Session L39: Pyrochlore Systems

Live

Pyrochlore iridates are a class of materials in which the confluence of electronic interactions and emergent topology leads to a plethora of exotic states of matter. In this work, we focus on an effective low-energy Luttinger model accounting for a quadratic band touching (QBT) around the Γ point, and study interaction-induced instabilities of the QBT. In particular, we analyze the impact of a new type of magnetic order transforming under the T_2u irreducible representation of the cubic point group. This magnetic order is of octupolar character. It breaks time-reversal symmetry but is inversion-invariant, and thus for example stabilized quadrupoles of Weyl points on different planes in the Brillouin zone. We detail the regime of critical couplings for which the T_2u order can occur in the phase diagram, and conclude with a discussion of possible experimental verifications.   

Live

We present a comprehensive neutron scattering study of the breathing pyrochlore magnet LiGaCr₄S₈ [1]. We observe an unconventional magnetic excitation spectrum with a separation of high- and low-energy spin dynamics above a spin-freezing transition at 12(2) K. By fitting to magnetic diffuse-scattering data, we parametrize the spin Hamiltonian. Interactions are ferromagnetic within tetrahedra of the breathing pyrochlore lattice, but antiferromagnetic further-neighbor interactions are also essential to explain our data, in qualitative agreement with density-functional-theory predictions [2]. We explain the origin of geometrical frustration in LiGaCr₄S₈ in terms of net antiferromagnetic coupling between emergent tetrahedral spin clusters that occupy a face-centered-cubic lattice. Our results provide insight into the emergence of frustration in the presence of strong further-neighbor couplings, and a blueprint for determining magnetic interactions in classical spin liquids.
[1] Pokharel et al., Phys. Rev. Lett. 125, 167201 (2020).
[2] Ghosh et al., npj Quantum Mater. 4, 63 (2019).   

Live

Breathing pyrochlore systems are composed of corner-sharing tetrahedra of different sizes pointing in opposing directions, leading to different intra- and inter-tetrahedra exchange interactions and the emergence of the Dzyaloshinskii-Moriya interaction due to loss of inversion symmetry. They are predicted to host exotic physics including quantum spin ice, quantum spin liquid, and field-tunable Weyl magnons. In this talk we will present single-crystal field-dependent neutron scattering measurements as well as heat capacity, ultra-sensitive magnetic susceptibility, thermal conductivity, and µSR measurements on Yb-based breathing pyrochlore system, Ba₃Yb₂Zn₅O₁₁. We will also present a theoretical model that can effectively describe some of our experimental findings.   

Live

Breathing Pyrochlore materials have emerged as a promising candidate to study frustrated
magnetism and topological phenomena, such as Weyl and Dirac magnons. We have initiated
design and synthesis of rare-earth based family of Breathing Pyrochlore compounds. Further,
we have been using magnetometry, heat capacity, neutron diffraction and inelastic neutron
scattering techniques to probe the static and dynamic properties of these compounds. In this
talk, we are going to present our latest experimental results for the Tm-based breathing
pyrochlore compound Ba3Tm2Zn5O11.   

Live

A quantum spin liquid (QSL) is an exotic state of matter where unpaired electrons’ spins, although being entangled, do not show magnetic order even at the zero-temperature. Because such a state may be important to the microscopic origin of high-transition temperature superconductivity and useful for quantum computation, the experimental realization of QSL is a long-sought goal in condensed matter physics. Previous neutron scattering experiments on the two-dimensional QSL candidates ZnCu₃(OD)₆Cl₂ and YbMgGaO₄ have found evidence for the hallmark of a QSL at very low temperature - a continuum of magnetic excitations. However, the presence of site disorder complicates the interpretation of the data. Recently, the three-dimensional (3D) Ce³⁺ pyrochlore lattice Ce₂Sn₂O₇ has been suggested as a clean, effective spin-1/2 QSL candidate, but the evidence of a spin excitation continuum is missing due to the lack of single crystals. Until 2019, the first single-crystal study of Ce₂Zr₂O₇, a compound isostructural to Ce₂Sn₂O7, reveals the absence of magnetic ordering/spin-glass down to 20 mK and the presence of a spin excitation continuum at 35 mK. With no evidence of oxygen deficiency and chemical disorder seen by diffuse scattering measurements and neutron diffraction, Ce₂Zr₂O₇ may be a 3D pyrochlore lattice QSL material with minimum magnetic and nonmagnetic chemical disorder. Recent works including elastic and inelastic neutron scattering measurements under magnetic fields, as well as diffusive scattering in Ce₂Zr₂O₇ in large Q ranges, may help identify the system as an octupolar U(1) QSL.   

Live

Recent neutron scattering measurements on the three-dimensional pyrochlore magnet Ce2Zr2O7 have revealed compelling signatures of quantum spin liquid behavior. This strongly spin-orbit coupled system is composed of interacting ground state doublets of cerium (J=5/2 mJ = ± 3/2), with dipole - octupole character with local Ising anisotropy. While it can be modelled as interacting effective pseudospin-1/2 degrees of freedom, the strengths of the interaction parameters of its spin Hamiltonian remain unknown. To address this issue, we perform extensive fits of this model to experimentally measured magnetization profiles (along [100] and [111]) and specific heat measurements (in zero and finite field) computed with the finite temperature Lanczos method. We assess the importance of quantum mechanical effects and explore the possibility of the existence of spin ice physics in this material. Using the obtained parameters, we perform classical Monte Carlo, Gaussian approximation, and Landau-Lifshitz dynamical calculations and compare them to the experimentally observed static and dynamic spin structure factor.   

Live

The pyrochlore magnet Tb₂Ti₂O₇ shows a lack of magnetic order to low temperatures and is considered to be a quantum spin liquid candidate. We perform time-domain THz spectroscopy on high quality Tb₂Ti₂O₇ crystal and study the low energy excitations as a function of [111] magnetic field with high energy resolution. The low energy crystal field excitations change their energies anomalously under magnetic field. Despite several sharp field dependent changes, we show that the material’s spectrum can be described not by a phase transitions, but by field dependent hybridization between the low energy crystal field levels. We highlight the strong coupling between spin and lattice degrees of freedom in Tb₂Ti₂O₇ as evidenced by the magnetic field tunable crystal field environment. Calculations based on single ion physics with field induced symmetry reduction of the crystal field environment can reproduce our data.   

Live

Pyrochlore compounds exhibit a variety of exotic magnetic properties due to the lattice structure which can foster frustration. Particularly interesting among them is Yb₂Ti₂O₇, which orders ferromagnetically with a first-order transition. We have measured the specific heat and magnetization of Yb₂Ti₂O₇ in magnetic fields along the [100] and [110] directions. At zero field, the specific heat exhibits a sharp peak at T_c = 0.21 K, indicative of a transition to an ordered phase. The H-vs-T phase boundary for H ‖ [110] has an unusual shape, shifting to low temperatures with increasing field, similar to that reported for H ‖ [111]. Our classical Monte Carlo simulations reveal that a first-order transition occurs at 0.27 K, in good agreement with experiment, whereas the mean-field calculation yields T_c = 3.0 K, very close to the temperature of a broad hump in the specific heat. Exact calculations at T = 0 and simulations show that the magnetic ground state of Yb₂Ti₂O₇ is a simple collinear ferromagnet with negligible canting, although the spins form a “two-in-two-out” canted ferromagnetic structure with a canting angle of 19°. The transition becomes continuous in a [110] field, whereas it remains first order in [111] fields down to T = 0.   

Live

The vast majority of materials expand when heated. However, some like water ice, elastic bands, and the alloy invar show the unusual phenomenon of negative thermal expansion (NTE). Recent experiments find that the magnetic spinel oxide CdCr₂O₄ also exhibits NTE within its ordered half-magnetisation plateau phase, a phenomenon which has been explained by a strong coupling between a flat band of classical spin-wave excitations and the lattice [1]. Here we use classical Monte Carlo simulations to directly calculate the NTE. Also, we extend calculations to the quantum case by performing spin wave calculations. We find that the theory developed in [1] is robust against the inclusion of thermal and quantum fluctuations, and argue that it provides a scenario for NTE in a wide range of frustrated magnets.

[1] L. Rossi et al., Phys. Rev. Lett. 123, 027205 (2019).   

Live

Magnetic pyrochlore oxides have attracted significant interest due to their geometrically frustrated lattice, which acts to suppress long range magnetic order and leads to a variety of unusual magnetic ground states and exotic excitations.

Some of the most studied pyrochlores are the spin ices Ho₂Ti₂O₇ and Dy₂Ti₂O₇ – here the rare earth ions are ferromagnetic whilst the Ti is nonmagnetic. Recently, the pyrochlore iridates (R₂Ir₂O₇, R = rare earth) have risen to prominence. Here, both the rare earth and the Ir are magnetic; the added complexity afforded by the Ir magnetism may be expected to yield a rich variety of physical phenomena. For instance, most of the pyrochlore iridates exhibit a metal to insulator transition which accompanies the ordering of the Ir into an ‘all-in-all-out’ configuration.

Here we report on magnetisation and resistivity measurements on new single crystals of pyrochlore iridates. We present a systematic study of the evolution of these properties with magnetic field, temperature and angle. Supported by Monte Carlo simulations we present our interpretation of the highly anisotropic and hysteretic behaviour observed as well as its wider significance.   

Live

Over the last decade, the search for deconfined quantum critical points on a variety of models and lattices has produced many concrete numerical examples and revealed opportunities for finding exotic quantum phases, such as spin liquids. Having studied all two-dimensional lattices of interest, our goal was to expand our computational method’s functionality to be able to handle a three-dimensional lattice, namely the Pyrochlore lattice (Fd3m). On this lattice, we deployed an SO(N)-symmetric singlet-projector model using a stochastic series expansion quantum Monte Carlo simulation (the “computational method”). We used this method to gather evidence for the existence of a magnetically (quadrupolar) ordered phase of Pyrochlore up to N=N1, beyond which we expect that no such phase can occur. We discuss what is known about the phase of Pyrochlore when N>>N1, and the particularities of the transition to this phase, from the magnetically ordered (N<N1) phase. Finally, we discuss our plans for the project going forward.   

Live

We point out the experimental relevance and the detection scheme of symmetry-enriched U(1) quantum spin liquids (QSLs) outside the perturbative spin-ice regime. Recent experiments on Ce-based pyrochlore QSL materials suggest that the candidate QSL may not be proximate to the well-known spin-ice regime, and thus differs fundamentally from other pyrochlore QSL materials. We consider the possibility of the π-flux U(1) QSL favored by frustrated transverse exchange interactions rather than the usual quantum spin ice. It was previously suggested that both dipolar U(1) QSL and octupolar U(1) QSL can be realized for the generic spin model for the dipole-octupole doublets of the Ce³⁺ local moments on the pyrochlore magnets Ce₂Sn₂O₇ and Ce₂Zr₂O₇. We explain and predict the experimental signatures, especially the magnetic field response of the octupolar π-flux U(1) QSL. Fundamentally, this remarkable state is a mixture of symmetry enrichments from point-group symmetry and from translational symmetry. We discuss the relevant experiments for pyrochlore U(1) QSLs and further provide some insights to the pyrochlore Heisenberg model.   

Live

Machine-learning is drawing enormous attention in physics and has proven useful for sovling various physical problems. However, there are still very few instances of such techniques being applied to hard problems and providing new insights. In this work, we apply the tensorial-kernel support-vector-machine (TK-SVM) method to a classical anti-ferromagnet with Dzyaloshinskii–Moriya interaction on the breathing pyrochlore lattice, where we uncover the nature of the q = W phase below a rank-2 U(1) spin liquid found in PRL 124, 127203 (2020). Our machine identifies the previously unknown order parameter of this phase and the constraint that selects the ground states, whose construction is sufficiently intricate and was not realized using traditional methods.