Probing Flat Band Physics in Spin Ice Systems via Polarized Neutron Scattering

In this Letter, we illustrate how polarized neutron scattering can be used to isolate the spin-spin correlations of modes forming flat bands in a frustrated magnetic system hosting a classical spin liquid phase. In particular, we explain why the nearest-neighbor spin ice model, whose interaction matrix has two flat bands, produces a dispersionless (i.e., "flat") response in the non-spin-flip (NSF) polarized neutron scattering channel and demonstrate that NSF scattering is a highly sensitive probe of correlations induced by weak perturbations that lift the flat band degeneracy. We use this to explain the experimentally measured dispersive (i.e., nonflat) NSF channel of the dipolar spin ice compound Ho_{2}Ti_{2}O_{7}.

Understanding Reentrance in Frustrated Magnets: The Case of the Er_{2}Sn_{2}O_{7} Pyrochlore

Reentrance, the return of a system from an ordered phase to a previously encountered less-ordered one as a controlled parameter is continuously varied, is a recurring theme found in disparate physical systems, yet its microscopic cause is often not investigated thoroughly. Here, through detailed characterization and theoretical modeling, we uncover the microscopic mechanism behind reentrance in the strongly frustrated pyrochlore antiferromagnet Er_{2}Sn_{2}O_{7}. We use single crystal heat capacity measurements to expose that Er_{2}Sn_{2}O_{7} exhibits multiple instances of reentrance in its magnetic field B vs temperature T phase diagram for magnetic fields along three cubic high symmetry directions. Through classical Monte Carlo simulations, mean field theory, and classical linear spin-wave expansions, we argue that the origins of the multiple occurrences of reentrance observed in Er_{2}Sn_{2}O_{7} are linked to soft modes. These soft modes arise from phase competition and enhance thermal fluctuations that entropically stabilize a specific ordered phase, resulting in an increased transition temperature for certain field values and thus the reentrant behavior. Our work represents a detailed examination into the mechanisms responsible for reentrance in a frustrated magnet and may serve as a template for the interpretation of reentrant phenomena in other physical systems.

Behavior of the breathing pyrochlore lattice Ba3Yb2Zn5O11 in applied magnetic field

The breathing pyrochlore lattice material Ba₃Yb₂Zn₅O₁₁ exists in the nearly decoupled limit, in contrast to most other well-studied breathing pyrochlore compounds. As a result, it constitutes a useful platform to benchmark theoretical calculations of exchange interactions in insulating Yb³⁺ magnets. Here we study Ba₃Yb₂Zn₅O₁₁ at low temperatures in applied magnetic fields as a further probe of the physics of this model system. Experimentally, we consider the behavior of polycrystalline samples of Ba₃Yb₂Zn₅O₁₁ with a combination of inelastic neutron scattering and heat capacity measurements down to 75 mK and up to fields of 10 T. Consistent with previous work, inelastic neutron scattering finds a level crossing near 3 T, but no significant dispersion of the spin excitations is detected up to the highest applied fields. Refinement of the theoretical model previously determined at zero field can reproduce much of the inelastic neutron scattering spectra and specific heat data. A notable exception is a low temperature peak in the specific heat at  ∼0.1 K. This may indicate the scale of interactions between tetrahedra or may reflect undetected disorder in Ba₃Yb₂Zn₅O₁₁.

Special temperatures in frustrated ferromagnets

The description and detection of unconventional magnetic states, such as spin liquids, is a recurring topic in condensed matter physics. While much of the efforts have traditionally been directed at geometrically frustrated antiferromagnets, recent studies reveal that systems featuring competing antiferromagnetic and ferromagnetic interactions are also promising candidate materials. We find that this competition leads to the notion of special temperatures, analogous to those of gases, at which the competing interactions balance, and the system is quasi-ideal. Although induced by weak perturbing interactions, these special temperatures are surprisingly high and constitute an accessible experimental diagnostic of eventual order or spin-liquid properties. The well characterised Hamiltonian and extended low-temperature susceptibility measurement of the canonical frustrated ferromagnet Dy₂Ti₂O₇ enables us to formulate both a phenomenological and microscopic theory of special temperatures for magnets. Other members of this class of magnets include kapellasite Cu₃Zn(OH)₆Cl₂ and the spinel GeCo₂O₄.

Competing interactions in frustrated magnets give rise to complex emergent phenomena, which challenge a full microscopic understanding but invite comparison to other systems. Bovo et al. find an analogy to classical gases and identify special temperatures that reveal fine details of the microscopic Hamiltonian.

Spin ice Thin Film: Surface Ordering, Emergent Square ice, and Strain Effects

Motivated by recent realizations of Dy_{2}Ti_{2}O_{7} and Ho_{2}Ti_{2}O_{7} spin ice thin films, and more generally by the physics of confined gauge fields, we study a model spin ice thin film with surfaces perpendicular to the [001] cubic axis. The resulting open boundaries make half of the bonds on the interfaces inequivalent. By tuning the strength of these inequivalent "orphan" bonds, dipolar interactions induce a surface ordering equivalent to a two-dimensional crystallization of magnetic surface charges. This surface ordering may also be expected on the surfaces of bulk crystals. For ultrathin films made of one cubic unit cell, once the surfaces have ordered, a square ice phase is stabilized over a finite temperature window. The square ice degeneracy is lifted at lower temperature and the system orders in analogy with the well-known F transition of the 6-vertex model. To conclude, we consider the addition of strain effects, a possible consequence of interface mismatches at the film-substrate interface. Our simulations qualitatively confirm that strain can lead to a smooth loss of Pauling entropy upon cooling, as observed in recent experiments on Dy_{2}Ti_{2}O_{7} films.

Anisotropic Exchange within Decoupled Tetrahedra in the Quantum Breathing Pyrochlore Ba_{3}Yb_{2}Zn_{5}O_{11}

The low energy spin excitation spectrum of the breathing pyrochlore Ba_{3}Yb_{2}Zn_{5}O_{11} has been investigated with inelastic neutron scattering. Several nearly resolution limited modes with no observable dispersion are observed at 250 mK while, at elevated temperatures, transitions between excited levels become visible. To gain deeper insight, a theoretical model of isolated Yb^{3+} tetrahedra parametrized by four anisotropic exchange constants is constructed. The model reproduces the inelastic neutron scattering data, specific heat, and magnetic susceptibility with high fidelity. The fitted exchange parameters reveal a Heisenberg antiferromagnet with a very large Dzyaloshinskii-Moriya interaction. Using this model, we predict the appearance of an unusual octupolar paramagnet at low temperatures and speculate on the development of intertetrahedron correlations.

Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets

The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare-earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Spin ices provide one of very few experimentally realized examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterized by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges with a mutual Coulomb interaction, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focusing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.

Vindication of Yb2Ti2O7 as a model exchange quantum spin ice

We use numerical linked-cluster expansions to compute the specific heat C(T) and entropy S(T) of a quantum spin ice Hamiltonian for Yb2Ti2O7 using anisotropic exchange interactions, recently determined from inelastic neutron scattering measurements, and find good agreement with experimental calorimetric data. This vindicates Yb2Ti2O7 as a model quantum spin ice. We find that in the perturbative weak quantum regime, such a system has a ferrimagnetic ordered ground state, with two peaks in C(T): a Schottky anomaly signaling the paramagnetic to spin ice crossover, followed at a lower temperature by a sharp peak accompanying a first-order phase transition to the ordered state. We suggest that the two C(T) features observed in Yb2Ti2O7 are associated with the same physics. Spin excitations in this regime consist of weakly confined spinon-antispinon pairs. We anticipate that the conventional ground state with exotic quantum dynamics will prove a prevalent characteristic of many real quantum spin ice materials.

Spin ice: magnetic excitations without monopole signatures using muon spin rotation

Theory predicts the low temperature magnetic excitations in spin ices consist of deconfined magnetic charges, or monopoles. A recent transverse-field (TF) muon spin rotation (μSR) experiment [S. T. Bramwell et al., Nature (London) 461, 956 (2009)] reports results claiming to be consistent with the temperature and magnetic field dependence anticipated for monopole nucleation-the so-called second Wien effect. We demonstrate via a new series of μSR experiments in Dy(2)Ti(2)O(7) that such an effect is not observable in a TF μSR experiment. Rather, as found in many highly frustrated magnetic materials, we observe spin fluctuations which become temperature independent at low temperatures, behavior which dominates over any possible signature of thermally nucleated monopole excitations.

Local susceptibility of the Yb(2)Ti(2)O(7) rare earth pyrochlore computed from a Hamiltonian with anisotropic exchange

The rare earth pyrochlore magnet Yb(2)Ti(2)O(7) is among a handful of materials that apparently exhibit no long range order down to the lowest explored temperatures and well below the Curie-Weiss temperature. Paramagnetic neutron scattering on a single crystal sample has revealed the presence of anisotropic correlations and recent work has led to the proposal of a detailed microscopic Hamiltonian for this material involving significantly anisotropic exchange. In this paper, we compute the local sublattice susceptibility of Yb(2)Ti(2)O(7) from the proposed model and compare with the measurements of Cao et al (2009 Phys. Rev. Lett. 103 056402), finding quite good agreement. In contrast, a model with only isotropic exchange and long range magnetostatic dipolar interactions gives rise to a local susceptibility that is inconsistent with the data.

Calculation of the expected zero-field muon relaxation rate in the geometrically frustrated rare earth pyrochlore Gd(2)Sn(2)O(7) antiferromagnet

The magnetic insulator Gd(2)Sn(2)O(7) is one of many geometrically frustrated magnetic materials known to exhibit a nonzero muon spin polarization relaxation rate, λ(T), down to the lowest temperature (T) studied. Such behaviour is typically interpreted as signalling the presence of persistent spin dynamics (PSD) of the host material. In the case of Gd(2)Sn(2)O(7), such PSD comes as a surprise since magnetic specific heat measurements suggest conventional gapped magnons, which would naively lead to an exponentially vanishing λ(T) as T → 0. In contrast to most materials that display PSD, the ordered phase of Gd(2)Sn(2)O(7) is well characterized and both the nature and the magnitude of the interactions have been inferred from the magnetic structure and the temperature dependence of the magnetic specific heat. Based on this understanding, the temperature dependence of the muon spin polarization relaxation through the scattering of spin waves (magnons) is calculated. The result explicitly shows that, despite the unusual extensive number of weakly dispersive (gapped) excitations characterizing Gd(2)Sn(2)O(7), a remnant of the zero modes of the parent frustrated pyrochlore Heisenberg antiferromagnet, the temperature dependence of the calculated λ(T) differs dramatically from the experimental one. Indeed, the calculation conforms to the naive expectation of an exponential collapse of λ(T) at temperatures below ∼ 0.7 K. This result, for the first time, illustrates crisply and quantitatively the paradox that presents itself with the pervasive occurrence of PSD in highly frustrated magnetic systems as evinced by muon spin relaxation measurements.

Proposal for a [111] magnetization plateau in the spin liquid state of Tb(2)Ti(2)O(7)

Despite a Curie-Weiss temperature θ(CW)∼-14 K, the Tb(2)Ti(2)O(7) pyrochlore magnetic material lacks long range magnetic order down to at least T(*)≈50 mK. It has recently been proposed that the low temperature collective paramagnetic or spin liquid regime of this material may be akin to a spin ice state subject to both thermal and quantum fluctuations-a quantum spin ice (QSI) of sorts. Here we explore the effect of a magnetic field B along the [111] direction on the QSI state. To do so, we investigate the magnetic properties of a microscopic model of Tb(2)Ti(2)O(7) in an independent tetrahedron approximation in a finite field B along [111]. Such a model describes semi-quantitatively the collective paramagnetic regime where nontrivial spin correlations start to develop at the shortest length scale, that is over a single tetrahedron, but where no long range order is yet present. Our results show that a magnetization plateau develops at low temperatures as the system develops B = 0 ferromagnetic spin ice like 'two-in/two-out' correlations at the shortest length scale. From these results, we are led to propose that the observation of such a [111] magnetization plateau in Tb(2)Ti(2)O(7) would provide compelling evidence for a QSI at B = 0 in this material and help guide the development of a theory for the origin of its spin liquid state.

Evidence for gapped spin-wave excitations in the frustrated Gd2Sn2O7 pyrochlore antiferromagnet from low-temperature specific heat measurements

We have measured the low-temperature specific heat of the geometrically frustrated pyrochlore Heisenberg antiferromagnet Gd2Sn2O7 in zero magnetic field. The specific heat is found to drop exponentially below approximately 350 mK. This provides evidence for a gapped spin-wave spectrum due to an anisotropy resulting from single-ion effects and long-range dipolar interactions. The data are well fitted by linear spin-wave theory, ruling out unconventional low-energy magnetic excitations in this system, and allowing a determination of the pertinent exchange interactions in this material.

Induced random fields in the LiHoxY1-xF4 quantum Ising magnet in a transverse magnetic field

The LiHoxY1-xF4 magnetic material in a transverse magnetic field Bx x perpendicular to the Ising spin direction has long been used to study tunable quantum phase transitions in a random disordered system. We show that the Bx-induced magnetization along the x direction, combined with the local random dilution-induced destruction of crystalline symmetries, generates, via the predominant dipolar interactions between Ho3+ ions, random fields along the Ising z direction. This identifies LiHoxY1-xF4 in Bx as a new random field Ising system. The random fields explain the rapid decrease of the critical temperature in the diluted ferromagnetic regime and the smearing of the nonlinear susceptibility at the spin-glass transition with increasing Bx and render the Bx-induced quantum criticality in LiHoxY1-xF4 likely inaccessible.

Pressure-induced crystallization of a spin liquid

Liquids are expected to crystallize at low temperature. The only exception is helium, which can remain liquid at 0 K, owing to quantum fluctuations. Similarly, the atomic magnetic moments (spins) in a magnet are expected to order at a temperature scale set by the Curie-Weiss temperature theta(CW) (ref. 3). Geometrically frustrated magnets represent an exception. In these systems, the pairwise spin interactions cannot be simultaneously minimized because of the lattice symmetry. This can stabilize a liquid-like state of short-range-ordered fluctuating moments well below theta(CW) (refs 5-7). Here we use neutron scattering to observe the spin liquid state in a geometrically frustrated system, Tb(2)Ti(2)O(7), under conditions of high pressure (approximately 9 GPa) and low temperature (approximately 1 K). This compound is a three-dimensional magnet with theta(CW) = -19 K, where the negative value indicates antiferromagnetic interactions. At ambient pressure Tb(2)Ti(2)O(7) remains in a spin liquid state down to at least 70 mK (ref. 8). But we find that, under high pressure, the spins start to order or 'crystallize' below 2.1 K, with antiferromagnetic order coexisting with liquid-like fluctuations. These results indicate that a spin liquid/solid mixture can be induced by pressure in geometrically frustrated systems.