We report inelastic neutron scattering measurements from our newly synthesized single crystals of... more We report inelastic neutron scattering measurements from our newly synthesized single crystals of the structurally metastable antiferromagnetic pyrochlore Yb 2 Ge 2 O 7. We determine the four symmetry-allowed nearest-neighbor anisotropic exchange parameters via fits to linear spin wave theory supplemented by fits of the high-temperature specific heat using the numerical linked-cluster expansion method. The exchange parameters so-determined are strongly correlated to the values determined for the g-tensor components, as previously noted for the related Yb pyrochlore Yb 2 Ti 2 O 7. To address this issue, we directly determined the g-tensor from electron paramagnetic resonance of 1% Yb-doped Lu 2 Ge 2 O 7 , thus enabling an unambiguous determination of the exchange parameters. Our results show that Yb 2 Ge 2 O 7 resides extremely close to the classical phase boundary between an antiferromagnetic Γ 5 phase and a splayed ferromagnet phase. By juxtaposing our results with recent ones on Yb 2 Ti 2 O 7 , our work illustrates that the Yb pyrochlore oxides represent ideal systems for studying quantum magnets in close proximity to classical phase boundaries.
We present a general framework for deriving effective spin Hamiltonians of correlated magnetic sy... more We present a general framework for deriving effective spin Hamiltonians of correlated magnetic systems based on a combination of relativistic ab initio density functional theory calculations (DFT), exact diagonalization of a generalized Hubbard Hamiltonian on finite clusters and spin projections onto the low-energy subspace. A key motivation is to determine anisotropic bilinear exchange couplings in materials of interest. As an example, we apply this method to the pyrochlore Lu2V2O7 where the vanadium ions form a lattice of corner-sharing spin-1/2 tetrahedra. In this compound, anisotropic Dzyaloshinskii-Moriya interactions (DMI) play an essential role in inducing a magnon Hall effect. We obtain quantitative estimates of the nearest-neighbor Heisenberg exchange, the DMI, and the symmetric part of the anisotropic exchange tensor. Finally, we compare our results with experimental ones on the Lu2V2O7 compound.
The description and detection of unconventional magnetic states, such as spin liquids, is a recur... more 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 Dy 2 Ti 2 O 7 enables us to formulate both a phenomenological and microscopic theory of special temperatures for magnets. Other members of this class of magnets include kapellasite Cu 3 Zn(OH) 6 Cl 2 and the spinel GeCo 2 O 4 .
Bulletin of the American Physical Society, Mar 14, 2016
Order-by-disorder (ObD) is a concept of central importance in the field of frustrated magnetism. ... more Order-by-disorder (ObD) is a concept of central importance in the field of frustrated magnetism. Saddled with large accidental degeneracies, a subset of states, those that support the largest quantum and/or thermal fluctuations, may be selected to form true long-range order. More formally, one often begins describing a system in terms of some order parameter m with the low-energy description framed in terms of an effective action Γ(m). In each ObD scenario, one starts from an artificial limit where there is an accidental degeneracy; that is the effective action at this point, Γ 0 (m), has an accidental symmetry. One may then view ObD phenomena as cases where the corrections to Γ 0 (m) arise through some form of fluctuation corrections, may they be thermal, quantum or virtual, towards an enlarged higher energy Hilbert space. In the rare-earth pyrochlore oxides, of formula R 2 M 2 O 7 , the trivalent magnetic rare-earth ions R 3+ (e.g R =Gd, Er, Yb; M =Ti, Sn is non-magnetic) reside on a three-dimensional pyrochlore lattice of corner-sharing tetrahedra. This architecture is prone to a high degree of magnetic frustration, with the R 2 M 2 O 7 pyrochlore materials having been found over the past twenty years to display a gamut of exotic phenomena. In this talk, I will discuss three such phenomena: (i) the intermediate partially-ordered multiple-k state between 0.7K and 1K in the Gd 2 Ti 2 O 7 Heisenberg antiferromagnet 1 , (ii) the ordered ψ 2 state selection in the XY Er 2 Ti 2 O 7 antiferromagnet 2 and (iii) the puzzling high sample sensitivity of the Yb 2 Ti 2 O 7 "quantum spin ice" candidate 3. I will argue that in all three cases, some form of fluctuation corrections to their simplest Γ 0 (m) description play a significant role in the state selection and experimentally observed behaviors.
Pinch point singularities, associated with flat band magnetic excitations, are telltale signature... more Pinch point singularities, associated with flat band magnetic excitations, are telltale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary non-analytic features-shaped as half-moons and stars-arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state from flat bands to being governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudo-fermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half-moons in its structure factor. Our work thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, He, Nat. Commun. 10, 4254 (2019)]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by star-like patterns.
Bulletin of the American Physical Society, Mar 15, 2016
Neutron scattering is a sensitive probe of correlations in condensed matter physics, and measurem... more Neutron scattering is a sensitive probe of correlations in condensed matter physics, and measurements of spin correlations by diffuse neutron scattering is one of the foremost methods of constraining the Hamiltonian of spin ice materials such as Dy 2 Ti 2 O 7. Recent investigations of spin ices have highlighted the possibility of very slow equilibration at low temperature and/or structural defects in samples, effects which were not taken into account in the original parametrizations of the Hamiltonian. Hence, we have in this study performed a new set of diffuse magnetic neutron scattering experiments on an oxygen-annealed single crystal of the spin ice 162 Dy 2 Ti 2 O 7. Compensation coils and an in-situ AC-susceptometer were used to control the zero magnetic field at the sample position as well as determining the thermal equilibrium of the magnetic spins respectively. In addition, we performed large-scale Monte Carlo simulations as to make a statistical fit of the dipolar spin ice model to the measured structure factor in the temperature range [0.65, 2] K, where the spin ice physics starts to develop. This will enable a most carefully controlled determination of the Hamiltonian of Dy 2 Ti 2 O 7 .
The demagnetizing factor N is of both conceptual interest and practical importance. Considering l... more The demagnetizing factor N is of both conceptual interest and practical importance. Considering localized magnetic moments on a lattice, we show that for non-ellipsoidal samples, N depends on the spin dimensionality (Ising, XY, or Heisenberg) and orientation, as well as the sample shape and susceptibility. The generality of this result is demonstrated by means of a recursive analytic calculation as well as detailed Monte Carlo simulations of realistic model spin Hamiltonians. As an important check and application, we also make an accurate experimental determination of N for a representative collective paramagnet (i.e. the Dy2Ti2O7 spin ice compound) and show that the temperature dependence of the experimentally determined N agrees closely with our theoretical calculations. Our conclusion is that the well established practice of approximating the true sample shape with "corresponding ellipsoids" for systems with long-range interactions will in many cases overlook important effects stemming from the microscopic aspects of the system under consideration.
Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferro... more Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferromagnet, we study the problem of quantum order-by-disorder in pyrochlore XY systems. We consider the most general nearest-neighbor pseudo spin-1/2 Hamiltonian for such a system characterized by anisotropic spin-spin couplings Je ≡{J±, J±±, Jz±, Jzz} and construct zero-temperature phase diagrams. Combining symmetry arguments and spin-wave calculations, we show that the ground state phase boundaries between the two candidate ground states of the Γ5 irreducible representation, the ψ2 and ψ3 (basis) states, are rather accurately determined by a cubic equation in (J±J±±)/J 2 z±. Depending on the value of Jzz, there can be one or three phase boundaries that separate alternating regions of ψ2 and ψ3 states. In particular, we find for sufficiently small Jzz/J± a narrow ψ2 sliver sandwiched between two ψ3 regions in the J±±/J± vs Jz±/J± phase diagram. From our results, one would be able to predict which state (ψ2 or ψ3) may be realized in a real material given its set of Je couplings. Our results further illustrate the very large potential sensitivity of the ground state of XY pyrochlore systems to minute changes in their spin Hamiltonian. Finally, using the experimentally determined Je ≡{J±, J±±, Jz±, Jzz} and g-tensor values for Er2Ti2O7, we show that the heretofore neglected long-range 1/r 3 magnetostatic dipole-dipole interactions do not change the conclusion that Er2Ti2O7 has a ψ2 ground state induced via a quantum order-by-disorder mechanism. As a new avenue of research in XY pyrochlore materials distinct from the rare-earth pyrochlore oxides, we propose that the Cd2Dy2Se4 chalcogenide spinel, in which the Dy 3+ ions form a pyrochlore lattice and may be XY-like, could prove interesting to investigate.
Bulletin of the American Physical Society, Mar 3, 2015
The magnetic susceptibility of a spin ice material is a sensitive probe of the relevant physics i... more The magnetic susceptibility of a spin ice material is a sensitive probe of the relevant physics in different temperature ranges. At high temperatures, where crystal field excitations dominate the susceptibility, the spin ice picture is not applicable. However, at temperatures below 10 K, the Ising anisotropy is well developed and the dipolar spin ice model (DSIM) can be employed. In this study we present experimental susceptibility data between 0.4 K and 10 K and revisit the DSIM in order to theoretically model this data. We find that the DSIM provides a good semi-quantitative description of both the temperature dependence of the uniform bulk susceptibility and the Q-dependent susceptibility measured by neutron scattering.
Bulletin of the American Physical Society, Mar 23, 2005
The antiferromagnetic pyrochlore Tb 2 Ti 2 O 7 presents a challenging puzzle to experimentalists ... more The antiferromagnetic pyrochlore Tb 2 Ti 2 O 7 presents a challenging puzzle to experimentalists and theorists studying frustrated magnets. Results from muon spin resonance and neutron scattering experiments for Tb 2 Ti 2 O 7 reveal a paramagnetic structure down to 50mK despite an antiferromagnetic Curie-Weiss temperature, θ CW = −20K. Crystal field calculations show that the Tb 3+ ion in Tb 2 Ti 2 O 7 is a ground state doublet with local ⟨111⟩ anisotropy and is separated from the first excited doublet state by a gap of 20K. To understand the quantum nature of Tb 2 Ti 2 O 7 , we apply the Rayleigh-Schrodinger method to map the four state problem with exchange and dipole-dipole interactions onto an effective Hamiltonian with two states per ion. We give some properties of this effective hamiltonian and compare the neutron scattering results with the experimental data.
is exceptional among breathing pyrochlore compounds for being in the nearly-decoupled limit where... more is exceptional among breathing pyrochlore compounds for being in the nearly-decoupled limit where intertetrahedron interactions are weak, hosting isolated clusters or molecular magnet-like tetrahedra of magnetic ytterbium (Yb 3+) ions. In this work, we present the study carried out on single-crystal samples of the breathing pyrochlore Ba 3 Yb 2 Zn 5 O 11 , using a variety of magnetometry and neutron scattering techniques along with theoretical modeling. We employ inelastic neutron scattering to investigate the magnetic dynamics as a function of applied field (with respect to both magnitude and direction) down to a temperature of 70 mK, where inelastic scattering reveals dispersionless bands of excitations as found in earlier powder sample studies, in good agreement with a single-tetrahedron model. However, diffuse neutron scattering at zero field and dc-susceptibility at finite field exhibit features suggesting the presence of excitations at low-energy that are not captured by the single tetrahedron model. Analysis of the local structure down to 2 K via pair distribution function analysis finds no evidence of structural disorder. We conclude that effects beyond the single tetrahedron model are important in describing the low-energy, low-temperature physics of Ba 3 Yb 2 Zn 5 O 11 , but their nature remains undetermined.
We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interacti... more We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interaction in the semiclassical limit. The classical ground state manifold of the model contains an extensively large family of non-coplanar spin states known as "color ice states". Starting from a color ice state, a subset of spins may rotate collectively at no energy cost. Such excitation may be viewed in this three-dimensional system as a "membrane-like" analog of the well-known weathervane modes in the classical kagome Heisenberg antiferromagnet. We investigate the weathervane modes in detail and elucidate their physical properties. Furthermore, we study the order by disorder phenomenon in this model, focusing on the role of harmonic fluctuations. Our computationally-limited phase space search suggests that quantum fluctuations select three different states as the magnitude of the biquadratic interaction increases relative to the bilinear interaction, implying a sequence of phase transitions solely driven by fluctuations.
Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the stronges... more Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er 2 Ti 2 O 7 , with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er 2 Ti 2 O 7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed ψ 2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets.
Reentrance, the return of a system from an ordered phase to a previously encountered less-ordered... more 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, from condensed matter to black holes. While diverse in its many incarnations and generally unsuspected, the cause of reentrance at the microscopic level 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 Er2Sn2O7. Taking advantage of the recent advance in rare earth stannate single crystal synthesis, we use heat capacity measurements to expose that Er2Sn2O7 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 Er2Sn2O7 are linked to soft modes. Depending on the field direction, these arise either from a direct T = 0 competition between the field-evolved ground states, or from a field-induced enhancement of the competition with a distinct zero-field antiferromagnetic phase. In both scenarios, the phase competition enhances thermal fluctuations which entropically stabilize a specific ordered phase. This results 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.
We consider a system of spins on the sites of a three-dimensional pyrochlore lattice of corner-sh... more We consider a system of spins on the sites of a three-dimensional pyrochlore lattice of corner-sharing tetrahedra interacting with a predominant effective xy exchange. In particular, we investigate the selection of a long-range ordered state with broken discrete symmetry induced by thermal fluctuations near the critical region. At the standard mean-field theory (s-MFT) level, in a region of the parameter space of this Hamiltonian that we refer to as Γ5 region, the ordered state possesses an accidental U (1) degeneracy. In this paper, we show that fluctuations beyond s-MFT lift this degeneracy by selecting one of two states (so-called ψ2 and ψ3) from the degenerate manifold, thus exposing a certain form of order-by-disorder (ObD). We analytically explore this selection at the microscopic level and close to criticality by elaborating upon and using an extension of the socalled TAP method, originally developed by Thouless, Anderson and Palmer to study the effect of fluctuations in spin glasses. We also use a single-tetrahedron cluster-mean-field theory (c-MFT) to explore over what minimal length scale fluctuations can lift the degeneracy. We find the phase diagrams obtained by these two methods to be somewhat different since c-MFT only includes the shortest-range fluctuations. General symmetry arguments used to construct a Ginzburg-Landau theory to lowest order in the order parameters predict that a weak magnetic moment, mz, along the local 111 (ẑ) direction is generically induced for a system ordering into a ψ2 state, but not so for ψ3 ordering. Both E-TAP and c-MFT calculations confirm this weak fluctuation-induced mz moment. Using a Ginzburg-Landau theory, we discuss the phenomenology of multiple phase transitions below the paramagnetic phase transition and within the Γ5 long-range ordered phase.
Journal of Physics: Condensed Matter, Oct 16, 2004
We present a detailed theoretical overview of the thermodynamic properties of the dipolar spin ic... more We present a detailed theoretical overview of the thermodynamic properties of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy2Ti2O7 and Ho2Ti2O7. We show that the dipolar spin ice model can reproduce an effective quasi macroscopically degenerate ground state and spin-ice behavior of these materials when the long-range nature of dipole-dipole interaction is handled carefully using Ewald summation techniques. This degeneracy is, however, ultimately lifted at low temperature. The long-range ordered state is identified via mean field theory and Monte Carlo simulation techniques. Finally, we investigate the behavior of the dipolar spin ice model in an applied magnetic field, and compare our predictions with experimental results. We find that a number of different long-range ordered states are favored by the model depending on field direction.
Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualit... more Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the spin ice model proposed by Harris et al. Phys. Rev. Lett. 79, 2554 (1997). We discuss the dipolar energy scale present in both these materials and consider how they can display spin ice behavior despite the presence of long range interactions. Specifically, we present numerical simulations and a mean field analysis of pyrochlore Ising systems in the presence of nearest neighbor exchange and long range dipolar interactions. We find that two possible phases can occur, a long range ordered antiferromagnetic one and the other dominated by spin ice features. Our quantitative theory is in very good agreement with experimental data on both Ho2Ti2O7 and Dy2Ti2O7. We suggest that the nearest neighbor exchange in Dy2Ti2O7 is antiferromagnetic and that spin ice behavior is induced by long range dipolar interactions.
We report inelastic neutron scattering measurements from our newly synthesized single crystals of... more We report inelastic neutron scattering measurements from our newly synthesized single crystals of the structurally metastable antiferromagnetic pyrochlore Yb 2 Ge 2 O 7. We determine the four symmetry-allowed nearest-neighbor anisotropic exchange parameters via fits to linear spin wave theory supplemented by fits of the high-temperature specific heat using the numerical linked-cluster expansion method. The exchange parameters so-determined are strongly correlated to the values determined for the g-tensor components, as previously noted for the related Yb pyrochlore Yb 2 Ti 2 O 7. To address this issue, we directly determined the g-tensor from electron paramagnetic resonance of 1% Yb-doped Lu 2 Ge 2 O 7 , thus enabling an unambiguous determination of the exchange parameters. Our results show that Yb 2 Ge 2 O 7 resides extremely close to the classical phase boundary between an antiferromagnetic Γ 5 phase and a splayed ferromagnet phase. By juxtaposing our results with recent ones on Yb 2 Ti 2 O 7 , our work illustrates that the Yb pyrochlore oxides represent ideal systems for studying quantum magnets in close proximity to classical phase boundaries.
We present a general framework for deriving effective spin Hamiltonians of correlated magnetic sy... more We present a general framework for deriving effective spin Hamiltonians of correlated magnetic systems based on a combination of relativistic ab initio density functional theory calculations (DFT), exact diagonalization of a generalized Hubbard Hamiltonian on finite clusters and spin projections onto the low-energy subspace. A key motivation is to determine anisotropic bilinear exchange couplings in materials of interest. As an example, we apply this method to the pyrochlore Lu2V2O7 where the vanadium ions form a lattice of corner-sharing spin-1/2 tetrahedra. In this compound, anisotropic Dzyaloshinskii-Moriya interactions (DMI) play an essential role in inducing a magnon Hall effect. We obtain quantitative estimates of the nearest-neighbor Heisenberg exchange, the DMI, and the symmetric part of the anisotropic exchange tensor. Finally, we compare our results with experimental ones on the Lu2V2O7 compound.
The description and detection of unconventional magnetic states, such as spin liquids, is a recur... more 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 Dy 2 Ti 2 O 7 enables us to formulate both a phenomenological and microscopic theory of special temperatures for magnets. Other members of this class of magnets include kapellasite Cu 3 Zn(OH) 6 Cl 2 and the spinel GeCo 2 O 4 .
Bulletin of the American Physical Society, Mar 14, 2016
Order-by-disorder (ObD) is a concept of central importance in the field of frustrated magnetism. ... more Order-by-disorder (ObD) is a concept of central importance in the field of frustrated magnetism. Saddled with large accidental degeneracies, a subset of states, those that support the largest quantum and/or thermal fluctuations, may be selected to form true long-range order. More formally, one often begins describing a system in terms of some order parameter m with the low-energy description framed in terms of an effective action Γ(m). In each ObD scenario, one starts from an artificial limit where there is an accidental degeneracy; that is the effective action at this point, Γ 0 (m), has an accidental symmetry. One may then view ObD phenomena as cases where the corrections to Γ 0 (m) arise through some form of fluctuation corrections, may they be thermal, quantum or virtual, towards an enlarged higher energy Hilbert space. In the rare-earth pyrochlore oxides, of formula R 2 M 2 O 7 , the trivalent magnetic rare-earth ions R 3+ (e.g R =Gd, Er, Yb; M =Ti, Sn is non-magnetic) reside on a three-dimensional pyrochlore lattice of corner-sharing tetrahedra. This architecture is prone to a high degree of magnetic frustration, with the R 2 M 2 O 7 pyrochlore materials having been found over the past twenty years to display a gamut of exotic phenomena. In this talk, I will discuss three such phenomena: (i) the intermediate partially-ordered multiple-k state between 0.7K and 1K in the Gd 2 Ti 2 O 7 Heisenberg antiferromagnet 1 , (ii) the ordered ψ 2 state selection in the XY Er 2 Ti 2 O 7 antiferromagnet 2 and (iii) the puzzling high sample sensitivity of the Yb 2 Ti 2 O 7 "quantum spin ice" candidate 3. I will argue that in all three cases, some form of fluctuation corrections to their simplest Γ 0 (m) description play a significant role in the state selection and experimentally observed behaviors.
Pinch point singularities, associated with flat band magnetic excitations, are telltale signature... more Pinch point singularities, associated with flat band magnetic excitations, are telltale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary non-analytic features-shaped as half-moons and stars-arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state from flat bands to being governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudo-fermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half-moons in its structure factor. Our work thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, He, Nat. Commun. 10, 4254 (2019)]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by star-like patterns.
Bulletin of the American Physical Society, Mar 15, 2016
Neutron scattering is a sensitive probe of correlations in condensed matter physics, and measurem... more Neutron scattering is a sensitive probe of correlations in condensed matter physics, and measurements of spin correlations by diffuse neutron scattering is one of the foremost methods of constraining the Hamiltonian of spin ice materials such as Dy 2 Ti 2 O 7. Recent investigations of spin ices have highlighted the possibility of very slow equilibration at low temperature and/or structural defects in samples, effects which were not taken into account in the original parametrizations of the Hamiltonian. Hence, we have in this study performed a new set of diffuse magnetic neutron scattering experiments on an oxygen-annealed single crystal of the spin ice 162 Dy 2 Ti 2 O 7. Compensation coils and an in-situ AC-susceptometer were used to control the zero magnetic field at the sample position as well as determining the thermal equilibrium of the magnetic spins respectively. In addition, we performed large-scale Monte Carlo simulations as to make a statistical fit of the dipolar spin ice model to the measured structure factor in the temperature range [0.65, 2] K, where the spin ice physics starts to develop. This will enable a most carefully controlled determination of the Hamiltonian of Dy 2 Ti 2 O 7 .
The demagnetizing factor N is of both conceptual interest and practical importance. Considering l... more The demagnetizing factor N is of both conceptual interest and practical importance. Considering localized magnetic moments on a lattice, we show that for non-ellipsoidal samples, N depends on the spin dimensionality (Ising, XY, or Heisenberg) and orientation, as well as the sample shape and susceptibility. The generality of this result is demonstrated by means of a recursive analytic calculation as well as detailed Monte Carlo simulations of realistic model spin Hamiltonians. As an important check and application, we also make an accurate experimental determination of N for a representative collective paramagnet (i.e. the Dy2Ti2O7 spin ice compound) and show that the temperature dependence of the experimentally determined N agrees closely with our theoretical calculations. Our conclusion is that the well established practice of approximating the true sample shape with "corresponding ellipsoids" for systems with long-range interactions will in many cases overlook important effects stemming from the microscopic aspects of the system under consideration.
Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferro... more Motivated by recent experimental and theoretical progress on the Er2Ti2O7 pyrochlore XY antiferromagnet, we study the problem of quantum order-by-disorder in pyrochlore XY systems. We consider the most general nearest-neighbor pseudo spin-1/2 Hamiltonian for such a system characterized by anisotropic spin-spin couplings Je ≡{J±, J±±, Jz±, Jzz} and construct zero-temperature phase diagrams. Combining symmetry arguments and spin-wave calculations, we show that the ground state phase boundaries between the two candidate ground states of the Γ5 irreducible representation, the ψ2 and ψ3 (basis) states, are rather accurately determined by a cubic equation in (J±J±±)/J 2 z±. Depending on the value of Jzz, there can be one or three phase boundaries that separate alternating regions of ψ2 and ψ3 states. In particular, we find for sufficiently small Jzz/J± a narrow ψ2 sliver sandwiched between two ψ3 regions in the J±±/J± vs Jz±/J± phase diagram. From our results, one would be able to predict which state (ψ2 or ψ3) may be realized in a real material given its set of Je couplings. Our results further illustrate the very large potential sensitivity of the ground state of XY pyrochlore systems to minute changes in their spin Hamiltonian. Finally, using the experimentally determined Je ≡{J±, J±±, Jz±, Jzz} and g-tensor values for Er2Ti2O7, we show that the heretofore neglected long-range 1/r 3 magnetostatic dipole-dipole interactions do not change the conclusion that Er2Ti2O7 has a ψ2 ground state induced via a quantum order-by-disorder mechanism. As a new avenue of research in XY pyrochlore materials distinct from the rare-earth pyrochlore oxides, we propose that the Cd2Dy2Se4 chalcogenide spinel, in which the Dy 3+ ions form a pyrochlore lattice and may be XY-like, could prove interesting to investigate.
Bulletin of the American Physical Society, Mar 3, 2015
The magnetic susceptibility of a spin ice material is a sensitive probe of the relevant physics i... more The magnetic susceptibility of a spin ice material is a sensitive probe of the relevant physics in different temperature ranges. At high temperatures, where crystal field excitations dominate the susceptibility, the spin ice picture is not applicable. However, at temperatures below 10 K, the Ising anisotropy is well developed and the dipolar spin ice model (DSIM) can be employed. In this study we present experimental susceptibility data between 0.4 K and 10 K and revisit the DSIM in order to theoretically model this data. We find that the DSIM provides a good semi-quantitative description of both the temperature dependence of the uniform bulk susceptibility and the Q-dependent susceptibility measured by neutron scattering.
Bulletin of the American Physical Society, Mar 23, 2005
The antiferromagnetic pyrochlore Tb 2 Ti 2 O 7 presents a challenging puzzle to experimentalists ... more The antiferromagnetic pyrochlore Tb 2 Ti 2 O 7 presents a challenging puzzle to experimentalists and theorists studying frustrated magnets. Results from muon spin resonance and neutron scattering experiments for Tb 2 Ti 2 O 7 reveal a paramagnetic structure down to 50mK despite an antiferromagnetic Curie-Weiss temperature, θ CW = −20K. Crystal field calculations show that the Tb 3+ ion in Tb 2 Ti 2 O 7 is a ground state doublet with local ⟨111⟩ anisotropy and is separated from the first excited doublet state by a gap of 20K. To understand the quantum nature of Tb 2 Ti 2 O 7 , we apply the Rayleigh-Schrodinger method to map the four state problem with exchange and dipole-dipole interactions onto an effective Hamiltonian with two states per ion. We give some properties of this effective hamiltonian and compare the neutron scattering results with the experimental data.
is exceptional among breathing pyrochlore compounds for being in the nearly-decoupled limit where... more is exceptional among breathing pyrochlore compounds for being in the nearly-decoupled limit where intertetrahedron interactions are weak, hosting isolated clusters or molecular magnet-like tetrahedra of magnetic ytterbium (Yb 3+) ions. In this work, we present the study carried out on single-crystal samples of the breathing pyrochlore Ba 3 Yb 2 Zn 5 O 11 , using a variety of magnetometry and neutron scattering techniques along with theoretical modeling. We employ inelastic neutron scattering to investigate the magnetic dynamics as a function of applied field (with respect to both magnitude and direction) down to a temperature of 70 mK, where inelastic scattering reveals dispersionless bands of excitations as found in earlier powder sample studies, in good agreement with a single-tetrahedron model. However, diffuse neutron scattering at zero field and dc-susceptibility at finite field exhibit features suggesting the presence of excitations at low-energy that are not captured by the single tetrahedron model. Analysis of the local structure down to 2 K via pair distribution function analysis finds no evidence of structural disorder. We conclude that effects beyond the single tetrahedron model are important in describing the low-energy, low-temperature physics of Ba 3 Yb 2 Zn 5 O 11 , but their nature remains undetermined.
We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interacti... more We study the pyrochlore Heisenberg antiferromagnet with additional positive biquadratic interaction in the semiclassical limit. The classical ground state manifold of the model contains an extensively large family of non-coplanar spin states known as "color ice states". Starting from a color ice state, a subset of spins may rotate collectively at no energy cost. Such excitation may be viewed in this three-dimensional system as a "membrane-like" analog of the well-known weathervane modes in the classical kagome Heisenberg antiferromagnet. We investigate the weathervane modes in detail and elucidate their physical properties. Furthermore, we study the order by disorder phenomenon in this model, focusing on the role of harmonic fluctuations. Our computationally-limited phase space search suggests that quantum fluctuations select three different states as the magnitude of the biquadratic interaction increases relative to the bilinear interaction, implying a sequence of phase transitions solely driven by fluctuations.
Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the stronges... more Conclusive evidence of order by disorder is scarce in real materials. Perhaps one of the strongest cases presented has been for the pyrochlore XY antiferromagnet Er 2 Ti 2 O 7 , with the ground state selection proceeding by order by disorder induced through the effects of quantum fluctuations. This identification assumes the smallness of the effect of virtual crystal field fluctuations that could provide an alternative route to picking the ground state. Here we show that this order by virtual crystal field fluctuations is not only significant, but competitive with the effects of quantum fluctuations. Further, we argue that higher-multipolar interactions that are generically present in rare-earth magnets can dramatically enhance this effect. From a simplified bilinear-biquadratic model of these multipolar interactions, we show how the virtual crystal field fluctuations manifest in Er 2 Ti 2 O 7 using a combination of strong coupling perturbation theory and the random phase approximation. We find that the experimentally observed ψ 2 state is indeed selected and the experimentally measured excitation gap can be reproduced when the bilinear and biquadratic couplings are comparable while maintaining agreement with the entire experimental spin-wave excitation spectrum. Finally, we comments on possible tests of this scenario and discuss implications for other order-by-disorder candidates in rare-earth magnets.
Reentrance, the return of a system from an ordered phase to a previously encountered less-ordered... more 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, from condensed matter to black holes. While diverse in its many incarnations and generally unsuspected, the cause of reentrance at the microscopic level 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 Er2Sn2O7. Taking advantage of the recent advance in rare earth stannate single crystal synthesis, we use heat capacity measurements to expose that Er2Sn2O7 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 Er2Sn2O7 are linked to soft modes. Depending on the field direction, these arise either from a direct T = 0 competition between the field-evolved ground states, or from a field-induced enhancement of the competition with a distinct zero-field antiferromagnetic phase. In both scenarios, the phase competition enhances thermal fluctuations which entropically stabilize a specific ordered phase. This results 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.
We consider a system of spins on the sites of a three-dimensional pyrochlore lattice of corner-sh... more We consider a system of spins on the sites of a three-dimensional pyrochlore lattice of corner-sharing tetrahedra interacting with a predominant effective xy exchange. In particular, we investigate the selection of a long-range ordered state with broken discrete symmetry induced by thermal fluctuations near the critical region. At the standard mean-field theory (s-MFT) level, in a region of the parameter space of this Hamiltonian that we refer to as Γ5 region, the ordered state possesses an accidental U (1) degeneracy. In this paper, we show that fluctuations beyond s-MFT lift this degeneracy by selecting one of two states (so-called ψ2 and ψ3) from the degenerate manifold, thus exposing a certain form of order-by-disorder (ObD). We analytically explore this selection at the microscopic level and close to criticality by elaborating upon and using an extension of the socalled TAP method, originally developed by Thouless, Anderson and Palmer to study the effect of fluctuations in spin glasses. We also use a single-tetrahedron cluster-mean-field theory (c-MFT) to explore over what minimal length scale fluctuations can lift the degeneracy. We find the phase diagrams obtained by these two methods to be somewhat different since c-MFT only includes the shortest-range fluctuations. General symmetry arguments used to construct a Ginzburg-Landau theory to lowest order in the order parameters predict that a weak magnetic moment, mz, along the local 111 (ẑ) direction is generically induced for a system ordering into a ψ2 state, but not so for ψ3 ordering. Both E-TAP and c-MFT calculations confirm this weak fluctuation-induced mz moment. Using a Ginzburg-Landau theory, we discuss the phenomenology of multiple phase transitions below the paramagnetic phase transition and within the Γ5 long-range ordered phase.
Journal of Physics: Condensed Matter, Oct 16, 2004
We present a detailed theoretical overview of the thermodynamic properties of the dipolar spin ic... more We present a detailed theoretical overview of the thermodynamic properties of the dipolar spin ice model, which has been shown to be an excellent quantitative descriptor of the Ising pyrochlore materials Dy2Ti2O7 and Ho2Ti2O7. We show that the dipolar spin ice model can reproduce an effective quasi macroscopically degenerate ground state and spin-ice behavior of these materials when the long-range nature of dipole-dipole interaction is handled carefully using Ewald summation techniques. This degeneracy is, however, ultimately lifted at low temperature. The long-range ordered state is identified via mean field theory and Monte Carlo simulation techniques. Finally, we investigate the behavior of the dipolar spin ice model in an applied magnetic field, and compare our predictions with experimental results. We find that a number of different long-range ordered states are favored by the model depending on field direction.
Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualit... more Recent experiments suggest that the Ising pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 display qualitative properties of the spin ice model proposed by Harris et al. Phys. Rev. Lett. 79, 2554 (1997). We discuss the dipolar energy scale present in both these materials and consider how they can display spin ice behavior despite the presence of long range interactions. Specifically, we present numerical simulations and a mean field analysis of pyrochlore Ising systems in the presence of nearest neighbor exchange and long range dipolar interactions. We find that two possible phases can occur, a long range ordered antiferromagnetic one and the other dominated by spin ice features. Our quantitative theory is in very good agreement with experimental data on both Ho2Ti2O7 and Dy2Ti2O7. We suggest that the nearest neighbor exchange in Dy2Ti2O7 is antiferromagnetic and that spin ice behavior is induced by long range dipolar interactions.
Uploads
Papers by Michel Gingras