Are Multiphase Competition and Order by Disorder the Keys to Understanding Yb(2)Ti(2)O(7)?

Dynamical Scaling as a Signature of Multiple Phase Competition in Yb_{2}Ti_{2}O_{7}

Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.

Possible Inversion Symmetry Breaking in the S=1/2 Pyrochlore Heisenberg Magnet

We address the ground-state properties of the long-standing and much-studied three-dimensional quantum spin liquid candidate, the S=1/2 pyrochlore Heisenberg antiferromagnet. By using SU(2) density-matrix renormalization group (DMRG), we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground-state energy, E_{0}/N_{sites}=-0.490(6)J, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.

Multiphase magnetism in Yb2Ti2O7

We use neutron scattering to show that ferromagnetism and antiferromagnetism coexist in the low T state of the pyrochlore quantum magnet [Formula: see text] While magnetic Bragg peaks evidence long-range static ferromagnetic order, inelastic scattering shows that short-range correlated antiferromagnetism is also present. Small-angle neutron scattering provides direct evidence for mesoscale magnetic structure that we associate with metastable antiferromagnetism. Classical Monte Carlo simulations based on exchange interactions inferred from [Formula: see text]-oriented high-field spin wave measurements confirm that antiferromagnetism is metastable within the otherwise ferromagnetic ground state. The apparent lack of coherent spin wave excitations and strong sensitivity to quenched disorder characterizing [Formula: see text] is a consequence of this multiphase magnetism.

Quantum Versus Classical Spin Fragmentation in Dipolar Kagome Ice Ho3Mg2Sb3O14

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material Ho3Mg2Sb3O14 unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the Ho3+ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at T * ≈ 0.32 K to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to T ≈ 0.12 K . These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In Ho3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.

Order out of a Coulomb Phase and Higgs Transition: Frustrated Transverse Interactions of Nd_{2}Zr_{2}O_{7}

The pyrochlore material Nd_{2}Zr_{2}O_{7} with an "all-in-all-out" (AIAO) magnetic order shows novel quantum moment fragmentation with gapped flat dynamical spin ice modes. The parametrized spin Hamiltonian with a dominant frustrated ferromagnetic transverse term reveals a proximity to a U(1) spin liquid. Here we study the magnetic excitations of Nd_{2}Zr_{2}O_{7} above the ordering temperature (T_{N}) using high-energy-resolution inelastic neutron scattering. We find strong spin ice correlations at zero energy with the disappearance of gapped magnon excitations of the AIAO order. It seems that the gap to the dynamical spin ice closes above T_{N} and the system enters a quantum spin ice state competing with and suppressing the AIAO order. Classical Monte Carlo simulations, molecular dynamics, and quantum boson calculations support the existence of a Coulombic phase above T_{N}. Our findings relate the magnetic ordering of Nd_{2}Zr_{2}O_{7} with the Higgs mechanism and provide explanations for several previously reported experimental features.

Magnetic Order with Fractionalized Excitations in Pyrochlore Magnets with Strong Spin-Orbit Coupling

A recent inelastic neutron scattering experiment on the pyrochlore magnet Yb₂Ti₂O₇ uncovers an unusual scattering continuum in the spin excitation spectrum despite the splayed ferromagnetic order in the ground state. While there exist well defined spin wave excitations at high magnetic fields, the one magnon modes and the two magnon continuum start to strongly overlap upon decreasing the field, and eventually they become the scattering continuum at zero field. Motivated by these observations, we investigate the possible emergence of a magnetically ordered ground state with fractionalized excitations in the spin model with the exchange parameters determined from two previous experiments. Using the fermionic parton mean field theory, we show that the magnetically ordered state with fractionalized excitations can arise as a stable mean field ground state in the presence of sufficiently strong quantum fluctuations. The spin excitation spectrum in such a ground state is computed and shown to have the scattering continuum. Upon increasing the field, the fractionalized magnetically ordered state is suppressed, and is eventually replaced by the conventional magnetically ordered phase at high fields, which is consistent with the experimental data. We discuss further implications of these results to the experiments and possible improvements on the theoretical analysis.

Role of defects in determining the magnetic ground state of ytterbium titanate

Pyrochlore systems are ideally suited to the exploration of geometrical frustration in three dimensions, and their rich phenomenology encompasses topological order and fractional excitations. Classical spin ices provide the first context in which it is possible to control emergent magnetic monopoles, and anisotropic exchange leads to even richer behaviour associated with large quantum fluctuations. Whether the magnetic ground state of Yb₂Ti₂O₇ is a quantum spin liquid or a ferromagnetic phase induced by a Higgs transition appears to be sample dependent. Here we have determined the role of structural defects on the magnetic ground state via the diffuse scattering of neutrons. We find that oxygen vacancies stabilise the spin liquid phase and the stuffing of Ti sites by Yb suppresses it. Samples in which the oxygen vacancies have been eliminated by annealing in oxygen exhibit a transition to a ferromagnetic phase, and this is the true magnetic ground state.

Exploring the role of structural defect is essential to understand the exotic quantum spin phenoma in rare earth pyrochlores. Here the authors show oxygen vacancies can stabilise the spin liquid phase and reveal the ferromagnetic ground state when oxygen vacancies are eliminated in Yb₂Ti₂O₇.

Synthesis, crystal growth and characterization of the pyrochlore Er2Ti2O7

A stoichiometric and high crystalline quality Er₂Ti₂O₇ single crystal was successfully grown using the traveling solvent floating zone technique for the first time.

Pseudo-Goldstone Gaps and Order-by-Quantum Disorder in Frustrated Magnets

In systems with competing interactions, continuous degeneracies can appear which are accidental, in that they are not related to any symmetry of the Hamiltonian. Accordingly, the pseudo-Goldstone modes associated with these degeneracies are also unprotected. Indeed, through a process known as "order-by-quantum disorder," quantum zero-point fluctuations can lift the degeneracy and induce a gap for these modes. We show that this gap can be exactly computed at leading order in 1/S in spin-wave theory from the mean curvature of the classical and quantum zero-point energies-without the need to consider any spin-wave interactions. We confirm this equivalence through direct calculations of the spin-wave spectrum to O(1/S^{2}) in a wide variety of theoretically and experimentally relevant quantum spin models. We prove this equivalence through the use of an exact sum rule that provides the required mixing of different orders of 1/S. Finally, we discuss some implications for several leading order-by-quantum-disorder candidate materials, clarifying the expected pseudo-Goldstone gap sizes in Er_{2}Ti_{2}O_{7} and Ca_{3}Fe_{2}Ge_{3}O_{12}.

Quantum Spin Ice with Frustrated Transverse Exchange: From a π-Flux Phase to a Nematic Quantum Spin Liquid

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalization, numerical linked-cluster and series expansions, we find that the previously studied U(1) quantum spin liquid, in its π-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.

Instabilities of a U(1) Quantum Spin Liquid in Disordered Non-Kramers Pyrochlores

Quantum spin liquids (QSLs) are exotic phases of matter exhibiting long-range entanglement and supporting emergent gauge fields. A vigorous search for experimental realizations of these states has identified several materials with properties hinting at QSL physics. A key issue in understanding these QSL candidates is often the interplay of weak disorder of the crystal structure with the spin liquid state. It has recently been pointed out that in at least one important class of candidate QSLs-pyrochlore magnets based on non-Kramers ions such as Pr^{3+} or Tb^{3+}-structural disorder can actually promote a U(1) QSL ground state. Here we set this proposal on a quantitative footing by analyzing the stability of the QSL state in the minimal model for these systems: a random transverse field Ising model. We consider two kinds of instability, which are relevant in different limits of the phase diagram: condensation of spinons and confinement of the U(1) gauge fields. Having obtained stability bounds on the QSL state, we apply our results directly to the disordered candidate QSL Pr_{2}Zr_{2}O_{7}. We find that the available data for currently studied samples of Pr_{2}Zr_{2}O_{7} are most consistent with it a ground state outside the spin liquid regime, in a paramagnetic phase with quadrupole moments near saturation due to the influence of structural disorder.

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.

Long-Range Order in the Dipolar XY Antiferromagnet Er_{2}Sn_{2}O_{7}

Er_{2}Sn_{2}O_{7} remains a puzzling case among the extensively studied frustrated compounds of the rare-earth pyrochlore family. Indeed, while a first-order transition towards a long-range antiferromagnetic state with the so-called Palmer-Chalker structure is theoretically predicted, it has not yet been observed, leaving the issue as to whether it is a spin-liquid candidate open. We report on neutron scattering and magnetization measurements which evidence a second-order transition towards this Palmer-Chalker ordered state around 108 mK. Extreme care was taken to ensure a proper thermalization of the sample, which has proved to be crucial to successfully observe the magnetic Bragg peaks. At the transition, a gap opens in the excitations, superimposed on a strong quasielastic signal. The exchange parameters, refined from a spin-wave analysis in applied magnetic field, confirm that Er_{2}Sn_{2}O_{7} is a realization of the dipolar XY pyrochlore antiferromagnet. The proximity of competing phases and the strong XY anisotropy of the Er^{3+} magnetic moment might be at the origin of enhanced fluctuations, leading to the unexpected nature of the transition, the low ordering temperature, and the observed multiscale dynamics.

Reentrant Phase Diagram of Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ Magnetic Field

We present a magnetic phase diagram of rare-earth pyrochlore Yb_{2}Ti_{2}O_{7} in a ⟨111⟩ magnetic field. Using heat capacity, magnetization, and neutron scattering data, we show an unusual field dependence of a first-order phase boundary, wherein a small applied field increases the ordering temperature. The zero-field ground state has ferromagnetic domains, while the spins polarize along ⟨111⟩ above 0.65 T. A classical Monte Carlo analysis of published Hamiltonians does account for the critical field in the low T limit. However, this analysis fails to account for the large bulge in the reentrant phase diagram, suggesting that either long-range interactions or quantum fluctuations govern low field properties.

Magnetic behavior of metallic kagome lattices, Tb3Ru4Al12 and Er3Ru4Al12

We report the magnetic behavior of two intermetallic-based kagome lattices, Tb₃Ru₄Al₁₂ and Er₃Ru₄Al₁₂, crystallizing in the Gd₃Ru₄Al₂-type hexagonal crystal structure, by measurements in the range 1.8-300 K with bulk experimental techniques (ac and dc magnetization, heat capacity, and magnetoresistance). The main finding is that the Tb compound, known to order antiferromagnetically below (T _N =) 22 K, shows glassy characteristics at lower temperatures ([Formula: see text]15 K), thus characterizing this compound as a re-entrant spin-glass. The data reveal that the glassy phase is quite complex and is of a cluster type. Since glassy behavior was not seen for the Gd analog in the past literature, this finding on the Tb compound emphasizes that this kagome family could provide an opportunity to explore the role of higher-order interactions (such as quadrupole) in bringing out magnetic frustration. Additional findings reported here for this compound are: (i) The plots of temperature dependence of magnetic susceptibility and electrical resistivity data in the range 12-20 K, just below T _N , are found to be hysteretic leading to a magnetic phase in this intermediate temperature range, mimicking disorder-broadened first-order magnetic phase transitions; (ii) features attributable to an interesting magnetic phase co-existence phenomenon in the isothermal magnetoresistance in zero field, after travelling across metamagnetic transition fields, are observed. With respect to the Er compound, we do not find any evidence for long-range magnetic ordering down to 2 K, but this compound appears to be on the verge of magnetic order at 2 K.

Quasiparticle Breakdown and Spin Hamiltonian of the Frustrated Quantum Pyrochlore Yb_{2}Ti_{2}O_{7} in a Magnetic Field

The frustrated pyrochlore magnet Yb_{2}Ti_{2}O_{7} has the remarkable property that it orders magnetically but has no propagating magnons over wide regions of the Brillouin zone. Here we use inelastic neutron scattering to follow how the spectrum evolves in cubic-axis magnetic fields. At high fields we observe, in addition to dispersive magnons, a two-magnon continuum, which grows in intensity upon reducing the field and overlaps with the one-magnon states at intermediate fields leading to strong renormalization of the dispersion relations, and magnon decays. Using heat capacity measurements we find that the low- and high-field regions are smoothly connected with no sharp phase transition, with the spin gap increasing monotonically in field. Through fits to an extensive data set of dispersion relations combined with magnetization measurements, we reevaluate the spin Hamiltonian, finding dominant quantum exchange terms, which we propose are responsible for the anomalously strong fluctuations and quasiparticle breakdown effects observed at low fields.

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.

An understanding of how quantum spin liquids arise in frustrated magnets at low temperatures remains elusive. Here the authors demonstrate a pressure-driven ferromagnetic transition out of a quantum spin liquid phase in the pyrochlore Yb₂Ti₂O₇, highlighting its proximity to a phase boundary.

Single crystal growth, structure and magnetic properties of Pr2Hf2O7 pyrochlore

Large single crystals of pyrochlore [Formula: see text] were successfully grown by the floating zone technique using an optical furnace equipped with high power xenon arc lamps. Structural investigations were carried out via powder synchrotron x-ray and neutron diffraction to establish the crystallographic structure of the materials produced. The magnetic properties of the single crystals were determined for magnetic fields applied along different crystallographic axes. The results revealed that [Formula: see text] is an interesting material for further investigation as a frustrated magnet. The high quality of the crystals produced makes them ideal for detailed investigation, especially using neutron scattering techniques.

Quantum spin liquids: a review

Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

A novel type of splayed ferromagnetic order observed in Yb2Ti2O7

The pyrochlore insulator Yb2Ti2O7 has attracted the attention of experimentalists and theoreticians alike for about 15 years. Conflicting neutron diffraction data on the possible existence of magnetic Bragg reflections at low temperature have been published. Here we report the observation of magnetic Bragg reflections by neutron powder diffraction at 60 mK. The magnetic diffraction pattern is analyzed using representation theory. We find Yb2Ti2O7 to be a splayed ferromagnet as reported for Yb2Sn2O7, a sibling compound with also dominating ferromagnetic interactions as inferred from the positive Curie-Weiss temperature. However, the configuration of the magnetic moment components perpendicular to the easy axis is of the all-in-all-out type in Yb2Ti2O7 while it is two-in-two-out in the Yb2Sn2O7. An overall experimental picture of the magnetic properties emerges.

Magnetic behavior of Gd3Ru4Al12, a layered compound with distorted kagomé net

The magnetic behavior of the compound, Gd₃Ru₄Al₁₂, which was reported about two decades ago to crystallize in a hexagonal structure (space group P6₃/mmc), has not been investigated in the past literature despite interesting structural features (that is, magnetic layers and triangular as well as kagomé-lattice features favoring frustrated magnetism) characterizing this compound. We report here the results of studies of magnetization, heat capacity and magnetoresistance in the temperature range T  =  1.8-300 K. The results establish that there is a long-range magnetic order of antiferromagnetic type below (T _N  =) 18.5 K, despite a much larger value (~80 K) of paramagnetic Curie temperature with a positive sign characteristic of ferromagnetic interaction. We attribute this to geometric frustration. The most interesting finding is that there is an additional magnetic anomaly below ~55 K before the onset of long-range order in the magnetic susceptibility data. Concurrent with this observation, the sign of isothermal change in entropy, ΔS  =  S(0)  -  S(H), where H is the externally applied magnetic field, remains positive above T _N, with a broad peak. This observation indicates the presence of ferromagnetic clusters before the onset of long-range magnetic order. Thus, this compound may serve as an example of a situation in which magnetic frustration due to geometrical reasons faces competition from such magnetic precursor effects. There is also a reversal of the sign of  -ΔS in the curves for lower final fields (H  <  30 kOe) on entering the magnetically ordered state consistent with the entrance to an antiferromagetic state. The magnetoresistance behavior is consistent with the above conclusions.

A spin-liquid with pinch-line singularities on the pyrochlore lattice

The mathematics of gauge theories lies behind many of the most profound advances in physics in the past 200 years, from Maxwell's theory of electromagnetism to Einstein's theory of general relativity. More recently it has become clear that gauge theories also emerge in condensed matter, a prime example being the spin-ice materials which host an emergent electromagnetic gauge field. In spin-ice, the underlying gauge structure is revealed by the presence of pinch-point singularities in neutron-scattering measurements. Here we report the discovery of a spin-liquid where the low-temperature physics is naturally described by the fluctuations of a tensor field with a continuous gauge freedom. This gauge structure underpins an unusual form of spin correlations, giving rise to pinch-line singularities: line-like analogues of the pinch points observed in spin-ice. Remarkably, these features may already have been observed in the pyrochlore material Tb₂Ti₂O₇.

Neutron scattering measurements of spin-ice materials contain signature pinch-point singularities, demonstrating the existence of an emergent electromagnetic gauge field. Here, the authors propose a system in which correlations manifest in pinch lines, which may have already been observed experimentally.