantum corrections to the common Ising approximation also in the thermodynamic limit. We discuss its dependence on the driving strength and frequency as well as the crucial role that is played by lattice dissipation., Comment: 15 pages, 9 figures

Continuous quantum phase transitions involving all-in-all-out (AIAO) antiferromagnetic order in strongly spin-orbit-coupled 5d compounds could give rise to various exotic electronic phases and strongly-coupled quantum critical phenomena. Here we experimentally trace the AIAO spin order in Sm2Ir2O7 using direct resonant x-ray magnetic diffraction techniques under high pressure. The magnetic order is suppressed at a critical pressure Pc=6.30 GPa, while the lattice symmetry remains in the cubic Fd-3m space group across the quantum critical point. Comparing pressure tuning and the chemical series R2Ir2O7 reveals that the suppression of the AIAO order and the approach to the spin-disordered state is characterized by contrasting evolutions of both the pyrochlore lattice constant a and the trigonal distortion x. The former affects the 5d bandwidth, the latter the Ising anisotropy, and as such we posit that the opposite effects of pressure and chemical tuning lead to spin fluctuations with different Ising and Heisenberg character in the quantum critical region. Finally, the observed low-pressure scale of the AIAO quantum phase transition in Sm2Ir2O7 identifies a circumscribed region of P-T space for investigating the putative magnetic Weyl-semimetal state.

The statistics and form of avalanches in a driven system reveal the nature of the underlying energy landscape and dynamics. In conventional metallic ferromagnets, eddy-current back action can dominate the dynamics. Here, we study Barkhausen noise in Li(Ho,Y)F4, an insulating Ising ferromagnet that cannot sustain eddy currents. For large avalanches at temperatures approaching the Curie point, we find a symmetric response free of drag effects. In the low temperature limit, drag effects contribute to the dynamics, which we link to enhanced pinning from local random fields that are enabled by the microscopic dipole-coupled Hamiltonian (the Ising model in transverse field)., Comment: 14 pages, 3 figures

The phenomena of odd-parity magnetoresistance and the planar Hall effect are deeply entwined with ferromagnetism. The intrinsic magnetization of the ordered state permits these unusual and rarely observed manifestations of Onsager's theorem when time reversal symmetry is broken at zero applied field. Here we study two classes of ferromagnetic materials, rare-earth magnets with high intrinsic coercivity and antiferromagnetic pyrochlores with strongly-pinned ferromagnetic layers at domain walls, which both exhibit odd-parity magnetoresistive behavior. The peculiar angular variation of the response with respect to the relative alignments of the magnetization, magnetic field, and current reveal the two underlying microscopic mechanisms: spin-polarization-dependent scattering of a Zeeman-shifted Fermi surface and magnetoresistance driven by the anomalous velocity physics usually associated with the anomalous Hall effect.

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 [1], unusual topological band structures [2], and inhomogeneities that lead to wandering current paths [3, 4] can induce a crossover from quadratic to linear magnetoresistance with increasing magnetic field. Here we explore a series of metallic charge- and spin-density-wave systems that exhibit extremely large positive linear magnetoresistance. 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 semi-classical narrative for a broad category of materials with partially-gapped Fermi surfaces due to density waves.

Dimensionality and symmetry play deterministic roles in the laws of Nature. They are important tools to characterize and understand quantum phase transitions, especially in the limit of strong correlations between spin, orbit, charge, and structural degrees of freedom. Using newly-developed, high-pressure resonant x-ray magnetic and charge diffraction techniques, we have discovered a quantum critical point in Cd2Os2O7 as the all-in-all-out (AIAO) antiferromagnetic order is continuously suppressed to zero temperature and, concomitantly, the cubic lattice structure continuously changes from space group Fd-3m to F-43m. Surrounded by three phases of different time reversal and spatial inversion symmetries, the quantum critical region anchors two phase lines of opposite curvature, with striking departures from a mean-field form at high pressure. As spin fluctuations, lattice breathing modes, and quasiparticle excitations interact in the quantum critical region, we argue that they present the necessary components for strongly-coupled quantum criticality in this three-dimensional compound.

Quantum states cohere and interfere. Quantum systems composed of many atoms arranged imperfectly rarely display these properties. Here we demonstrate an exception in a disordered quantum magnet that divides itself into nearly isolated subsystems. We probe these coherent clusters of spins by driving the system beyond its linear response regime at a single frequency and measuring the resulting "hole" in the overall linear spectral response. The Fano shape of the hole encodes the incoherent lifetime as well as coherent mixing of the localized excitations. For the disordered Ising magnet, $\mathrm{LiHo_{0.045}Y_{0.955}F_4}$, the quality factor $Q$ for spectral holes can be as high as 100,000. We tune the dynamics of the quantum degrees of freedom by sweeping the Fano mixing parameter $q$ through zero via the amplitude of the ac pump as well as a static external transverse field. The zero-crossing of $q$ is associated with a dissipationless response at the drive frequency, implying that the off-diagonal matrix element for the two-level system also undergoes a zero-crossing. The identification of localized two-level systems in a dense and disordered dipolar-coupled spin system represents a solid state implementation of many-body localization, pushing the search forward for qubits emerging from strongly-interacting, disordered, many-body systems., Comment: 22 pages, 6 figures

Magnetism and superconductivity often compete for preeminence as a material's ground state, and in the right circumstances the fluctuating remains of magnetic order can induce superconducting pairing. The intertwining of the two on the microscopic level, independent of lattice excitations, is especially pronounced in heavy fermion compounds, rare earth cuprates, and iron pnictides. Here we point out that for a helical arrangement of localized spins, a variable magnetic pitch length provides a unique tuning process from ferromagnetic to antiferromagnetic ground state in the long and short wavelength limits, respectively. Such chemical or pressure adjustable helical order naturally provides the possibility for continuous tuning between ferromagnetically and antiferromagnetically mediated superconductivity. At the same time, phonon mediated superconductivity is suppressed because of the local ferromagnetic spin configuration. We employ synchrotron-based magnetic x-ray diffraction techniques to test these ideas in the recently discovered superconductor, MnP. This sensitive probe directly reveals a reduced-moment, helical spin order at high pressure proximate to the superconducting state, with a tightened pitch in comparison to that at ambient pressure where superconductivity is absent. The correlation between magnetic pitch length and superconducting transition temperature in the (Cr/Mn/Fe)(P/As) family suggests a strategy for using spiral magnets as interlocutors for spin fluctuation mediated superconductivity.

With sintered needles aligned and a magnetic field applied transverse to its easy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a room-temperature realization of the Random Field Ising Model. The transverse field tunes the pinning potential of the magnetic domains in a continuous fashion. We study the magnetic domain reversal and avalanche dynamics between liquid helium and room temperatures at a series of transverse fields using a Barkhausen noise technique. The avalanche size and energy distributions follow power-law behavior with a cutoff dependent on the pinning strength dialed in by the transverse field, consistent with theoretical predictions for Barkhausen avalanches in disordered materials. A scaling analysis reveals two regimes of behavior: one at low temperature and high transverse field, where the dynamics are governed by the randomness, and the second at high temperature and low transverse field where thermal fluctuations dominate the dynamics., Comment: 16 pages, 7 figures. Under review at Phys. Rev. B

The geometrically-frustrated, triangular antiferromagnet GGG exhibits a rich mix of short-range order and isolated quantum states. We investigate the effects of up to 1% Neodymium substitution for Gallium on the ac magnetic response at temperatures below 1 K in both the linear and nonlinear regimes. Substitutional disorder actually drives the system towards a more perfectly frustrated state, apparently compensating for the effect of imperfect Gadolinium/Gallium stoichiometry, while at the same time more closely demarcating the boundaries of isolated, coherent clusters composed of hundreds of spins. Optical measurements of the local Nd environment substantiate the picture of an increased frustration index with doping., Comment: 5 pages, 5 figures

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 $LiHo_xY_{1-x}F_4$ 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 non-linear response of the system explicitly demonstrates quantum interference between internal and external relaxation pathways., Comment: 23 pages, 4 figures. Accepted for publication in PNAS

The Shastry-Sutherland model, which consists of a set of spin 1/2 dimers on a 2-dimensional 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, SrCu2(BO3)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., Comment: 16 pages, 4 figures. Accepted for publication in PNAS

CeFe$_2$ is a geometrically frustrated ferromagnet that lies close to an instability at which a subtle change in the lattice symmetry couples to a transition to antiferromagnetism. We use x-ray diffraction, diamond-anvil-cell techniques, and numerical simulation to identify the ground states and to quantitatively illustrate effects of competing magnetic energy scales and geometrical frustration on the magnetic phase diagram. Comparison of phase transitions under both chemical substitution and applied pressure suggests a general solution to the physics of pyrochlore rare earth inter-metallic magnets., Comment: 5 pages, 4 figures

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-NbSe2 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 longstanding expectations of enhanced quantum fluctuations in low dimensional systems, and may help to constrain theories of the quantum critical Fermi surface., Comment: to be published in PNAS

We simulate the dc magnetic response of the diluted dipolar-coupled Ising magnet LiHo\(_{0.045}\)Y\(_{0.955}\)F\(_4\) in a transverse field, using exact diagonalization of a two-spin Hamiltonian averaged over nearest-neighbour configurations. The pairwise model, incorporating hyperfine interactions, accounts for the observed drop-off in the longitudinal (c-axis) susceptibility with increasing transverse field; with the inclusion of a small tilt in the transverse field, it also accounts for the behavior of the off-diagonal magnetic susceptibility. The hyperfine interactions do not appear to lead to qualitative changes in the pair susecptibilities, although they do renormalize the crossover fields between different regimes. Comparison with experiment indicates that antiferromagnetic correlations are more important than anticipated based on simple pair statistics and our first-principles calculations of the pair response. This means that larger clusters will be needed for a full description of the reduction in the diagonal response at small transverse fields., Comment: 18 pages, 10 figures

We use synchrotron x-ray diffraction and electrical transport under pressure to probe both the magnetism and the structure of single crystal NiS2 across its Mott-Hubbard transition. In the insulator, the low-temperature antiferromagnetic order results from superexchange among correlated electrons and couples to a (1/2, 1/2, 1/2) superlattice distortion. Applying pressure suppresses the insulating state, but enhances the magnetism as the superexchange increases with decreasing lattice constant. By comparing our results under pressure to previous studies of doped crystals we show that this dependence of the magnetism on the lattice constant is consistent for both band broadening and band filling. In the high pressure metallic phase the lattice symmetry is reduced from cubic to monoclinic, pointing to the primary influence of charge correlations at the transition. There exists a wide regime of phase separation that may be a general characteristic of correlated quantum matter., Comment: 5 pages, 3 figures

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., Comment: 10 pages, 4 figures

The inability of systems of interacting objects to satisfy all constraints simultaneously leads to frustration. A particularly important consequence of frustration is the ability to access certain protected parts of a system without disturbing the others. For magnets such "protectorates" have been inferred from theory and from neutron scattering, but their practical consequences have been unclear. We show that a magnetic analogue of optical hole-burning can address these protected spin clusters in a well-known, geometrically frustrated Heisenberg system, gadolinium gallium garnet. Our measurements additionally provide a resolution of a famous discrepancy between the bulk magnetometry and neutron diffraction results for this magnetic compound.

We investigate transport in weakly-coupled metal nanoparticle arrays, focusing on the regime where tunneling is competing with strong single electron charging effects. This competition gives rise to an interplay between two types of charge transport. In sequential tunneling, transport is dominated by independent electron hops from a particle to its nearest neighbor along the current path. In inelastic cotunneling, transport is dominated by cooperative, multi-electron hops that each go to the nearest neighbor but are synchronized to move charge over distances of several particles. In order to test how the temperature-dependent cotunnel distance affects the current-voltage ($I-V$) characteristics we perform a series of systematic experiments on highly-ordered, close-packed nanoparticle arrays. The arrays consist of $\sim 5.5$nm diameter gold nanocrystals with tight size dispersion, spaced $\sim 1.7$nm apart by interdigitating shells of dodecanethiol ligands. We present $I-V$ data for mono-, bi-, tri- and tetralayer arrays. For stacks 2-4 layers thick we compare in-plane measurements with data for vertical transport, perpendicular to the array plane. Our results support a picture whereby transport inside the Coulomb blockade regime occurs by inelastic cotunneling, while sequential tunneling takes over at large bias above the global Coulomb blockade threshold $V_t(T)$, and at high temperatures., Comment: 7 figures, 9 pages; Missing abstract

The spin- and charge-density-wave order parameters of the itinerant antiferromagnet chromium are measured directly with non-resonant x-ray diffraction as the system is driven towards its quantum critical point with high pressure using a diamond anvil cell. The exponential decrease of the spin and charge diffraction intensities with pressure confirms the harmonic scaling of spin and charge, while the evolution of the incommensurate ordering vector provides important insight into the difference between pressure and chemical doping as means of driving quantum phase transitions. Measurement of the charge density wave over more than two orders of magnitude of diffraction intensity provides the clearest demonstration to date of a weakly-coupled, BCS-like ground state. Evidence for the coexistence of this weakly-coupled ground state with high-energy excitations and pseudogap formation above the ordering temperature in chromium, the charge-ordered perovskite manganites, and the blue bronzes, among other such systems, raises fundamental questions about the distinctions between weak and strong coupling., Comment: 11 pages, 9 figures (8 in color)

The Random-Field Ising Model (RFIM) has been extensively studied as a model system for understanding the effects of disorder in magnets. Since the late 1970s, there has been a particular focus on realizations of the RFIM in site-diluted antiferromagnets. We observe random-field effects in the dilute dipole-coupled ferromagnet $\mathrm{LiHo}_x\mathrm{Y}_{1-x}\mathrm{F}_4$. In the presence of a magnetic field transverse to the Ising axis ($H_t$), the behavior of $\mathrm{LiHo}_x\mathrm{Y}_{1-x}\mathrm{F}_4$ becomes increasingly dominated by the influence of random-field terms in the effective Hamiltonian. This is seen experimentally in the shape of the ferromagentic-paramagnetic phase boundary and in changes to the critical exponents near the classical critical point. We find that above the classical critical point the magnetic susceptibility diverges as $H_t\to0$, and that the susceptibility both above and below the classical critical point can be collapsed onto a single universal curve using a modified Curie law which explicitly incorporates random-field contributions. The discovery of a ferromagnetic realization of the RFIM opens the door to investigation of the random-field problem with the wide variety of techniques available for probing ferromagnets, including the ability to examine both the statics and dynamics of the random-field problem. It also allows studying the effects of controlled amounts of randomness on the dynamics of domain pinning and the energetics of domain reversal.

When performed in the proper low field, low frequency limits, measurements of the dynamics and the nonlinear susceptibility in the model Ising magnet in transverse field, $\text{LiHo}_x\text{Y}_{1-x}\text{F}_4$, prove the existence of a spin glass transition for $x$ = 0.167 and 0.198. The classical behavior tracks for the two concentrations, but the behavior in the quantum regime at large transverse fields differs because of the competing effects of quantum entanglement and random fields., Comment: 5 pages, 5 figures. Updated figure 3 with corrected calibration information for thermometry

Elemental chromium orders antiferromagnetically near room temperature, but the ordering temperature can be driven to zero by applying large pressures. We combine diamond anvil cell and synchrotron x-ray diffraction techniques to measure directly the spin and charge order in the pure metal at the approach to its quantum critical point. Both spin and charge order are suppressed exponentially with pressure, well beyond the region where disorder cuts off such a simple evolution, and they maintain a harmonic scaling relationship over decades in scattering intensity. By comparing the development of the order parameter with that of the magnetic wavevector, it is possible to ascribe the destruction of antiferromagnetism to the growth in electron kinetic energy relative to the underlying magnetic exchange interaction.

A transverse magnetic field is used to scan the diagonal and off-diagonal susceptibility of the uniaxial quantum magnet, $\text{LiHo}_{0.045}\text{Y}_{0.955}\text{F}_4$. Clusters of strongly-coupled spins act as the primary source for the response functions, which result from a field-induced quantum projection of the system into a classically forbidden (meaning non-Ising) regime. Calculations based on spin pairs reproduce only some features of the data and fail to predict the measured off-diagonal response, providing evidence of a multi-spin collective state., Comment: 5 pages, 4 figures

The silver chalcogenides provide a striking example of the benefits of imperfection. Nanothreads of excess silver cause distortions in the current flow that yield a linear and non-saturating transverse magnetoresistance (MR). Associated with the large and positive MR is a negative longitudinal MR. The longitudinal MR only occurs in the three-dimensional limit and thereby permits the determination of a characteristic length scale set by the spatial inhomogeneity. We find that this fundamental inhomogeneity length can be as large as ten microns. Systematic measurements of the diagonal and off-diagonal components of the resistivity tensor in various sample geometries show clear evidence of the distorted current paths posited in theoretical simulations. We use a random resistor network model to fit the linear MR, and expand it from two to three dimensions to depict current distortions in the third (thickness) dimension. When compared directly to experiments on Ag$_{2\pm\delta}$Se and Ag$_{2\pm\delta}$Te, in magnetic fields up to 55 T, the model identifies conductivity fluctuations due to macroscopic inhomogeneities as the underlying physical mechanism. It also accounts reasonably quantitatively for the various components of the resistivity tensor observed in the experiments., Comment: 10 pages, 7 figures

Measurements of magnetic noise emanating from ferromagnets due 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, but this must be sampled at spatial wavelengths of order several interatomic spacings, rather than the macroscopic scales characteristic of ferromagnets. Here we present the first direct measurement of the fluctuations in the nanometre-scale spin- (charge-) density wave superstructure 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 micron distances. While the domain wall motion is thermally activated at temperatures above 100K, it is not so at lower temperatures, and indeed has a rate which saturates at a finite value - consistent with quantum fluctuations - on cooling below 40K. Our work is important because it provides an important new measurement tool for antiferromagnetic domain engineering as well as revealing a fundamental new fact about spin dynamics in the simplest antiferromagnet., Comment: 19 pages, 4 figures

Magnetotransport measurements on small single crystals of Cr, the elemental antiferromagnet, reveal the hysteretic thermodynamics of the domain structure. The temperature dependence of the transport coefficients is directly correlated with the real-space evolution of the domain configuration as recorded by x-ray microprobe imaging, revealing the effect of antiferromagnetic domain walls on electron transport. A single antiferromagnetic domain wall interface resistance is deduced to be of order $5\times10^{-5}\mathrm{\mu\Omega\cdot cm^{2}}$ at a temperature of 100 K., Comment: 3 color figures

The excitation spectrum of a model magnetic system, LiHoF$_4$, has been studied using neutron spectroscopy as the system is tuned to its quantum critical point by an applied magnetic field. The electronic mode softening expected for a quantum phase transition is forestalled by hyperfine coupling to the nuclear spins. We show that interactions with the nuclear spin bath control the length scale over which the excitations can be entangled. This generic result limits how far it is possible to approach intrinsic electronic quantum criticality., Comment: 13 pages, 3 figures, pre-proof version

The rare earth hydride YH$_{3-\delta}$ can be tuned through the metal-insulator transition both by changing $\delta$ and by illumination with ultraviolet light. The transition is dominated by strong electron-electron interactions, with transport in the insulator sensitive to both a Coulomb gap and persistent quantum fluctuations. Via a systematic variation of UV illumination time, photon flux, Coulomb gap depth, and temperature, we demonstrate that polycrystalline YH$_{3-\delta}$ serves as a model system for studying the properties of the interacting electron glass. Prominent among its features are logarithmic relaxation, aging, and universal scaling of the conductivity.

Free magnetic moments usually manifest themselves in Curie Laws, where weak external magnetic fields produce magnetizations diverging as the reciprocal 1/T of the temperature. for a variety of materials that do not disply static magnetism, including doped semiconductors and certain rare earth intermetallics, the 1/T law is changed to a power law T^-a with a<1. We report here that a considerably simpler material, namely an insulating magneticsalt can also display such a power law, and show via comparison to specific heat data and numerical simulations that quantum mechanics is crucial for its formation. Two quantum mechanical phenomena are needed, namely level splitting - which affects the spectrum of excited states - and 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. Entanglement effects become visible for remarkably small tunnelling terms, and are turned on well before tunnelling has visible effects on the spectrum. Our work is significant because it illustrates that entanglement is at the very heart of a very simple experimental observation for an insulating quantum spin system., Comment: 17 pages, 4 figures

High fidelity pressure measurements in the zero temperature limit provide a unique opportunity to study the behavior of strongly interacting, itinerant electrons with coupled spin and charge degrees of freedom. Approaching the exactitude that has become the hallmark of experiments on classical critical phenomena, we characterize the quantum critical behavior of the model, elemental antiferromagnet chromium, lightly doped with vanadium. We resolve the sharp doubling of the Hall coefficient at the quantum critical point and trace the dominating effects of quantum fluctuations up to surprisingly high temperatures., Comment: 5 pages, 4 figures

Most materials freeze when cooled to sufficiently low temperature. We find that magnetic dipoles randomly distributed in a solid matrix condense into a spin liquid with spectral properties on cooling that are the diametric opposite of those for conventional glasses. Measurements of the non-linear magnetic dynamics in the low temperature liquid reveal the presence of coherent spin oscillations composed of hundreds of spins with lifetimes up to ten seconds. These excitations can be labeled by frequency, manipulated by the magnetic fields from a loop of wire, and permit the encoding of information at multiple frequencies simultaneously., Comment: 11 pages, 4 figures

We investigate how temperature affects transport through large networks of nonlinear conductances with distributed thresholds. In monolayers of weakly-coupled gold nanocrystals, quenched charge disorder produces a range of local thresholds for the onset of electron tunneling. Our measurements delineate two regimes separated by a cross-over temperature $T^*$. Up to $T^*$ the nonlinear zero-temperature shape of the current-voltage curves survives, but with a threshold voltage for conduction that decreases linearly with temperature. Above $T^*$ the threshold vanishes and the low-bias conductance increases rapidly with temperature. We develop a model that accounts for these findings and predicts $T^*$., Comment: 5 pages including 3 figures; replaced 3/30/04: minor changes; final version

Magnetic domain wall tunneling is observed in the disordered Ising ferromagnet LiHo_{0.44}Y_{0.56}F_4. The tunneling can be tuned by applying a magnetic field transverse to the Ising axis, and is readily modeled with a WKB formalism., Comment: 16 pages, includes 4 figures

Traditional simulated annealing utilizes thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales. We compare thermal and quantum annealing in a model disordered Ising magnet, Li\sub{Ho}{0.44}\sub{Y}{0.56}\sub{F}{4}, where the effects of quantum mechanics can be tuned in the laboratory by varying a magnetic field applied transverse to the Ising axis. Our results indicate that quantum annealing indeed hastens convergence to the optimum state., Comment: 10 pages, 5 figures