Charge Density Wave Order and Fluctuations above T_{CDW} and below Superconducting T_{c} in the Kagome Metal CsV_{3}Sb_{5}.

The phase diagram of the kagome metal family AV_{3}Sb_{5} (A=K, Rb, Cs) features both superconductivity and charge density wave (CDW) instabilities, which have generated tremendous recent attention. Nonetheless, significant questions remain. In particular, the temperature evolution and demise of the CDW state has not been extensively studied, and little is known about the coexistence of the CDW with superconductivity at low temperatures. We report an x-ray scattering study of CsV_{3}Sb_{5} over a broad range of temperatures from 300 to ∼2 K, below the onset of its superconductivity at T_{c}∼2.9 K. Order parameter measurements of the 2×2×2 CDW structure show an unusual and extended linear temperature dependence onsetting at T^{*}∼160 K, much higher than the susceptibility anomaly associated with CDW order at T_{CDW}=94 K. This implies strong CDW fluctuations exist to ∼1.7×T_{CDW}. The CDW order parameter is observed to be constant from T=16 to 2 K, implying that the CDW and superconducting order coexist below T_{c}, and, at ambient pressure, any possible competition between the two order parameters is manifested at temperatures well below T_{c}, if at all. Anomalies in the temperature dependence in the lattice parameters coincide with T_{CDW} for c(T) and with T^{*} for a(T).

Octupolar versus Néel Order in Cubic 5d

We report time-of-flight neutron spectroscopy and neutron and x-ray diffraction studies of the 5d^{2} double perovskite magnets, Ba_{2}MOsO_{6} (M=Zn,Mg,Ca). These materials host antiferromagnetically coupled 5d^{2} Os^{6+} ions decorating a face-centered cubic (fcc) lattice and are found to remain cubic down to the lowest temperatures. They all exhibit thermodynamic anomalies consistent with a single phase transition at a temperature T^{*}, and a gapped magnetic excitation spectrum with spectral weight concentrated at wave vectors typical of type-I antiferromagnetic orders. However, while muon spin resonance experiments show clear evidence for time-reversal symmetry breaking below T^{*}, we observe no corresponding magnetic Bragg scattering signal. These results are shown to be consistent with ferro-octupolar symmetry breaking below T^{*}, and are discussed in the context of other 5d double perovskite magnets and theories of exotic orders driven by multipolar interactions.

Quantum Spin Ice Dynamics in the Dipole-Octupole Pyrochlore Magnet Ce_{2}Zr_{2}O_{7}.

Neutron scattering measurements on the pyrochlore magnet Ce_{2}Zr_{2}O_{7} reveal an unusual crystal field splitting of its lowest J=5/2 multiplet, such that its ground-state doublet is composed of m_{J}=±3/2, giving these doublets a dipole-octupole (DO) character with local Ising anisotropy. Its magnetic susceptibility shows weak antiferromagnetic correlations with θ_{CW}=-0.4(2) K, leading to a naive expectation of an all-in, all-out ordered state at low temperatures. Instead, our low-energy inelastic neutron scattering measurements show a dynamic quantum spin ice state, with suppressed scattering near |Q|=0, and no long-range order at low temperatures. This is consistent with recent theory predicting symmetry-enriched U(1) quantum spin liquids for such DO doublets decorating the pyrochlore lattice. Finally, we show that disorder, especially oxidation of powder samples, is important in Ce_{2}Zr_{2}O_{7} and could play an important role in the low-temperature behavior of this material.

Thermodynamic signatures of quantum criticality in cuprate superconductors.

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram1. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range2 that includes p*. As a function of doping, we find that Cel/T is strongly peaked at p* (where Cel is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point3-5, as observed in heavy-fermion6 and iron-based7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

Phase Competition in the Palmer-Chalker XY Pyrochlore Er_{2}Pt_{2}O_{7}.

We report neutron scattering measurements on Er_{2}Pt_{2}O_{7}, a new addition to the XY family of frustrated pyrochlore magnets. Symmetry analysis of our elastic scattering data shows that Er_{2}Pt_{2}O_{7} orders into the k=0, Γ_{7} magnetic structure (the Palmer-Chalker state), at T_{N}=0.38 K. This contrasts with its sister XY pyrochlore antiferromagnets Er_{2}Ti_{2}O_{7} and Er_{2}Ge_{2}O_{7}, both of which order into Γ_{5} magnetic structures at much higher temperatures, T_{N}=1.2 and 1.4 K, respectively. In this temperature range, the magnetic heat capacity of Er_{2}Pt_{2}O_{7} contains a broad anomaly centered at T^{*}=1.5 K. Our inelastic neutron scattering measurements reveal that this broad heat capacity anomaly sets the temperature scale for strong short-range spin fluctuations. Below T_{N}=0.38 K, Er_{2}Pt_{2}O_{7} displays a gapped spin-wave spectrum with an intense, flat band of excitations at lower energy and a weak, diffusive band of excitations at higher energy. The flat band is well described by classical spin-wave calculations, but these calculations also predict sharp dispersive branches at higher energy, a striking discrepancy with the experimental data. This, in concert with the strong suppression of T_{N}, is attributable to enhanced quantum fluctuations due to phase competition between the Γ_{7} and Γ_{5} states that border each other within a classically predicted phase diagram.

Evidence for the confinement of magnetic monopoles in quantum spin ice.

Magnetic monopoles are hypothesised elementary particles connected by Dirac strings that behave like infinitely thin solenoids (Dirac 1931 Proc. R. Soc. A 133 60). Despite decades of searching, free magnetic monopoles and their Dirac strings have eluded experimental detection, although there is substantial evidence for deconfined magnetic monopole quasiparticles in spin ice materials (Castelnovo et al 2008 Nature 326 411). Here we report the detection of a hierarchy of unequally-spaced magnetic excitations via high resolution inelastic neutron spectroscopic measurements on the quantum spin ice candidate [Formula: see text] [Formula: see text] [Formula: see text]. These excitations are well-described by a simple model of monopole pairs bound by a linear potential (Coldea et al Science 327 177) with an effective tension of 0.642(8) K [Formula: see text] at 1.65 K. The success of the linear potential model suggests that these low energy magnetic excitations are direct spectroscopic evidence for the confinement of magnetic monopole quasiparticles in the quantum spin ice candidate [Formula: see text] [Formula: see text] [Formula: see text].

Ground state selection under pressure in the quantum pyrochlore magnet Yb2Ti2O7.

A quantum spin liquid is a state of matter characterized by quantum entanglement and the absence of any broken symmetry. In condensed matter, the frustrated rare-earth pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7, so-called spin ices, exhibit a classical spin liquid state with fractionalized thermal excitations (magnetic monopoles). Evidence for a quantum spin ice, in which the magnetic monopoles become long range entangled and an emergent quantum electrodynamics arises, seems within reach. The magnetic properties of the quantum spin ice candidate Yb2Ti2O7 have eluded a global understanding and even the presence or absence of static magnetic order at low temperatures is controversial. Here we show that sensitivity to pressure is the missing key to the low temperature behaviour of Yb2Ti2O7. By combining neutron diffraction and muon spin relaxation on a stoichiometric sample under pressure, we evidence a magnetic transition from a disordered, non-magnetic, ground state to a splayed ferromagnetic ground state.

Field-stepped broadband NMR in pulsed magnets and application to SrCu2(BO3)2 at 54T.

Pulsed magnets generate the highest magnetic fields as brief transients during which the observation of NMR is difficult, however, this is the only route to unique insight into material properties up to the regime of 100T. Here, it is shown how rather broad NMR spectra can be assembled in a pulsed magnet during a single field pulse by using the inherent time dependence of the field for the recording of field-stepped free induction decays that cover a broad frequency range. The technique is then applied to (11)B NMR of the spin-dimer system SrCu2(BO3)2, a magnetic insulator known to undergo a series of field-driven changes of the magnetic ground state. At peak fields of about 54T at the Dresden High Magnetic Field Laboratory, (11)B NMR spectra spanning a total of about 9MHz width are reconstructed. The results are in good accordance with a change from a high-temperature paramagnetic state to a low-temperature commensurate superstructure of field-induced spin-dimer triplets.

Crystallization of spin superlattices with pressure and field in the layered magnet SrCu2(BO3)2.

An exact mapping between quantum spins and boson gases provides fresh approaches to the creation of quantum condensates and crystals. Here we report on magnetization measurements on the dimerized quantum magnet SrCu2(BO3)2 at cryogenic temperatures and through a quantum-phase transition that demonstrate the emergence of fractionally filled bosonic crystals in mesoscopic patterns, specified by a sequence of magnetization plateaus. We apply tens of Teslas of magnetic field to tune the density of bosons and gigapascals of hydrostatic pressure to regulate the underlying interactions. Simulations help parse the balance between energy and geometry in the emergent spin superlattices. The magnetic crystallites are the end result of a progression from a direct product of singlet states in each short dimer at zero field to preferred filling fractions of spin-triplet bosons in each dimer at large magnetic field, enriching the known possibilities for collective states in both quantum spin and atomic systems.

From spin glass to quantum spin liquid ground states in molybdate pyrochlores.

We present new magnetic heat capacity and neutron scattering results for two magnetically frustrated molybdate pyrochlores: S=1 oxide Lu_{2}Mo_{2}O_{7} and S=1/2 oxynitride Lu_{2}Mo_{2}O_{5}N_{2}. Lu_{2}Mo_{2}O_{7} undergoes a transition to an unconventional spin glass ground state at T_{f}∼16 K. However, the preparation of the corresponding oxynitride tunes the nature of the ground state from spin glass to quantum spin liquid. The comparison of the static and dynamic spin correlations within the oxide and oxynitride phases presented here reveals the crucial role played by quantum fluctuations in the selection of a ground state. Furthermore, we estimate an upper limit for a gap in the spin excitation spectrum of the quantum spin liquid state of the oxynitride of Δ∼0.05 meV or Δ/|θ|∼0.004, in units of its antiferromagnetic Weiss constant θ∼-121 K.

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.

Order by disorder spin wave gap in the XY pyrochlore magnet Er2Ti2O7.

The recent determination of a robust spin Hamiltonian for the antiferromagnetic XY pyrochlore Er2Ti2O7 reveals a most convincing case of the "Order-by-Quantum-Disorder" mechanism for ground state selection. This mechanism relies on quantum fluctuations to remove an accidental symmetry of the magnetic ground state, and selects a particular ordered spin structure below TN=1.2 K. The removal of the continuous degeneracy results in an energy gap in the spectrum of spin wave excitations, long wavelength pseudo-Goldstone modes. We have measured the Order-by-Quantum-Disorder spin wave gap at a zone center in Er2Ti2O7, using low incident energy neutrons and the time-of-flight inelastic scattering method. We report a gap of Δ=0.053±0.006 meV, which is consistent with upper bounds placed on it from heat capacity measurements and roughly consistent with the theoretical estimate of ∼0.02 meV, further validating the spin Hamiltonian that led to that prediction. The gap is observed to vary with the square of the order parameter, and goes to zero for T∼TN.

Thermal conductivity of Ho2Ti2O7 along the [111] direction.

Thermal transport measurements have been made on the spin-ice material Ho(2)Ti(2)O(7) in an applied magnetic field with both the heat current and the field parallel to the [111] direction for temperatures from 50 mK to 1.2 K. A large magnetic field >6 T is applied to suppress the magnetic contribution to the thermal conductivity in order to extract the lattice conductivity. The low field thermal conductivity thus reveals a magnetic field dependent contribution to the conductivity which both transfers heat and scatters phonons. We interpret these magnetic excitations as monopolelike excitations and describe their behavior via existing Debye-Hückel theory.

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.

Neutron Laue diffraction study on the magnetic phase diagram of multiferroic MnWO4 under pulsed high magnetic fields.

We have combined time-of-flight neutron Laue diffraction and pulsed high magnetic fields at the Spallation Neutron Source to study the phase diagram of the multiferroic material MnWO(4). The control of the field-pulse timing enabled an exploration of magnetic Bragg scattering through the time dependence of both the neutron wavelength and the pulsed magnetic field. This allowed us to observe several magnetic Bragg peaks in different field-induced phases of MnWO(4) with a single instrument configuration. These phases were not previously amenable to neutron diffraction studies due to the large fields involved.

Singlet-triplet excitations in the unconventional spin-Peierls TiOBr compound.

We have performed time-of-flight neutron scattering measurements on powder samples of the unconventional spin-Peierls compound TiOBr using the fine-resolution Fermi chopper spectrometer (SEQUOIA) at the Spallation Neutron Source at Oak Ridge National Laboratory. These measurements reveal two branches of magnetic excitations within the commensurate and incommensurate spin-Peierls phases, which we associate with n=1 and n=2 triplet excitations out of the singlet ground state. These results represent the first direct measurement of the singlet-triplet energy gap in TiOBr, which has a value of E(g)=21.2±1.0 meV.

Magnetoelastics of a spin liquid: X-ray diffraction studies of Tb2Ti2O7 in pulsed magnetic fields.

We report high resolution single crystal x-ray diffraction measurements of the frustrated pyrochlore magnet Tb2Ti2O7, collected using a novel low temperature pulsed magnet system. This instrument allows characterization of structural degrees of freedom to temperatures as low as 4.4 K, and in applied magnetic fields as large as 30 T. We show that Tb2Ti2O7 manifests intriguing structural effects under the application of magnetic fields, including strongly anisotropic giant magnetostriction, a restoration of perfect pyrochlore symmetry in low magnetic fields, and ultimately a structural phase transition in high magnetic fields. It is suggested that the magnetoelastic coupling thus revealed plays a significant role in the spin liquid physics of Tb2Ti2O7 at low temperatures.

Two-dimensional kagome correlations and field induced order in the ferromagnetic XY pyrochlore Yb2Ti2O7.

Neutron scattering measurements show the ferromagnetic XY pyrochlore Yb2Ti2O7 to display strong quasi-two-dimensional (2D) spin correlations at low temperature, which give way to long range order (LRO) under the application of modest magnetic fields. Rods of scattering along 111 directions due to these 2D spin correlations imply a magnetic decomposition of the cubic pyrochlore system into decoupled kagome planes. A magnetic field of approximately 0.5 T applied along the [110] direction induces a transition to a 3D LRO state characterized by long-lived, dispersive spin waves. Our measurements map out a complex low temperature-field phase diagram for this exotic pyrochlore magnet.

Fractalization drives crystalline states in a frustrated spin system.

The fractalized Hofstadter butterfly energy spectrum predicted for magnetically confined fermions diffracted by a crystal lattice has remained beyond the reach of laboratory-accessible magnetic fields. We find the geometrically frustrated spin system SrCu(2)(BO(3))(2) to provide a sterling demonstration of a system in which bosons confined by a magnetic and lattice potential mimic the behavior of fermions in the extreme quantum limit, giving rise to a sequence of plateaus at all magnetization m(z)/m(sat) = 1/q ratios 9 > or = q > or = 2 and p/q = 2/9 (m(sat) is the saturation magnetization) in magnetic fields up to 85 T and temperatures down to 29 mK, within the sequence of previously identified plateaus at 1/8, 1/4, and 1/3 of the saturated magnetization. We identify this hierarchy of plateaus as a consequence of confined bosons in SrCu(2)(BO(3))(2) mimicking the high magnetic field fractalization predicted by the Hofstadter butterfly for fermionic systems. Such an experimental realization of the Hofstadter problem for interacting fermions has not been previously achieved in real materials, given the unachievably high magnetic flux densities or large lattice periods required. By a theoretical treatment that includes short-range repulsion in the Hofstadter treatment, stripe-like spin density-modulated phases are revealed in SrCu(2)(BO(3))(2) as emergent from a fluidic fractal spectrum.